Intercube allreduce: center root + bidirectional reduce
Move the algorithmic root cube from the corner (cube_w-1, cube_h-1) to the geometric center (cube_w//2, cube_h//2) and have each phase converge bidirectionally so the intra-SIP critical path drops from ~12 hops to ~8 hops on a 4×4 mesh (left half W→E + right half E→W in row reduce; top half N→S + bottom half S→N in col reduce; mirrored on broadcast). Result on torus_2d 6 SIPs at 96 KB / PE on TCM: before (corner root) : 22.0 µs after (center root) : 17.2 µs (−22%) Same shape on ring_1d (−7%) and mesh_2d_no_wrap (−12%); also holds across SRAM and HBM (~−20% each). Phase 1 test (test_intercube_root_center.py) asserts the torus_2d 96 KB latency drops below 20.5 µs and that all 96 cubes still validate (correctness preserved). Plot updates: - overview.png: replace constant 10.6 µs theoretical line with user-supplied hand-derived curve (per-cube packet count = bytes_per_pe × 8 PEs ÷ 128 B; 1346 ns startup + 1.20 ns/pkt). - All summary.csv numbers and per-topology PNGs regenerated. - pe2pe_latency_plots and ipcq diagram emitter PNGs refreshed. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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@@ -289,7 +289,8 @@ _SWEEP_TOPOLOGIES = [
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# parametrized invocation writes one JSON file here; the aggregator
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# (run from conftest.pytest_sessionfinish) reads them and emits the
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# combined CSV + PNG plots.
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_SWEEP_OUT_DIR = Path(__file__).parent / "allreduce_latency_plots"
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_SWEEP_OUT_DIR = (Path(__file__).parent.parent / "docs" / "diagrams"
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/ "allreduce_latency_plots")
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_SWEEP_ROWS_DIR = _SWEEP_OUT_DIR / "_rows"
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@@ -447,7 +448,7 @@ def _aggregate_sweep_plots() -> bool:
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ax.plot(xs, ys, marker="o", color="tab:blue")
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ax.set_xscale("log", base=2)
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ax.set_xlabel("Bytes per PE (log scale)")
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ax.set_ylabel("max pe_exec_ns (critical path)")
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ax.set_ylabel("Time (ns)")
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ax.set_title(title)
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ax.grid(True, alpha=0.3)
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ax.xaxis.set_major_formatter(_bytes_fmt)
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@@ -457,7 +458,28 @@ def _aggregate_sweep_plots() -> bool:
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colors = {"ring_1d": "tab:blue", "torus_2d": "tab:orange",
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"mesh_2d_no_wrap": "tab:green"}
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THEORETICAL_TORUS_2D_6SIP_NS = 10600.0
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# ── Hand-derived theoretical model for torus_2d (6 SIPs) ──
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# Critical-path analysis (per packet, packet = 128 B at NoC):
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# local intra-SIP reduce + broadcast = 8 hops × 57 ns = 456 ns
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# global X-direction reduce = 5 UCIe + 1 UAL = 445 ns
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# global Y-direction reduce = 5 UCIe + 1 UAL = 445 ns
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# per-packet startup latency = 456 + 445 + 445 = 1346 ns
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# Packet count is PER CUBE (8 PEs/cube cooperate on the cube tile).
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# At 6144 packets/cube the pipelined total is 8741 ns, so the
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# bottleneck-stage interval τ = (8741 − 1346) / (6144 − 1) ≈ 1.204 ns.
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# T_theoretical(N) = 1346 + (N − 1) × τ
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# where N = ceil((bytes_per_pe × 8) / 128) = ceil(bytes_per_pe / 16)
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NOC_PACKET_BYTES = 128
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PES_PER_CUBE = 8
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T_STARTUP_NS = 1346.0
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TAU_NS = (8741.0 - 1346.0) / (6144 - 1) # ≈ 1.2038 ns/packet
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def _theoretical_torus_2d_ns(bytes_per_pe: int) -> float:
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bytes_per_cube = int(bytes_per_pe) * PES_PER_CUBE
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n_packets = max(1, -(-bytes_per_cube // NOC_PACKET_BYTES)) # ceil
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return T_STARTUP_NS + (n_packets - 1) * TAU_NS
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fig, ax = plt.subplots(figsize=(9, 6))
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for topo_name in topologies:
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rs = sorted(
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@@ -473,64 +495,28 @@ def _aggregate_sweep_plots() -> bool:
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label=f"{topo_name} (n_sips={rs[0]['n_sips']})",
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color=colors.get(topo_name),
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)
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ax.axhline(
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y=THEORETICAL_TORUS_2D_6SIP_NS,
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color="tab:red", linestyle="--", linewidth=1.5,
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label=f"theoretical torus_2d (6 SIPs) = "
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f"{THEORETICAL_TORUS_2D_6SIP_NS:.0f} ns",
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# Theoretical torus_2d curve across all payload sizes.
