AIM: Accelerating Arbitrary-precision Integer Multiplication on Heterogeneous Reconfigurable Computing Platform Versal ACAP

Arbitrary-precision integer multiplication is the core kernel of many applications including scientific computing, cryptographic algorithms, etc. Existing acceleration of arbitrary-precision integer multiplication includes CPUs, GPUs, FPGAs, and ASICs. To leverage the hardware intrinsics low-bit function units (32/64-bit), arbitrary-precision integer multiplication can be calculated using Karatsuba decomposition, and Schoolbook decomposition by decomposing the two large operands into several small operands, generating a set of low-bit multiplications that can be processed either in a spatial or sequential manner on the low-bit function units, e.g., CPU vector instructions, GPU CUDA cores, FPGA digital signal processing (DSP) blocks. Among these accelerators, reconfigurable computing, e.g., FPGA accelerators are promised to provide both good energy efficiency and flexibility. We implement the state-of-the-art (SOTA) FPGA accelerator and compare it with the SOTA libraries on CPUs and GPUs. Surprisingly, in terms of energy efficiency, we find that the FPGA has the lowest energy efficiency, i.e., 0.29x of the CPU and 0.17x of the GPU with the same generation fabrication. Therefore, key questions arise: Where do the energy efficiency gains of CPUs and GPUs come from? Can reconfigurable computing do better? If can, how to achieve that? We first identify that the biggest energy efficiency gains of the CPUs and GPUs come from the dedicated vector units, i.e., vector instruction units in CPUs and CUDA cores in GPUs. FPGA uses DSPs and lookup tables (LUTs) to compose the needed computation, which incurs overhead when compared to using vector units directly. New reconfigurable computing, e.g., "FPGA+vector units" is a novel and feasible solution to improve energy efficiency. In this paper, we propose to map arbitrary-precision integer multiplication onto such a "FPGA+vector units" platform, i.e., AMD/Xilinx Versal ACAP architecture, a heterogeneous reconfigurable computing platform that features 400 AI engine tensor cores (AIE) running at 1 GHz, FPGA programmable logic (PL), and a general-purpose CPU in the system fabricated with the TSMC 7nm technology. Designing on Versal ACAP incurs several challenges and we propose AIM: Arbitrary-precision Integer Multiplication on Versal ACAP to automate and optimize the design. AIM accelerator is composed of AIEs, PL, and CPU. AIM framework includes analytical models to guide design space exploration and AIM automatic code generation to facilitate the system design and on-board design verification. We deploy the AIM framework on three different applications, including large integer multiplication (LIM), RSA, and Mandelbrot, on the AMD/Xilinx Versal ACAP VCK190 evaluation board. Our experimental results show that compared to existing accelerators, AIM achieves up to 12.6x, and 2.1x energy efficiency gains over the Intel Xeon Ice Lake 6346 CPU, and NVidia A5000 GPU respectively, which brings reconfigurable computing the most energy-efficient platform among CPUs and GPUs.