High-Speed Parallel Decimal Multiplication with Redundant Internal Encodings
Bibliographic record
Abstract
The decimal multiplication is one of the most important decimal arithmetic operations which have a growing demand in the area of commercial, financial, and scientific computing. In this paper, we propose a parallel decimal multiplication algorithm with three components, which are a partial product generation, a partial product reduction, and a final digit-set conversion. First, a redundant number system is applied to recode not only the multiplier, but also multiples of the multiplicand in signed-digit (SD) numbers. Furthermore, we present a multioperand SD addition algorithm to reduce the partial product array. Finally, a digit-set conversion algorithm with a hybrid prefix network to decrease the number of the logic gates on the critical path is discussed. An analysis of the timing delay and an HDL model synthesized under 90 nm technology show that by considering the tradeoff of designs among three components, the overall delay of the proposed 16 × 16-digit multiplier takes about 11 percent less timing delay with 2 percent less area compared to the current fastest design.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".