A novel algorithm for signed-digit online multiply-accumulate operation and its purely signed-binary hardware implementation
Bibliographic record
Abstract
This paper presents a novel algorithm for purely signed-digit online multiply-accumulate (MAC) operation, and a corresponding architecture unit for a subsequent FPGA implementation using VHDL. In the proposed algorithm, a recursion formula for MAC operation is derived in terms of new input-independent variables (permitting a generalization of the algorithm to the evaluation of all affine functions), considering the relative positions of the MSDs of the signed-digit operands as design parameters. In a given iteration of the MAC algorithm, one adds an incoming partial result to the scaled error from the previous iteration, followed by estimating and generating a result digit, and saving an induced error. Context-free bounds on the internal variables are derived, and a lower bound on the latency is obtained in terms of various MAC operation parameters. The salient features of the proposed MAC architecture are that, (a) it offers the same input and output flow of digits as in practical analog-to-digital (A/D) and digital-to-analog (D/A) converters, (b) it permits a control of the precision of the result, and (c) it produces a MAC result that can be consumed by itself or by another online unit only after a small (constant) number of clock cycles. The correct functionality of the algorithm is confirmed through Matlab as well as Max+Plus II simulations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 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".