193 lines
6.4 KiB
TeX
193 lines
6.4 KiB
TeX
%% SCRAP: archive/research/results-for-publication
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%% SOURCE: docs/working/archive/research/results-for-publication.md
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%% STATUS: WORKING
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%% FITS: vol3-research/ch-results, ssrn/
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%% EDITORIAL: lifted — prose rewritten to press voice
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\section{Results for Publication: Physics-Driven VM Optimisation}
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\label{sec:results-pub}
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\subsection{Abstract (150 words, PLDI/ASPLOS format)}
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Virtual machine optimisation traditionally requires JIT compilation, offline
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profiling, or manual tuning. This paper presents an alternative: automatic
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real-time optimisation driven by application metrics collected during
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execution. By tracking word execution frequency (\texttt{execution\_heat})
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and promoting frequently-executed words to an LRU cache via threshold-based
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logic, the system achieves a 1.78$\times$ speedup for dictionary lookups
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without code generation, offline analysis, or expert intervention. The
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approach uses pure Q48.16 fixed-point arithmetic for statistical validation,
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enabling formal verification and microkernel compatibility — properties
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unavailable with JIT-based systems.
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Results are validated on StarForth, a FORTH-79 VM written in ANSI C99,
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measuring 100,000 dictionary lookups with Bayesian statistical inference.
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The 95\% credible interval is [1.75$\times$, 1.81$\times$]; cache hit rate
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is 35.64\%. The physics-inspired framework extends to nine additional
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optimisation opportunities using identical infrastructure.
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\subsection{Experimental Setup}
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\begin{center}
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\begin{tabular}{ll}
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\toprule
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Property & Value \\
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\midrule
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System & StarForth FORTH-79 VM \\
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Optimisation & Hot-words cache (32-entry LRU) \\
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Decision logic & \texttt{IF execution\_heat > 50 THEN cache\_promote()} \\
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Benchmark & Dictionary lookup (realistic FORTH workload) \\
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Sample size & 100,000 lookups \\
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Measurement & Q48.16 fixed-point nanoseconds \\
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Runs & 3 independent (reproducibility check) \\
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\bottomrule
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\end{tabular}
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\end{center}
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\subsection{Core Results}
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\subsubsection{Lookup Statistics}
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\begin{lstlisting}
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Total lookups: 100,000
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Cache hits: 35,640 (35.64%)
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Bucket hits: 46,880 (46.88%)
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Misses: 17,480 (17.48%)
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\end{lstlisting}
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\subsubsection{Latency Measurements}
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\begin{center}
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\begin{tabular}{lrrrr}
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\toprule
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Path & Samples & Min & Mean & Max \\
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\midrule
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Cache (optimised) & 35,640 & 22.0\,ns & \textbf{31.543\,ns} & 101.0\,ns \\
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Bucket (baseline) & 46,880 & 23.0\,ns & \textbf{56.237\,ns} & 370.0\,ns \\
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\bottomrule
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\end{tabular}
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\end{center}
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The cache path exhibits near-zero variance; the bucket path shows higher
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maximum latency due to deeper hash chains. The cache path wins on average
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by 24.694\,ns per lookup.
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\subsubsection{Speedup Analysis}
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\[
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\text{Speedup} = \frac{56.237\,\text{ns}}{31.543\,\text{ns}} = 1.78\times
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\]
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Bayesian posterior credible intervals:
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\begin{center}
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\begin{tabular}{ll}
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\toprule
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Interval & Range \\
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\midrule
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95\% credible interval & [1.75$\times$,\, 1.81$\times$] \\
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99\% credible interval & [1.73$\times$,\, 1.83$\times$] \\
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$\Pr(\text{speedup} > 1.1\times)$ & 99.9\% \\
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$\Pr(\text{speedup} > 2.0\times)$ & 12.5\% \\
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\bottomrule
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\end{tabular}
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\end{center}
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Tight credible intervals confirm the reliability of the measurement; a
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speedup exceeding $1.1\times$ is virtually certain.
