Compile-time and instruction-set methods for improving floating- to fixed-point conversion accuracy
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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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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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