Fitting the model

The corpus is 12 ground-truth (n_row, n_col) → cycles rows. Fitting turns it into the timing model. The headline is how little is fit.

Fit the primitives, not the whole-kernel

The discipline is to fit each physical primitive, never the emergent whole-kernel directly (that would manufacture a fudge term — see the playbook). For FIR three of the four terms need no fit at all:

• Channel occupancy — read off the transfer-beat counts: exactly nwords, slope 1. Deterministic.
• Compute body — trips + (n_row−1)·row_depth; the II=1 part fits single-row points to R²=1.0. Exact.
• fill_const — one scalar, the residual command→bus latency.

The only fitted curve is row_depth(n_col) — the per-row ping-pong refill depth — recovered from the inter-row gaps and carried as a saturating InterpCalibModel lookup (not a sqrt basis fudge):

db = CalibDataFrame.load("results/cosim_grid.json")
# row_depth measured from the inter-row gap: (y_write_span - trips) / (n_row - 1), per n_col
row_depth = InterpCalibModel(basis=["n_col"], target="row_depth").fit(gaps)   # the one curve
# occupancy + II=1 compute are deterministic; only fill_const is a scalar mean

Measured, it saturates — row_depth(64) ≈ 70, (256) ≈ 260, (1024) ≈ 268 cycles — at the FIR pipeline depth. The fitted model is committed in results/fir_calibration.json, and the full derivation in results/fir_calibration_results.md.

The result

The simulation loads the calibration and composes whole = fill + max(write_occ, compute_body). Against the RTL cosim it reproduces the whole-kernel to ≤ 1.3% across the grid, with the honest generalization tests well inside that:

gate	point	sim	cosim	rel-err
interior held-out (n_row=2 out; row_depth(256) trained)	(2, 256)	1341.5	1343	0.11%
untrained n_col (row_depth interpolated)	(4, 128)	1211.3	1213	0.14%
untrained n_col (row_depth interpolated)	(4, 512)	3651.0	3673	0.60%

Panel (a) is the parity of predicted vs measured: every grid point — and the untrained-column held-out points — lands on the diagonal. Panel (b) is the single fitted curve.

What the residual says

The one fitted term, row_depth(n_col), is a per-row quantity. At this block (per-matrix) granularity the model can only see it summed as n_row·row_depth and must carry it as a measured curve. A finer per-row (row-LT) model would treat it as each row’s pipeline depth and obtain it fit-free — so the residual is a single, physically-named, per-row quantity rather than diffuse curvature. That is the quantified motivation for the next fidelity level.

Reproducing the figure

The figure regenerates from the committed JSONs alone — no Vitis, no cosim — via fir_figures.py, deterministic (fixed svg.hashsalt), with --check for a byte-match gate:

PYTHONPATH=. ../pysilicon-venv/Scripts/python.exe examples/rowwise_fir/fir_figures.py          # regenerate
PYTHONPATH=. ../pysilicon-venv/Scripts/python.exe examples/rowwise_fir/fir_figures.py --check  # byte-identical?

See also

• The timing model — the decomposition these terms fill in.
• Calibration — the corpus and models (row_depth is an InterpCalibModel).
• Fitting a timing model — the general fit this specializes.