Quick-Div: Rethinking Integer Divider Design for FPGA-based Soft-processors
Bibliographic record
Abstract
In today’s FPGA-based soft-processors, one of the slowest instructions is integer division. Compared to the low single-digit latency of other arithmetic operations, the fixed 32-cycle latency of radix-2 division is substantially longer. Given that today’s soft-processors typically only implement radix-2 division—if they support hardware division at all—there is significant potential to improve the performance of integer dividers. In this work, we present a set of high-performance, data-dependent, variable-latency integer dividers for FPGA-based soft-processors that we call Quick-Div . We compare them to various radix-N dividers and provide a thorough analysis in terms of latency and resource usage. In addition, we analyze the frequency scaling for such divider designs when (1) treated as a stand-alone unit and (2) integrated as part of a high-performance soft-processor. Moreover, we provide additional theoretical analysis of different dividers’ behaviour and develop a new better-performing Quick-Div variant, called Quick-radix-4 . Experimental results show that our Quick-radix-4 design can achieve up to 6.8× better performance and 6.1× better performance-per-LUT over the radix-2 divider for applications such as random number generation. Even in cases where division operations constitute as little as 1% of all executed instructions, Quick-radix-4 provides a performance uplift of 16% compared to the radix-2 divider.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".