Intercube allreduce: pe0 cube-mesh reduce + multi-SIP ring/torus/mesh

New intercube allreduce kernel replacing the old flat ring algorithms.
Reduces across the 4x4 cube mesh within each SIP (pe0-only, same-lane),
then inter-SIP exchange on root cube, then broadcast back. Supports
ring_1d, torus_2d, and mesh_2d_no_wrap SIP topologies driven by
topology.yaml. Integrated with dist.init_process_group / dist.all_reduce.

New files:
- src/kernbench/ccl/algorithms/intercube_allreduce.py (kernel)
- src/kernbench/ccl/sfr_config.py (configure_sfr_intercube_multisip)
- tests/test_allreduce_multidevice.py (config-driven, 3 topologies)
- tests/test_distributed_intercube_allreduce.py (full distributed path)
- tests/test_intercube_sfr_config.py (SFR wiring verification)

Modified:
- distributed.py: AhbmCCLBackend uses configure_sfr_intercube_multisip
- topologies.py: added torus_2d, mesh_2d_no_wrap
- install.py: global_E/W/N/S in _OPPOSITE_DIR
- topology.yaml: added system.sips.topology
- ccl.yaml: single intercube_allreduce algorithm
- benches/ccl_allreduce.py: row_wise cube-mesh tensor layout

Removed old flat-ring algorithms and their tests.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
This commit is contained in:
2026-04-16 17:33:42 -07:00
parent cfc2d74ec4
commit 1d8b9401e5
30 changed files with 876 additions and 2892 deletions
@@ -1,29 +0,0 @@
"""Hello-world CCL kernel for the docs/ccl-author-guide.md walkthrough.
Each PE sends its tile to the E neighbor and receives one tile from W,
then stores the received tile back into its own HBM slice. The simplest
possible demonstration of ``tl.send`` / ``tl.recv``.
"""
from __future__ import annotations
def kernel_args(world_size: int, n_elem: int) -> tuple:
"""Return the positional kernel arguments for the ahbm backend."""
return (n_elem,)
def kernel(t_ptr, n_elem, tl):
local_pe = tl.program_id(axis=0)
cube_id = tl.program_id(axis=1)
pes_per_cube = tl.num_programs(axis=0)
rank = cube_id * pes_per_cube + local_pe
nbytes = n_elem * 2
pe_addr = t_ptr + rank * nbytes
# Send our local HBM tile to the E neighbor.
src = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
tl.send(dir="E", src=src)
# Receive a tile from W and store it into our slice (overwrite).
recv = tl.recv(dir="W", shape=(n_elem,), dtype="f16")
tl.store(pe_addr, recv)
@@ -1,192 +0,0 @@
"""Hierarchical all-reduce kernel (ADR-0023).
3-level reduce + broadcast exploiting the topology hierarchy:
Level 1 — Intra-cube (8 PEs, E/W, fastest link):
Bidirectional ring reduce to PE 0.
Level 2 — Inter-cube within SIP (16 cubes, N/S, UCIe):
Bidirectional ring reduce of PE 0s to cube 0 PE 0.
Level 3 — Inter-SIP (2 SIPs, parent):
Pair exchange between SIP representatives.
Broadcast — Reverse chain through levels 2 and 1.
Bidirectional reduce: left-half sends toward node 0 via dir_dec,
right-half sends via dir_inc (wrapping). Representative receives from
both sides. Rounds per level = ceil((group_size - 1) / 2).
Direction pairing (ring):
Send via dir_dec at PE K → recv via dir_inc at PE K-1
Send via dir_inc at PE K → recv via dir_dec at PE K+1
"""
from __future__ import annotations
def kernel_args(world_size: int, n_elem: int) -> tuple:
"""Positional kernel args for the ahbm backend."""
pes_per_cube = 8
num_sips = max(1, world_size // 128) if world_size > 128 else 1
cubes_per_sip = world_size // (pes_per_cube * num_sips)
return (n_elem, pes_per_cube, cubes_per_sip, num_sips)
def neighbors(rank: int, world_size: int, neighbor_map: dict) -> dict:
"""Build the 3-level neighbor map."""
