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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
A Fast x86 Implementation of Select
Prashant Pandey, Michael A. Bender, Rob Johnson · 2017-06-04 · via cs.DS updates on arXiv.org

Rank and select are fundamental operations in succinct data structures, that is, data structures whose space consumption approaches the information-theoretic optimal. The performance of these primitives is central to the overall performance of succinct data structures. Traditionally, the select operation is the harder to implement efficiently, and most prior implementations of select on machine words use 50--80 machine instructions. (In contrast, rank on machine words can be implemented in only a handful of instructions on machines that support POPCOUNT.) However, recently Pandey et al. gave a new implementation of machine-word select that uses only four x86 machine instructions; two of which were introduced in Intel's Haswell CPUs. In this paper, we investigate the impact of this new implementation of machine-word select on the performance of general bit-vector-select. We first compare Pandey et al.'s machine-word select to the state-of-the-art implementations of Zhou et al. (which is not specific to Haswell) and Gog et al. (which uses some Haswell-specific instructions). We exhibit a speedup of 2X to 4X. We then study the impact of plugging Pandey et al.'s machine-word select into two state-of-the-art bit-vector-select implementations. Both Zhou et al.'s and Gog et al.'s select implementations perform a single machine-word select operation for each bit-vector select. We replaced the machine-word select with the new implementation and compared performance. Even though there is only a single machine- word select operation, we still obtained speedups of 20% to 68%. We found that the new select not only reduced the number of instructions required for each bit-vector select, but also improved CPU instruction cache performance and memory-access parallelism.