A comprehensive study of three moduli sets for residue arithmetic
Bibliographic record
Abstract
One important problem in residue arithmetic is the choice of modulo sets to represent the binary numbers in a certain range. In recent years, several general three-modulo sets have been introduced, and each of them is claimed to have some advantages. In this paper, we carry out a comprehensive study for all these modulo sets from the point of view of the hardware complexity and the speed of their residue-to-binary converters. Based on a performance evaluation of the VLSI implementation in terms of area and delay, we conclude that to represent 8-bit, 16-bit, 32-bit and 64-bit binary numbers, the set of moduli {2/sup n/-1, 2/sup n/, 2/sup n/+1} has the fastest residue-to-binary converter requiring the smallest area. The converter for this moduli set is designed based on the new Chinese remainder theorem of Y. Wang (1998).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".