A New Recursive Trigonometric Technique for FPGA-Design Implementation
Bibliographic record
Abstract
This paper presents a new recursive trigonometric (RT) technique for Field-Programmable Gate Array (FPGA) design implementation. The traditional implementation of trigonometric functions on FPGAs requires a significant amount of data storage space to store numerous reference values in the lookup tables. Although the coordinate rotation digital computer (CORDIC) can reduce the required FPGA storage space, their implementation process can be very complex and time-consuming. The proposed RT technique aims to provide a new approach for generating trigonometric functions to improve communication accuracy and reduce response time in the FPGA. This new RT technique is based on the trigonometric transformation; the output is calculated directly from the input values, so its accuracy depends only on the accuracy of the inputs. The RT technique can prevent complex iterative calculations and reduce the computational errors caused by the scale factor K in the CORDIC. Its effectiveness in generating highly accurate cosine waveform is verified by simulation tests undertaken on an FPGA.
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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 | 0.001 |
| 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) | 0.006 | 0.003 |
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".