The solution of sparse matrix equations is essential in scientific computing. However, traditional solvers on digital computing platforms are limited by memory bottlenecks in largescale sparse matrix storage and computation. Resistive Random Access Memory (ReRAM)-based computing-in-memory (CIM) offers a promising solution to this challenge but faces constraints in achieving high solution precision and energy efficiency simultaneously in sparse matrix computations. In this work, we propose ReSMiPS, a ReRAM-accelerated sparse mixed-precision solver. ReSMiPS incorporates a novel Fast Sparse Matrix Reordering (FSMR) algorithm and introduces an In-memory float64 (IF64) data format, enabling efficient floating-point sparse matrix computation directly within the analog ReRAM array. By combining our floating-point CIM macro design with a hybrid-domain solution framework, ReSMiPS achieves precision comparable to CPU and GPU-based BiCGSTAB solvers (with errors below $10^{-15}$) on real-world workloads, while demonstrating over two orders of magnitude improvement in both computational speed and energy efficiency.

Analog Computing-in-memory (ACIM) breaks the von Neumann bottleneck and significantly improves energy efficiency by enabling parallel matrix-vector-multiplication (MVM) operations. However, most existing ACIM accelerators are highly customized for specific precision formats, lacking the generality to support efficiently arbitrary precision in both integer (INT) and floating-point (FP) formats. In this work, we present an arbitrary precision analog computing-in-memory (ArPCIM) accelerator with unified INT/FP arithmetic to address this limitation. We introduce a CIM-friendly INT/FP arithmetic to convert FP numbers into INT numbers for efficient execution on CIM, minimizing precision loss through local pre-alignment and dynamic bit-weight slicing methods. In addition, we implement multi-level reconfigurable precision circuits, featuring both intra- and inter-processing element (PE) reconfigurability, which supports precision ranging from 1-bit to 47-bit. Experimental results show that our ArPCIM accelerator achieves up to$4.09\times $and$5.37\times $improvement in energy efficiency and area efficiency, respectively, compared with state-of-the-art arbitrary precision digital CIM. Our ArPCIM accelerator offers the flexibility to meet diverse computational needs while maintaining high energy efficiency and accuracy, paving the way for versatile CIM acceleration across various fields.

The utilization of memristive analog-digital mixed in-memory computing has significantly tackled the issues of massive computing resources and time delays in solving combinatorial optimization problems. However, further improvements in computing energy efficiency are still desirable for resource-constrained conditions and practical applications. Therefore, in this work, a memristive analog transiently chaotic neural network (TCNN) system is proposed to solve the traveling salesman problems (TSPs), which is consisted of 1) a memristor array to perform matrix-vector multiplication for the network iteration; 2) neuronal modules and nonlinear activation function modules to emulate the basic functions of the network; 3) chaotic simulated annealing (CSA) modules to improve the solution performance at extremely low hardware overhead. Based on these, after mapping the TSPs onto the memristor array, the proposed TCNN can self-iterate to convergence states to solve the problems with high performance. Compared to prior analog-digital mixed ones, the analog system can eliminate the extra control and data conversions during the network solving process, and achieve an$8\times $reduction in the total energy consumption in consecutive solving tasks.