Fully Homomorphic Encryption (FHE), particularly the CKKS scheme, enables computation on encrypted data, facilitating secure task offloading to untrusted servers. CKKS allows packing multiple complex values into a single ciphertext, crucial for fixed-point arithmetic in machine learning, while leveraging SIMD parallelism at the plaintext level. However, operations such as reductions can degrade performance by creating a large number of bubbles (or gaps) in intermediate ciphertexts, leading to wasted computational resources. We introduce Qiwu, a ciphertext-level vectorization approach that enhances performance by fusing multiple ciphertexts containing bubbles. Qiwu uses a DSL to specify zero bubbles in input ciphertexts and nonzero bubbles in output ciphertexts, employs data-flow analysis to track them, and formulates a fusion plan guided by a cost-benefit assessment. Implemented in an existing FHE compiler, Qiwu was evaluated on four applications (including three machine learning tasks) and three kernels. It achieves speedups of up to 18.0× on CPUs, averaging 3.4× (geometric mean), compared to the state-of-the-art compiler that exploit only plaintext-level parallelism.

SIMD extensions are widely adopted in multi-core processors to exploit data-level parallelism. However, when co-running workloads on different cores, compute-intensive workloads cannot take advantage of the underutilized SIMD lanes allocated to memoryintensive workloads, reducing the overall performance. This paper proposes Occamy, a SIMD co-processor that can be shared by multiple CPU cores, so that their co-running workloads can spatially share its SIMD lanes. The key idea is to enable elastic spatial sharing by dynamically partitioning all the SIMD lanes across different workloads based on their phase behaviors, so that each workload may execute in variable-length SIMD mode. We also introduce an Occamy compiler to support such variable-length vectorization by analyzing such phase behaviors and generating the vectorized code that works with varying vector lengths. We demonstrate that Occamy can improve SIMD utilization, and consequently, performance over three representative SIMD architectures, with negligible chip area cost.

Quantum perturbation theory is pivotal in determining the critical physical properties of materials. The first-principles computations of these properties have yielded profound and quantitative insights in diverse domains of chemistry and physics. In this work, we propose a portable and scalable OpenCL implementation for quantum perturbation theory, which can be generalized across various high-performance computing (HPC) systems. Optimal portability is realized through the utilization of a cross-platform unified interface and a collection of performance-portable heterogeneous optimizations. Exceptional scalability is attained by addressing major constraints on memory and communication, employing a locality-enhancing task mapping strategy and a packed hierarchical collective communication scheme. Experiments on two advanced supercomputers demonstrate that our implementation exhibits remarkably performance on various material systems, scaling the system to 200,000 atoms with all-electron precision. This research enables all-electron quantum perturbation simulations on substantially larger molecular scales, with a potentially significant impact on progress in material sciences.