Area efficient floating‐point FFT butterfly architectures based on multi‐operand adders
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Bibliographic record
Abstract
Hardware implementation of the fast Fourier transform (FFT) function consists of multiple consecutive arithmetic operations over complex numbers. Applying floating‐point arithmetic to FFT coprocessors leads to a wider dynamic range and allows the coprocessor to collaborate with general purpose processors via the standard floating‐point arithmetic. This offloads compute‐intensive tasks from the primary processor and overcomes floating‐point concerns such as scaling and overflow/underflow detection. The downside, however, is that floating‐point units are slower than the fixed‐point counterparts. One of the popular ways to improve the speed of floating‐point FFT units is to merge the arithmetic operations inside the butterfly units of a FFT architecture. This leads to a butterfly architecture based on multi‐operand adders. Butterfly units are designed, in two of the most recent works, using three‐operand and four‐operand adders. However, the work reported here by the present authors goes further and a butterfly architecture based on a five‐operand adder is proposed. Simulation results demonstrate that the proposed butterfly architecture is 50% smaller than the fastest previous work with about 17% latency overhead. Compared with the smallest previous work, the proposed design is 47% smaller and 8% faster.
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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