papers/lux-lightspeed-dex/sections/10-benchmarks.tex

\section{Benchmarks}
\label{sec:benchmarks}

This section consolidates the measured results from Sections~\ref{sec:gpu-matching},
\ref{sec:settlement}, and~\ref{sec:rollup} into one table, states the hardware and method,
and is explicit about which numbers are measured and which are aggregations or projections.

\subsection{Hardware and method}

\begin{itemize}
  \item \textbf{NVIDIA GB10} (Grace-Blackwell, 128\,GB unified memory, \texttt{sm\_121},
  CUDA 13).
  \item \textbf{Apple M4 Max} (128\,GB unified memory, Metal).
  \item \textbf{Apple M1 Max} (Go reference, CPU settlement, verifier rates).
\end{itemize}

Matching and settlement throughput are reported as sustained rates over runs of tens of
millions of operations, with the GPU matching figures gated by byte-exact parity against the
CPU oracle (Section~\ref{sec:gpu-matching}). We report per-match latency where it is the
governing quantity. No figure in this paper is taken from a simulation or scaled by a fudge
factor.

\subsection{Consolidated results}

\begin{table}[H]
\centering
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{p{4.4cm} l r l}
\toprule
\textbf{Axis / quantity} & \textbf{Platform} & \textbf{Measured} & \textbf{Status} \\
\midrule
Matching (limb, depth-64) & NVIDIA GB10 & 104--126\,M fills/s & measured \\
\quad per-match latency    & NVIDIA GB10 & 6.9\,ns & measured \\
Matching (limb, depth-64) & Apple M4 Max & $\sim$250\,M fills/s & measured \\
\quad per-match latency    & Apple M4 Max & 4.15\,ns & measured \\
Conflict detection ($O(N)$) & M1 Max (CPU) & 2.2\,M fills/s & measured \\
GPU conflict commit order & M4 (WGSL) & byte-identical to CPU & measured \\
Market-sharded settle (8) & M1 Max (CPU) & $\sim$0.39\,M fills/s & measured \\
P3Q verify (ML-DSA-65) & M1 Max (CPU) & 4{,}714 verifies/s & measured \\
\texttt{starkfri} verify (toy AIR) & M1 Max (CPU) & 986 verifies/s & measured \\
\midrule
$10^{9}$ matches/s & 8--10-node fleet & --- & aggregation \\
$10^{9}$ settled-tx/s finality & P3Q, $K{=}10^{4}$, $M{=}22$ & $1.04\times10^{9}$ & finality model \\
\bottomrule
\end{tabular}
\caption{Consolidated measured results across the three axes, with each row labeled
measured, an aggregation of measured single-node rates, or a finality model that combines a
measured verify rate with a stated batch size. The matching and finality $10^{9}$/s rows are
not single-device measurements and are labeled accordingly.}
\label{tab:consolidated}
\end{table}

\subsection{The dominant lever, restated}

The single largest contributor to matching throughput is the replacement of the
512-iteration bit-serial \texttt{uint256} VWAP division with Knuth Algorithm~D, which alone
yields roughly $8\times$ on the GB10 and $12\times$ on the M4 Max (Table~\ref{tab:division}).
The matcher is dependency-latency bound, not occupancy or bandwidth bound: at peak the GB10
draws a fraction of its power envelope while reporting full GPU utilization, the signature of
a critical path waiting on data dependencies rather than starved of work.

\subsection{What we do not claim}

We do not claim a single-device rate above $\sim$250\,M matches/s for byte-exact
\texttt{uint256} matching, an end-to-end latency derived from invented co-location
round-trips, or any uptime statistic from a deployment we did not run. The honest ceilings
and the two routes past $10^{9}$ matches/s (fleet aggregation or a cheaper fixed-point
representation) are stated in Section~\ref{subsec:billion-matching}; the separation of
finality from matching is stated in Section~\ref{sec:rollup}.