并行化阶乘空间：通过双通道AVX2执行实现Steinhaus-Johnson-Trotter算法的3倍SIMD加速
Parallelizing the Factorial Space: Multi-Core OpenMP Scaling and Scalable SIMD Acceleration of the Steinhaus-Johnson-Trotter Algorithm via Dual-Lane AVX2 Execution
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中文总结 AI 辅助
本文提出基于AVX2双通道SIMD的Steinhaus-Johnson-Trotter排列生成加速框架，通过组合空间划分和向量混洗实现3倍吞吐提升，并避免存储转发停顿。
中文摘要 AI 辅助
本文提出了一种针对Steinhaus-Johnson-Trotter排列生成算法的高性能SIMD加速框架，目标平台为使用AVX2指令集的现代x86-64架构。通过利用一种新颖的组合空间划分方法，结合预计算的索引偏移量和单周期向量字节混洗操作（_mm256_shuffle_epi8），我们的双通道向量化实现在统一的执行掩码下，于单个256位YMM寄存器中处理两个独立并发的排列流。实验评估表明，与Donald Knuth的算法P（TAOCP第4A卷）以及Yusheng Hu最近的Ring-Cascade算法相比，我们的性能吞吐量提升了3倍，其中算法P此前已通过标量代码实现了3倍加速。所提出的软件架构保持了跨编译器兼容性，在热循环中完全避免了存储转发内存停顿，并已针对n=11阶进行了验证，在原生硬件上n=13的基准性能约为12.7亿CPU周期。
英文摘要
This paper presents a high-performance SIMD acceleration framework for the Steinhaus-Johnson-Trotter algorithm, targeted at modern x86-64 architectures using the AVX2 instruction set. By exploiting a novel combinatorial space partitioning combined with single-cycle vector byte shuffling ($\texttt{\_mm256\_shuffle\_epi8}$), our dual-lane vectorized implementation processes two independent, concurrent permutation streams within a single 256-bit YMM register under a uniform execution mask. Empirical evaluations demonstrate a $3\times$ throughput increase over an optimized scalar baseline of Knuth's Algorithm P (accelerated by $3\times$ via isolated sweeping branches) and outperform the recent Ring-Cascade algorithm by Yusheng Hu, completely avoiding store-forwarding stalls during hot loops. To scale this engine across multi-core processors, we extend the framework into a highly concurrent environment via OpenMP using a localized mathematical state decoder and macro-period loop scheduling. The parallel performance is shown to scale strictly and linearly with the number of active physical processor cores ($\text{Speedup}(M) \approx M$) due to a lock-free thread-local accumulation pipeline that eliminates false sharing. On a 6-core processor, the multi-threaded engine delivers a $5.25\times$ throughput gain for $n=14$ ($3.25$ billion CPU cycles) and processes the massive $n=15$ space in just $16.0$ seconds, yielding a $5.25\times$ speedup over the sequential vector baseline, while Hyper-Threading virtual cores yield zero additional throughput due to physical SIMD port saturation.