pes_per_cube = 8
num_sips = max(1, world_size // 128) if world_size > 128 else 1
cubes_per_sip = world_size // (pes_per_cube * num_sips)
pe_id = rank % pes_per_cube
cube_global = rank // pes_per_cube
sip_id = cube_global // cubes_per_sip
local_cube_id = cube_global % cubes_per_sip
result = {}
# Level 1: intra-cube ring (E/W, all PEs)
cube_base = cube_global * pes_per_cube
result["E"] = cube_base + (pe_id + 1) % pes_per_cube
result["W"] = cube_base + (pe_id - 1) % pes_per_cube
# Level 2: inter-cube ring (N/S, PE 0 only)
if pe_id == 0 and cubes_per_sip > 1:
sip_base = sip_id * cubes_per_sip * pes_per_cube
next_cube_pe0 = sip_base + ((local_cube_id + 1) % cubes_per_sip) * pes_per_cube
prev_cube_pe0 = sip_base + ((local_cube_id - 1) % cubes_per_sip) * pes_per_cube
result["N"] = next_cube_pe0
result["S"] = prev_cube_pe0
# Level 3: inter-SIP (parent, PE 0 cube 0 only)
if pe_id == 0 and local_cube_id == 0 and num_sips > 1:
other_sip_pe0 = ((sip_id + 1) % num_sips) * cubes_per_sip * pes_per_cube
result["parent"] = other_sip_pe0
return result
def _bidir_reduce(tl, acc, my_id, group_size, dir_inc, dir_dec, shape, dtype):
"""Bidirectional ring reduce to node 0.
Left half (1..half): chain reduces via dir_dec (toward lower IDs).
Each PE recvs from higher PE (via dir_inc) and sends to lower (via dir_dec).
Right half (half+1..N-1): chain reduces via dir_inc (wraps to node 0).
Each PE recvs from lower PE (via dir_dec) and sends to higher (via dir_inc).
Node 0: recvs left sum via dir_inc, right sum via dir_dec.
Direction pairing: send dir_dec at K → recv dir_inc at K-1.
send dir_inc at K → recv dir_dec at K+1.
"""
if group_size <= 1:
return acc
half = group_size // 2
if my_id == 0:
# Representative: recv left-half sum via dir_inc (from PE 1)
recv = tl.recv(dir=dir_inc, shape=shape, dtype=dtype)
acc = acc + recv
# Recv right-half sum via dir_dec (from PE N-1, wrapped)
if group_size - half - 1 >= 1:
recv = tl.recv(dir=dir_dec, shape=shape, dtype=dtype)
acc = acc + recv
elif my_id <= half:
# Left half: recv from PE my_id+1 via dir_inc, send to PE my_id-1 via dir_dec
if my_id < half: # not the far-edge
recv = tl.recv(dir=dir_inc, shape=shape, dtype=dtype)
acc = acc + recv
tl.send(dir=dir_dec, src=acc)
else:
# Right half: recv from PE my_id-1 via dir_dec, send to PE my_id+1 via dir_inc
if my_id > half + 1: # not the near-edge
recv = tl.recv(dir=dir_dec, shape=shape, dtype=dtype)
acc = acc + recv
tl.send(dir=dir_inc, src=acc)
return acc
def _chain_broadcast(tl, acc, my_id, group_size, dir_inc, shape, dtype):
"""Linear chain broadcast from node 0 via dir_inc.
Node 0 sends via dir_inc → node 1. Node 1 recvs via dir_dec (implicit
from the ring pairing), stores, sends via dir_inc → node 2. Etc.
Recv direction = the opposite: send dir_inc at K → recv dir_dec at K+1.
"""
if group_size <= 1:
return acc
# In ring pairing: send via dir_inc at K → recv via dir_dec at K+1.
# dir_dec is the "other" direction. We infer it from the ring:
# if dir_inc is "E", peer recvs via "W"; if "N", peer recvs via "S".
_recv_dir = {"E": "W", "W": "E", "N": "S", "S": "N"}.get(dir_inc, dir_inc)
if my_id == 0:
tl.send(dir=dir_inc, src=acc)
else:
acc = tl.recv(dir=_recv_dir, shape=shape, dtype=dtype)
if my_id < group_size - 1:
tl.send(dir=dir_inc, src=acc)
return acc
def kernel(t_ptr, n_elem, pes_per_cube, cubes_per_sip, num_sips, tl):
"""Hierarchical all-reduce.
Args:
t_ptr: HBM base address (column-sharded VA).
n_elem: f16 elements per tile.
pes_per_cube: PEs per cube (typically 8).
cubes_per_sip: cubes per SIP (typically 16).
num_sips: number of SIPs (typically 2).
tl: TLContext (auto-injected).
