A Design Framework for Hardware-Efficient Logarithmic Floating-Point Multipliers
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The symbiotic use of logarithmic approximation in floating-point (FP) multiplication can significantly reduce the hardware complexity of a multiplier. However, it is difficult for a limited number of logarithmic FP multipliers (LFPMs) to fit in a specific error-tolerant application, such as neural networks (NNs) and digital signal processing, due to their unique error characteristics. This paper proposes a design framework for generating LFPMs. We consider two FP representation formats with different ranges of mantissas, the IEEE 754 Standard FP Format and the Nearest Power of Two FP Format. For both logarithm and anti-logarithm computation, the applicable regions of inputs are first evenly divided into several intervals, and then approximation methods with negative or positive errors are developed for each sub-region. By using piece-wise functions, different configurations of approximation methods throughout applicable regions are created, leading to LFPMs with various trade-offs between accuracy and hardware cost. The variety of error characteristics of LFPMs is discussed and the generic hardware implementation is illustrated. As case studies, two LFPM designs are presented and evaluated in applications of JPEG compression and NNs. They do not only increase the classification accuracy, but also achieve smaller PDPs compared to the exact FP multiplier, while being more accurate than a recent logarithmic FP design.
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.
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 it