Quick-Div: Rethinking Integer Divider Design for FPGA-based Soft-processors
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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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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it