"""
pe_id = tl.program_id(axis=0)
cube_global = tl.program_id(axis=1)
sip_id = cube_global // cubes_per_sip
local_cube_id = cube_global % cubes_per_sip
rank = cube_global * pes_per_cube + pe_id
nbytes = n_elem * 2
pe_addr = t_ptr + rank * nbytes
acc = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
shape = (n_elem,)
dtype = "f16"
# ── Level 1: intra-cube bidirectional reduce to PE 0 ──
acc = _bidir_reduce(
tl, acc, my_id=pe_id, group_size=pes_per_cube,
dir_inc="E", dir_dec="W", shape=shape, dtype=dtype,
)
# ── Level 2: inter-cube bidirectional reduce to cube 0 (PE 0 only) ──
if pe_id == 0 and cubes_per_sip > 1:
acc = _bidir_reduce(
tl, acc, my_id=local_cube_id, group_size=cubes_per_sip,
dir_inc="N", dir_dec="S", shape=shape, dtype=dtype,
)
# ── Level 3: inter-SIP exchange (PE 0 cube 0 only) ──
if pe_id == 0 and local_cube_id == 0 and num_sips > 1:
tl.send(dir="parent", src=acc)
recv = tl.recv(dir="parent", shape=shape, dtype=dtype)
acc = acc + recv
# ── Broadcast back ──
# Level 2: cube 0 PE 0 → all PE 0s via chain
if pe_id == 0 and cubes_per_sip > 1:
acc = _chain_broadcast(
tl, acc, my_id=local_cube_id, group_size=cubes_per_sip,
dir_inc="N", shape=shape, dtype=dtype,
)
# Level 1: PE 0 → all PEs in cube via chain
acc = _chain_broadcast(
tl, acc, my_id=pe_id, group_size=pes_per_cube,
dir_inc="E", shape=shape, dtype=dtype,
)
tl.store(pe_addr, acc)
@@ -0,0 +1,189 @@
"""Intercube all-reduce kernel (pe0-only, same-lane across cubes).
Reduces across the 4×4 cube mesh within each SIP, then exchanges
between SIPs using the configured SIP topology, and broadcasts back.
Supported SIP topologies (selected via ``sip_topo_kind``):
0 — ring_1d: global_E/global_W ring, n_sips-1 rounds
1 — torus_2d: row ring (global_E/W) + col ring (global_S/N)
2 — mesh_2d: row chain reduce+broadcast + col chain reduce+broadcast
IPCQ wiring is handled by ``configure_sfr_intercube_multisip``.
"""
from __future__ import annotations
SIP_TOPO_RING = 0
SIP_TOPO_TORUS = 1
SIP_TOPO_MESH = 2
TOPO_NAME_TO_KIND = {
"ring_1d": SIP_TOPO_RING,
"torus_2d": SIP_TOPO_TORUS,
"mesh_2d": SIP_TOPO_TORUS,
"mesh_2d_no_wrap": SIP_TOPO_MESH,
}
def kernel_args(world_size: int, n_elem: int) -> tuple:
cube_w = 4
cube_h = 4
return (n_elem, cube_w, cube_h, world_size)
def _inter_sip_ring(acc, n_sips, n_elem, tl):
current = acc
for _ in range(n_sips - 1):
tl.send(dir="global_E", src=current)
recv = tl.recv(dir="global_W", shape=(n_elem,), dtype="f16")
acc = acc + recv
current = recv
return acc
def _inter_sip_torus_2d(acc, sip_rank, sip_topo_w, sip_topo_h, n_elem, tl):
# Row ring (global_E / global_W)
current = acc
for _ in range(sip_topo_w - 1):
tl.send(dir="global_E", src=current)
recv = tl.recv(dir="global_W", shape=(n_elem,), dtype="f16")
acc = acc + recv
current = recv
# Col ring (global_S / global_N)
current = acc
for _ in range(sip_topo_h - 1):
tl.send(dir="global_S", src=current)
recv = tl.recv(dir="global_N", shape=(n_elem,), dtype="f16")
acc = acc + recv
current = recv
return acc
def _inter_sip_mesh_2d(acc, sip_rank, sip_topo_w, sip_topo_h, n_elem, tl):
sip_row = sip_rank // sip_topo_w
sip_col = sip_rank % sip_topo_w
# Row reduce W → E
if sip_col == 0:
tl.send(dir="global_E", src=acc)
elif sip_col < sip_topo_w - 1:
recv = tl.recv(dir="global_W", shape=(n_elem,), dtype="f16")
acc = acc + recv
tl.send(dir="global_E", src=acc)
else:
