Scheduling and optimal register placement for synchronous circuits derived using software pipelining techniques
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Bibliographic record
Abstract
Data dependency constraints constitute a lower bound P on the minimal clock period of single-phase clocked sequential circuits. In contrast to methods based on basic retiming, clocked sequential circuits with clock period P can always be obtained using software pipelining techniques. Such circuits can be derived by any method that can be framed in the following four-step process: Step 1, determine P; Step 2, compute a valid periodic schedule of the computational elements; Step 3, place registers back to the circuit; Step 4, assign the clock signals to control registers.Methods with polynomial run-time to implement this process are proposed in the literature. They implement these steps sequentially, starting with Step 1. These methods do not know how to optimally place registers which leads to an unnecessary number of registers. In this article, we address the problem of how to simultaneously implement Steps 2 and 3 in order to minimize the total number of registers. We conjecture that the problem is NP-hard in its general form. We formulate the problem for the first time in the literature, and devise a Mixed Integer Linear Program (MILP) to solve it. From this MILP, we derive a linear program to determine approximate solutions to the problem for large general circuits. We show that the proposed approach can handle nonzero clock skew. Experimental results confirm the effectiveness of the approach and show that significant reductions of the number of registers can be obtained although register sharing is not used. When the schedule is given, the proposed approach provides solutions to the problem of how to place the minimal number of registers in Step 3.
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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 | 0.000 | 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