Using the Minimum Set of Input Combinations to Minimize the Area of Local Routing Networks in Logic Clusters Containing Logically Equivalent I/Os in FPGAs
Bibliographic record
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Mapping digital circuits onto field-programmable gate arrays (FPGAs) usually consists of two steps. First, circuits are mapped into look-up tables (LUTs). Then, LUTs are mapped onto physical resources. The configuration of LUTs is usually determined during the first step and remains unchanged throughout the second. In this paper, we demonstrate that by reconfiguring LUTs during the second step, one can increase the flexibility of FPGA routing resources. This increase in flexibility can then be used to reduce the implementation area of FPGAs. In particular, it is shown that, for a logic cluster with <formula formulatype="inline"><tex Notation="TeX">$ I$</tex></formula> inputs and <formula formulatype="inline"><tex Notation="TeX">$ N$</tex></formula> <formula formulatype="inline"> <tex Notation="TeX">$ k$</tex></formula>-input LUTs, a set of <formula formulatype="inline"> <tex Notation="TeX">$N\times k\quad (I+N-k+1):1$</tex></formula> multiplexers can be used to connect logic cluster inputs to LUT inputs while maintaining logic equivalency among the logic cluster I/Os. The multiplexers (called a local routing network) are shown to be the minimum required to maintain logic equivalency. Comparing to the previous design, which employs a fully connected local routing network, the proposed design can reduce logic cluster area by 3%–25% and can reduce a significant amount of fanouts for logic cluster inputs. </para>
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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 | 0.001 | 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".