recv = tl.recv(dir="global_W", shape=(n_elem,), dtype="f16")
acc = acc + recv
# Row broadcast E → W
if sip_col == sip_topo_w - 1:
tl.send(dir="global_W", src=acc)
elif sip_col > 0:
acc = tl.recv(dir="global_E", shape=(n_elem,), dtype="f16")
tl.send(dir="global_W", src=acc)
else:
acc = tl.recv(dir="global_E", shape=(n_elem,), dtype="f16")
# Col reduce N → S
if sip_row == 0:
tl.send(dir="global_S", src=acc)
elif sip_row < sip_topo_h - 1:
recv = tl.recv(dir="global_N", shape=(n_elem,), dtype="f16")
acc = acc + recv
tl.send(dir="global_S", src=acc)
else:
recv = tl.recv(dir="global_N", shape=(n_elem,), dtype="f16")
acc = acc + recv
# Col broadcast S → N
if sip_row == sip_topo_h - 1:
tl.send(dir="global_N", src=acc)
elif sip_row > 0:
acc = tl.recv(dir="global_S", shape=(n_elem,), dtype="f16")
tl.send(dir="global_N", src=acc)
else:
acc = tl.recv(dir="global_S", shape=(n_elem,), dtype="f16")
return acc
def allreduce_intercube_multidevice(
t_ptr, n_elem, cube_w, cube_h, n_sips, sip_rank,
sip_topo_kind, sip_topo_w, sip_topo_h, tl,
):
"""Intercube all-reduce (pe0-only) with configurable SIP topology.
Args:
t_ptr: VA base of the row-wise-sharded tensor on this SIP.
n_elem: f16 elements per cube tile.
cube_w: cube mesh width (columns).
cube_h: cube mesh height (rows).
n_sips: number of SIPs.
sip_rank: this SIP's rank (0-based).
sip_topo_kind: 0=ring, 1=torus_2d, 2=mesh_2d.
sip_topo_w: SIP mesh width (for 2D topologies, 0 for ring).
sip_topo_h: SIP mesh height (for 2D topologies, 0 for ring).
tl: TLContext (auto-injected).
"""
cube_id = tl.program_id(axis=1)
row = cube_id // cube_w
col = cube_id % cube_w
nbytes = n_elem * 2
pe_addr = t_ptr + cube_id * nbytes
acc = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
# ── Phase 1: row reduce W → E ──
if col == 0:
tl.send(dir="E", src=acc)
elif col < cube_w - 1:
recv = tl.recv(dir="W", shape=(n_elem,), dtype="f16")
acc = acc + recv
tl.send(dir="E", src=acc)
else:
recv = tl.recv(dir="W", shape=(n_elem,), dtype="f16")
acc = acc + recv
# ── Phase 2: col reduce N → S on rightmost column ──
if col == cube_w - 1:
if row == 0:
tl.send(dir="S", src=acc)
elif row < cube_h - 1:
recv = tl.recv(dir="N", shape=(n_elem,), dtype="f16")
acc = acc + recv
tl.send(dir="S", src=acc)
else:
recv = tl.recv(dir="N", shape=(n_elem,), dtype="f16")
acc = acc + recv
# ── Phase 3: inter-SIP exchange on root cube ──
root_cube = (cube_h - 1) * cube_w + (cube_w - 1)
if cube_id == root_cube and n_sips > 1:
if sip_topo_kind == SIP_TOPO_RING:
acc = _inter_sip_ring(acc, n_sips, n_elem, tl)
elif sip_topo_kind == SIP_TOPO_TORUS:
acc = _inter_sip_torus_2d(acc, sip_rank, sip_topo_w, sip_topo_h, n_elem, tl)
elif sip_topo_kind == SIP_TOPO_MESH:
acc = _inter_sip_mesh_2d(acc, sip_rank, sip_topo_w, sip_topo_h, n_elem, tl)
# ── Phase 4: col broadcast S → N on rightmost column ──
if col == cube_w - 1:
if row == cube_h - 1:
tl.send(dir="N", src=acc)
elif row > 0:
acc = tl.recv(dir="S", shape=(n_elem,), dtype="f16")
tl.send(dir="N", src=acc)
else:
acc = tl.recv(dir="S", shape=(n_elem,), dtype="f16")
# ── Phase 5: row broadcast E → W ──
if col == cube_w - 1:
tl.send(dir="W", src=acc)
elif col > 0:
acc = tl.recv(dir="E", shape=(n_elem,), dtype="f16")
tl.send(dir="W", src=acc)
else:
acc = tl.recv(dir="E", shape=(n_elem,), dtype="f16")
tl.store(pe_addr, acc)
kernel = allreduce_intercube_multidevice
@@ -1,73 +0,0 @@
"""2D-mesh all-reduce kernel (ADR-0023).
