Compile-time and instruction-set methods for improving floating- to fixed-point conversion accuracy
Bibliographic record
Abstract
This paper proposes and evaluates compile time and instruction-set techniques for improving the accuracy of signal-processing algorithms run on fixed-point embedded processors. These techniques are proposed in the context of a profile guided floating- to fixed-point compiler-based conversion process. A novel fixed-point scaling algorithm (IRP) is introduced that exploits correlations between values in a program by applying fixed-point scaling, retaining as much precision as possible without causing overflow. This approach is extended into a more aggressive scaling algorithm (IRP-SA) by leveraging the modulo nature of 2's complement addition and subtraction to discard most significant bits that may not be redundant sign-extension bits. A complementary scaling technique (IDS) is then proposed that enables the fixed-point scaling of a variable to be parameterized, depending upon the context of its definitions and uses. Finally, a novel instruction-set enhancement—fractional multiplication with internal left shift(FMLS)—is proposed to further leverage interoperand correlations uncovered by the IRP-SA scaling algorithm. FMLS preserves a different subset of the full product's bits than traditional fractional fixed-point or integer multiplication. On average, FMLS combined with IRP-SA improves accuracy on processors with uniform bitwidth register architectures by the equivalent of 0.61 bits of additional precision for a set of signal-processing benchmarks (up to 2 bits). Even without employing FMLS, the IRP-SA scaling algorithm achieves additional accuracy over two previous fixed-point scaling algorithms by averages of 1.71 and 0.49 bits. Furthermore, as FMLS combines multiplication with a scaling shift, it reduces execution time by an average of 9.8%. An implementation of IDS, specialized to single-nested loops, is found to improve accuracy of a lattice filter benchmark by the equivalent of more than 16-bits of precision.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".