Optimizing FPGA Logic Block Architectures for Arithmetic
Bibliographic record
Abstract
Hardened adder and carry logic is widely used in commercial field-programmable gate arrays (FPGAs) to improve the efficiency of arithmetic functions. There are many design choices and complexities associated with such hardening, including circuit design, FPGA architectural choices, and the computer-aided design (CAD) flow. However, these choices have not been studied much and hence we explore a number of possibilities. We also highlight front-end elaboration optimization that helps ameliorate the restrictions placed on logic synthesis by hardened arithmetic. We show that hard adders and carry chains increase the performance of simple adders by a factor of 4 or more, but on larger benchmark designs that contain arithmetic improve the overall performance by 15%. Our results also show that for complete application circuits simple hardened ripple-carry adders perform as well as more complex carry-lookahead adders. Our best non-fracturable lookup table (non-fLUT) architecture with hardened arithmetic yields 12% better area-delay product than architectures without hardened arithmetic. We also investigate the impact of fLUTs and their interaction with hardened arithmetic. We find that fLUTs offer significant (12%-15%) area reduction, which is complementary to the delay reduction of hardened arithmetic. Therefore, our best fLUT architectures which use two bits of hardened arithmetic achieve 25% better area-delay product than non-fLUT architectures without hardened arithmetic.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".