Rethinking Integer Divider Design for FPGA-Based Soft-Processors
Why this work is in the frame
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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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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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