Two-phase reduce on a square mesh of side ``S`` (world_size = S*S):
1. Row reduce: ring all-reduce along E/W within each row.
2. Column reduce: ring all-reduce along N/S within each column.
After both phases, every rank holds the global sum.
Uses TensorHandle math (PE_MATH) for accumulation. Op_log captures the
data flow so Phase 2 produces correct final HBM contents. Math/recv
handles are passed directly to the next send, avoiding store→reload
which doesn't propagate correctly with timing-only Phase 1 math.
"""
from __future__ import annotations
import math
def kernel_args(world_size: int, n_elem: int) -> tuple:
"""Return the positional kernel arguments for the ahbm backend.
Mesh all-reduce requires ``world_size`` to be a perfect square —
the mesh side length is ``sqrt(world_size)``.
"""
side = int(round(math.sqrt(world_size)))
if side * side != world_size:
raise ValueError(
f"mesh_allreduce requires a square world_size; got {world_size}"
)
return (n_elem, side)
def kernel(t_ptr, n_elem, side, tl):
"""All-reduce on a square mesh.
Args:
t_ptr: HBM base address (column-sharded VA shared across ranks)
n_elem: number of f16 elements per tile
side: mesh side length (sqrt(world_size))
tl: TLContext (ADR-0022).
"""
local_pe = tl.program_id(axis=0)
cube_id = tl.program_id(axis=1)
pes_per_cube = tl.num_programs(axis=0)
rank = cube_id * pes_per_cube + local_pe
nbytes = n_elem * 2
pe_addr = t_ptr + rank * nbytes
acc = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
current = acc
# ── Phase 1: row ring (E direction) ──
# Ring forwards each received tile (not the cumulative acc) so every
# tile passes through every rank exactly once.
for _ in range(side - 1):
tl.send(dir="E", src=current)
recv = tl.recv(dir="W", shape=(n_elem,), dtype="f16")
acc = acc + recv
current = recv
# Phase 2 column ring starts from the row-phase accumulator. We do NOT
# store/reload here — the math handle's scratch addr is the source for
# the first column send and Phase 2 ipcq_copy replays from there.
current = acc
# ── Phase 2: column ring (S direction) ──
for _ in range(side - 1):
tl.send(dir="S", src=current)
recv = tl.recv(dir="N", shape=(n_elem,), dtype="f16")
acc = acc + recv
current = recv
tl.store(pe_addr, acc)
@@ -1,80 +0,0 @@
"""Ring all-reduce kernel for IPCQ-based PE collective (ADR-0023).
Algorithm: 1D ring of N PEs, each PE starts with one tile of data.
After ``world_size - 1`` rounds, every PE's accumulator holds the sum
of all PE tiles.
Strategy
--------
Each PE starts with its own tile in HBM. The kernel:
1. Loads the local tile into a TensorHandle (the accumulator).
2. In each of ``world_size - 1`` rounds:
- Sends the current accumulator/recv slot to the E neighbor.
- Receives a tile from the W neighbor — the recv handle points
into the per-direction TCM slot.
- Adds the received tile to the accumulator using the TensorHandle
operator overload, which dispatches to ``MathCmd`` (PE_MATH).
3. Stores the final accumulator back to HBM via tl.store. The store is
recorded in op_log with both src and dst, so Phase 2 will copy the
replayed math result from PE-local scratch into HBM.
ADR-0020 D3 split: Phase 1 simulates timing only — math results are
not yet computed, so the accumulator data flowing through Phase 1 may
be stale. Phase 2's DataExecutor replays math + IPCQ copies + dma_write
in stable t_start order, producing correct final HBM contents.
"""
from __future__ import annotations
def kernel_args(world_size: int, n_elem: int) -> tuple:
"""Return the positional kernel arguments for the ahbm backend.
Ring all-reduce takes (n_elem, world_size) after the tensor pointer.
"""
return (n_elem, world_size)
def kernel(t_ptr, n_elem, world_size, tl):
"""Ring all-reduce.
