Efficient computation of positional population counts using SIMD instructions
Bibliographic record
Abstract
Summary In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one‐hot encoded vectors. For example, given eight distinct values, we map each value to a byte where only a single bit has been set. We are motivated to quickly compute statistics over such encodings. Given a stream of k‐bit words, we seek to compute k distinct sums corresponding to bit values at indexes 0, 1, 2, …, k − 1. If the k‐bit words are one‐hot encoded then the sums correspond to a frequency histogram. This multiple‐sum problem is a generalization of the population‐count problem where we seek the sum of all bit values. Accordingly, we refer to the multiple‐sum problem as a positional population‐count. Using SIMD (Single Instruction, Multiple Data) instructions from recent Intel processors, we describe algorithms for computing the 16‐bit position population count using less than half of a CPU cycle per 16‐bit word. Our best approach uses up to 400 times fewer instructions and is up to 50 times faster than baseline code using only regular (non‐SIMD) instructions, for sufficiently large inputs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".