Rethinking Integer Divider Design for FPGA-Based Soft-Processors
Bibliographic record
Abstract
Most existing soft-processors on FPGAs today support a fixed-latency instruction pipeline. Therefore, for integer division, a simple fixed-latency radix-2 integer divider is typically used, or algorithm-level changes are made to avoid integer divisions. However, for certain important application domains the simple radix-2 integer divider becomes the performance bottleneck, as every 32-bit division operation takes 32 cycles. In this paper, we explore integer divider designs for FPGA-based soft-processors, by leveraging the recent support of variable-latency execution units in their instruction pipeline. We implement a high-performance, data-dependent, variable-latency integer divider called Quick-Div, optimize its performance on FPGAs, and integrate it into a RISC-V soft-processor called Taiga that supports a variable-latency instruction pipeline. We perform a comprehensive analysis and comparison-in terms of cycles, clock frequency, and resource usage-for both the fixed-latency radix-2/4/8/16 dividers and our variable-latency Quick-Div divider with various optimizations. Experimental results on a Xilinx Virtex UltraScale+ VCU118 FPGA board show that our Quick-Div divider can provide over 5x better performance and over 4x better performance/LUT compared to a radix-2 divider for certain applications like random number generation. Finally, through a case study of integer square root, we demonstrate that our Quick-Div divider provides opportunities for reconsidering simpler and faster algorithmic choices.
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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 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".