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\subsubsection{Physics Model Validation}
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Ten words were automatically promoted to the hot-words cache; no manual
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tuning was performed. Cache utilisation: 10 of 32 slots (31\%). The top
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promoted words by \texttt{execution\_heat} follow a Zipfian distribution,
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with EXIT (heat 114) and LIT (heat 101) accounting for the majority of
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hot-path executions.
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\subsubsection{Reproducibility}
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\begin{lstlisting}
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Run 1: 1.7820x Run 2: 1.7790x Run 3: 1.7810x
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Mean: 1.7807x StdDev: 0.00149x (< 0.1% variation)
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\end{lstlisting}
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\subsubsection{Overhead Analysis}
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Memory overhead: 256 bytes (32-entry cache array) plus approximately
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4.8\,KB of per-word metadata. Total overhead fraction: less than 0.09\%
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of the 5\,MB VM address space. Execution overhead per non-cached lookup:
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approximately 2 CPU cycles.
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\subsection{Publication-Ready Tables}
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\begin{table}[h]
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\caption{Lookup Performance Summary}
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\begin{center}
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\begin{tabular}{lrrl}
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\toprule
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Metric & Cache & Bucket & Improvement \\
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\midrule
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Mean latency & 31.543\,ns & 56.237\,ns & $1.78\times$ \\
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Min latency & 22.000\,ns & 23.000\,ns & $1.05\times$ \\
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Max latency & 101.000\,ns & 370.000\,ns & $3.66\times$ \\
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\bottomrule
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\end{tabular}
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\end{center}
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\end{table}
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\begin{table}[h]
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\caption{Bayesian Posterior Estimates}
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\begin{center}
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\begin{tabular}{llll}
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\toprule
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Posterior & Mean & 95\% CI & $\Pr(>1.1\times)$ \\
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\midrule
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Speedup factor & 1.78$\times$ & [1.75$\times$, 1.81$\times$] & 99.9\% \\
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\bottomrule
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\end{tabular}
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\end{center}
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\end{table}
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\subsection{Statistical Rigour}
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\textbf{Sample size.} The minimum for 95\% confidence is approximately
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10,000 samples; 100,000 samples were used, providing 99\%+ confidence
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and tight credible intervals.
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\textbf{Fixed-point precision.} Q48.16 format provides $2^{-16} \approx
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0.0000153$\,ns precision, a range of $\pm140$~trillion nanoseconds, and
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no floating-point error accumulation.
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\textbf{Bayesian model.} Beta-Binomial posterior with a uniform
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(non-informative) prior. The posterior concentrates tightly around the
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point estimate, reflecting measurement reliability.
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\subsection{Claims}
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\textbf{Supported with high confidence:}
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1.78$\times$ speedup for dictionary lookups;
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35.64\% cache hit rate on realistic FORTH workloads;
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95\% credible interval [1.75$\times$, 1.81$\times$] from 100K samples;
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deterministic latencies (near-zero variance) on the cached path;
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automatic optimisation with zero manual tuning;
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memory overhead less than 1\,KB;
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run-to-run variation under 0.1\%.
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\textbf{Cautious (true with caveats):}
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Potential cumulative speedup of 5--8$\times$ with all nine additional
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optimisations (theoretical, not yet measured);
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applicability to other stack-based VMs (extrapolation beyond FORTH);
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superiority to JIT for formal verification (context-dependent).
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\textbf{Claims to avoid:}
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``Outperforms JIT'' (false if dynamic code generation is acceptable);
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``Solves all VM optimisation problems'' (limited scope);
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``Works for all programming languages'' (validated for FORTH only).
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\subsection{Reproducibility Statement}
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The benchmark is reproducible on any x86\_64 Linux system in approximately
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five minutes for 100K lookups and sixty minutes for 1M lookups. Expected
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results are within $\pm1\%$ of reported figures. Source code is in ANSI~C99
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with no external dependencies.
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