A fast and accurate logarithm accelerator for scientific applications
Bibliographic record
Abstract
Many scientific applications rely on evaluation of elementary functions. Nowadays, high-level programming languages provide their own elementary function libraries in software by using lookup table and/or polynomial approximation. However, one downside is slow since lookup tables could keep cache thrashing and polynomial approximations require a number of iterations to converge. Thus, elementary functions evaluation becomes bottleneck for most scientific applications. With this motivation, we propose a generalized pipelined hardware architecture for elementary functions to accelerate scientific applications. This paper presents a pipelined, single precision logarithm hardware accelerator (SP-LHA). Throughput of SP-LHA is at least 2.5GFLOPS in 65nm ASICs, while the circuit consists of ≈60,000 logic gates. Average accuracy of SP-LHA is 22.5 out of 23 bits, which is achieved by using 7.8KB lookup table and parabolic interpolation.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 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 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".