Decimal floating‐point fused multiply‐add with redundant internal encodings
Bibliographic record
Abstract
Decimal floating‐point (DFP) arithmetic has attracted attention in the applications of financial and commercial computing. However, the processing efficiency of DFP is still far away from that of binary designs. On the other hand, a floating‐point fused multiply‐add (FMA) function is widely used in many processors within functional iterations to implement division, square root, and many other functions due to the better accuracy achieved by a single rounding of continuous multiplication and addition. In this work, a new architecture of FMA is proposed to speed up the DFP processing. Compared with previous architectures, first, the proposed design applies a specific decimal redundant encoding system. The circuits to decide and shift the rounding position on a redundant result are therefore simplified. Second, the only digit‐set conversion in the entire design is combined with the rounding operation to further reduce the critical path. Third, the techniques applied in different previous FMAs are merged in the proposed design. In addition the multiplier and adder referred to the previous designs are further optimised. Consequently, compared with the fastest previous design, the synthesis results show about 33.7% speed advantage and about 16.6% area advantage.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".