Args:
t_ptr: HBM base address of the column-sharded tensor — all PEs
share this base. The per-PE slice lives at
``t_ptr + global_rank * n_elem * 2``.
n_elem: number of f16 elements per tile.
world_size: total number of participating ranks (passed by host).
tl: TLContext (auto-injected, ADR-0022). The kernel derives the
global rank from ``program_id(axis=0)`` (local PE) and
``program_id(axis=1)`` (cube id):
rank = cube_id * pes_per_cube + local_pe
"""
local_pe = tl.program_id(axis=0)
cube_id = tl.program_id(axis=1)
pes_per_cube = tl.num_programs(axis=0)
rank = cube_id * pes_per_cube + local_pe
nbytes = n_elem * 2 # f16
# Each PE reads from its own slice of the shared base address
pe_addr = t_ptr + rank * nbytes
# Load the local tile — handle points at HBM[pe_addr].
acc = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
# The ring forwards each received tile to the next neighbor (NOT the
# cumulative accumulator), so every rank's tile passes through every
# rank exactly once. The accumulator sums the new arrival each round.
current = acc
for _step in range(world_size - 1):
tl.send(dir="E", src=current)
recv = tl.recv(dir="W", shape=(n_elem,), dtype="f16")
# TensorHandle add → MathCmd → PE_MATH (timing in Phase 1, real
# numpy in Phase 2 via DataExecutor). The result handle lives at
# an auto-allocated PE-local scratch addr.
acc = acc + recv
current = recv # forward W's tile to E next round
# Final result back to this PE's HBM slice. Op_log captures the
# source (scratch addr) and dst (HBM slice) so Phase 2 copies the
# accumulated value into HBM for verification.
tl.store(pe_addr, acc)
@@ -1,80 +0,0 @@
"""Tree all-reduce kernel for IPCQ-based PE collective (ADR-0023).
Two-phase binary tree all-reduce:
Phase 1 (reduce up):
- leaf nodes send their value to ``parent``
- internal nodes recv from each child, sum, then send to ``parent``
- root accumulates child contributions; final acc holds global sum
Phase 2 (broadcast down):
- root sends acc to ``child_left`` and ``child_right`` (if present)
- internal nodes recv from ``parent``, then forward to children
- all ranks store the final acc to HBM
Uses TensorHandle math (PE_MATH) for accumulation. Op_log captures the
data flow so Phase 2 produces correct final HBM contents. The kernel
deliberately avoids the store→reload→send pattern: math/recv handles
are passed directly to the next send so PE_DMA snapshots a deterministic
source addr that Phase 2 can replay.
"""
from __future__ import annotations
def kernel_args(world_size: int, n_elem: int) -> tuple:
"""Return the positional kernel arguments for the ahbm backend."""
return (n_elem, world_size)
def kernel(t_ptr, n_elem, world_size, tl):
"""Tree all-reduce.
Args:
t_ptr: HBM base address.
n_elem: number of f16 elements per tile.
world_size: total number of participating ranks (passed by host).
tl: TLContext (ADR-0022). Global rank from program_id(0/1).
"""
local_pe = tl.program_id(axis=0)
cube_id = tl.program_id(axis=1)
pes_per_cube = tl.num_programs(axis=0)
rank = cube_id * pes_per_cube + local_pe
nbytes = n_elem * 2
pe_addr = t_ptr + rank * nbytes
acc = tl.load(pe_addr, shape=(n_elem,), dtype="f16")
# Compute children/parent existence (matches tree_binary topology generator)
has_parent = rank > 0
left = 2 * rank + 1
right = 2 * rank + 2
has_left = left < world_size
has_right = right < world_size
# ── Phase 1: reduce up ──
if has_left:
recv = tl.recv(dir="child_left", shape=(n_elem,), dtype="f16")
acc = acc + recv
if has_right:
recv = tl.recv(dir="child_right", shape=(n_elem,), dtype="f16")
acc = acc + recv
if has_parent:
# Send the math/load handle directly — its addr is either the
# original HBM tile (leaf) or the PE-local scratch where the
# accumulator lives. Phase 2 ipcq_copy replays from the same addr.
tl.send(dir="parent", src=acc)
# ── Phase 2: broadcast down ──
if has_parent:
# Replace acc with the value broadcast from the parent (the global
# sum). The recv handle points at the parent-direction TCM slot.
acc = tl.recv(dir="parent", shape=(n_elem,), dtype="f16")
if has_left:
tl.send(dir="child_left", src=acc)
if has_right:
tl.send(dir="child_right", src=acc)
# Final store to HBM for the bench's verification path.
tl.store(pe_addr, acc)