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torus_rs = sorted(
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[r for r in records if r["sip_topology"] == "torus_2d"],
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key=lambda r: r["bytes_per_pe"],
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)
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BYTES_96KB = 96 * 1024
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ax.axvline(
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x=BYTES_96KB, ymin=0, ymax=1,
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color="tab:red", linestyle=":", linewidth=1.2,
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)
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ax.plot(
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[BYTES_96KB], [THEORETICAL_TORUS_2D_6SIP_NS],
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marker="x", color="tab:red", markersize=10, markeredgewidth=2,
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)
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# Find simulated torus_2d latency at 96 KB (if present) for direct
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# comparison with the theoretical value.
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sim_torus_at_96kb = next(
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(r["latency_ns"] for r in records
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if r["sip_topology"] == "torus_2d" and r["bytes_per_pe"] == BYTES_96KB),
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None,
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)
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if sim_torus_at_96kb is not None:
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if torus_rs:
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xs_th = [r["bytes_per_pe"] for r in torus_rs]
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ys_th = [_theoretical_torus_2d_ns(r["bytes_per_pe"]) for r in torus_rs]
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ax.plot(
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[BYTES_96KB], [sim_torus_at_96kb],
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marker="o", color="tab:orange",
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markersize=10, markeredgecolor="black", markeredgewidth=1.2,
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)
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ax.annotate(
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f"96 KB\n"
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f"theoretical = {THEORETICAL_TORUS_2D_6SIP_NS:.0f} ns\n"
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f"simulated = {sim_torus_at_96kb:.0f} ns",
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xy=(BYTES_96KB, sim_torus_at_96kb),
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xytext=(10, -20), textcoords="offset points",
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color="tab:red", fontsize=9,
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)
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else:
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ax.annotate(
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f"96 KB\n→ theoretical {THEORETICAL_TORUS_2D_6SIP_NS:.0f} ns",
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xy=(BYTES_96KB, THEORETICAL_TORUS_2D_6SIP_NS),
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xytext=(8, -20), textcoords="offset points",
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color="tab:red", fontsize=9,
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xs_th, ys_th,
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color="tab:red", linestyle="--", linewidth=1.6, marker="x",
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label="theoretical torus_2d (6 SIPs)",
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)
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ax.set_xscale("log", base=2)
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ax.set_xlabel("Bytes per PE (log scale)")
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ax.set_ylabel("max pe_exec_ns (critical path)")
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ax.set_ylabel("Time (ns)")
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ax.set_title("Multi-device allreduce latency by topology")
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ax.grid(True, alpha=0.3)
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# Drop 128 KB tick (overlaps visually with the explicit 96 KB marker)
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# and add 96 KB.
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BYTES_128KB = 128 * 1024
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existing_ticks = [t for t in ax.get_xticks() if int(t) != BYTES_128KB]
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if BYTES_96KB not in existing_ticks:
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existing_ticks.append(BYTES_96KB)
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ax.set_xticks(sorted(existing_ticks))
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ax.set_xlim(left=min(r["bytes_per_pe"] for r in records) / 2,
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right=BYTES_96KB * 1.5)
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right=max(r["bytes_per_pe"] for r in records) * 1.5)
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ax.legend()
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ax.xaxis.set_major_formatter(_bytes_fmt)
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fig.tight_layout()
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@@ -811,7 +797,7 @@ def _draw_cube_reduction(ax):
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def emit_topology_diagram() -> str:
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"""Emit a 2×2-panel topology diagram into allreduce_latency_plots/.
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"""Emit a 2×2-panel topology diagram into docs/diagrams/allreduce_latency_plots/.
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Top row: ring_1d | torus_2d (2×3)
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Bot row: mesh_2d_no_wrap (2×3) | cube-level reduction in SIP 0
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