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+# [RFC] Add collective_broadcast to the StableHLO specification
+
+Status: Review<br/>
+Initial version: 10/17/20223<br/>
+Last updated: 11/1/2023<br/>
+Discussion thread: [GitHub](https://github.com/openxla/stablehlo/pull/1809)
+
+## Motivation
+
+StableHLO currently has [five collective communication primitives](https://github.com/openxla/stablehlo/blob/main/docs/spec.md#collective-ops): `collective_permute`, `all_gather`, `all_to_all`, `all_reduce`, and `reduce_scatter`. However, one of the major collective communication primitives, `broadcast`, is missing from this list. This primitive allows for a one-to-many replication of a tensor to many devices efficiently. `broadcast` is a primitive in [MPI](https://www.open-mpi.org/doc/v4.1/man3/MPI_Bcast.3.php), [NCCL](https://docs.nvidia.com/deeplearning/nccl/user-guide/docs/api/colls.html#c.ncclBroadcast), and [PyTorch](https://pytorch.org/docs/stable/distributed.html#torch.distributed.broadcast). From here on out, we will refer to this operation as `collective_broadcast` for reasons discussed later.
+
+While it technically would be possible to replicate a broadcast with a conditional mask and a `psum`, that reduces to an `all_reduce` communication primitive, which is significantly more expensive than a simple `collective_broadcast`. Additionally, when dealing with network-switch environments, the explicit use of `collective_broadcast` allows the switch to greatly optimize it's throughput when replicating to many targets simultaneously. However, XLA currently has no ability to lower directly to a mesh's `collective_broadcast` primitive, so a lot of that optimization is left on the table.
+
+Additionally, a new compiler pass that detects usage of the old `psum` hack and replaces it with a `collective_broadcast` could be implemented only once and forever be supported by all hardware, future and current. This could have positive knock-on effects for users who don't even realize they're using it!
+
+`collective_broadcast` can be used to quickly replicate a tensor across an entire mesh, and would use less communication resources as compared to `all_gather` or `psum`. `collective_broadcast` is also the base primitive used in the [SUMMA](https://www.netlib.org/lapack/lawnspdf/lawn96.pdf) distributed GEMM algorithm. As AI computing grows larger, there likely will grow a need for these 2D distributed GEMM algorithms. Adding support for one of the needed primitives could help advance research in these areas. 
+
+## Alternatives considered
+
+Instead of adding `collective_broadcast` as a primitive, we considered loosening the restriction of `collective_permute` to allow a one-to-many communication schedule instead of the current restriction of a one-to-one schedule. Downstream compilers would then be responsible for detecting this and calling their own `collective_broadcast` primitive. However, loosening this restriction makes defining the transposition rule for `collective_permute` significantly more complicated. Questions of how to calculate that and do it efficiently given any communication configuration and do so in SPMD became difficult. However, the transposition rule for `collective_broadcast` is just `psum` with a source-device one-hot masking. This simplicity plus the broad usage of `collective_broadcast` in the wider ecosystem made us choose to ultimately add the new primitive instead.
+
+## Why call it collective_broadcast and not just broadcast?
+Unfortunately, the op name `broadcast` is already taken by [an op in XLA proper](https://www.tensorflow.org/xla/operation_semantics#broadcast), so we can't have the two names clash. `collective_broadcast` was the preferred alternative.
+
+## Proposed Specification
+
+### collective_broadcast
+
+#### Semantics
+
+Within each process group in the StableHLO process grid, send the value of the
+`operand` tensor from the source process to the target processes and produce a
+`result` tensor.
+
+The operation splits the StableHLO process grid into `process_groups` which is
+defined as follows:
+
+* `cross_replica(replica_groups)` if `channel_id <= 0`.
+* `cross_partition(replica_groups)` if `channel_id > 0`.
+
+Afterwards, `result@process` is given by:
+
+* `operand@process_groups[i, 0]` if there exists an `i` such that
+  the process is in `process_groups[i]`.
+* `broadcast_in_dim(constant(0, element_type(result)), [], type(result))` otherwise.
+
+
+#### Inputs
+
+| Label | Name                    | Type                                                             | Constraints |
+|-------|-------------------------|------------------------------------------------------------------|-------------|
+| (I1)  | `operand`               | tensor                                                           | (C3)        |
+| (I2)  | `replica_groups`        | variadic number of 1-dimensional tensor constants of type `si64` | (C1), (C2)  |
+| (I3)  | `channel_id`            | constant of type `si64`                                          |             |
+
+#### Outputs
+
+| Name     | Type   | Constraints |
+|----------|--------|-------------|
+| `result` | tensor | (C3)        |
+
+#### Constraints
+
+* (C1) `is_unique(replica_groups)`.
+* (C2) `0 <= replica_groups < N` where `N` is defined as:
+  * `num_replicas` if `cross_replica` is used.
+  * `num_partitions` if `cross_partition` is used.
+* (C3) `type(result) = type(operand)`.
+
+#### Examples
+
+```mlir
+// num_replicas: 4
+// num_partitions: 1
+// %operand@(0, 0): [[1, 2]]
+// %operand@(1, 0): [[3, 4]]
+// %operand@(2, 0): [[5, 6]]
+// %operand@(3, 0): [[7, 8]]
+%result = "stablehlo.collective_broadcast"(%operand) {
+  replica_groups = dense<[[2, 1]]> : tensor<1x2xi64>,
+  channel_handle = #stablehlo.channel_handle<handle = 0, type = 0>
+} : (tensor1x2xi64>) -> tensor<1x2xi64>
+// %result@(0, 0): [[0, 0]]
+// %result@(1, 0): [[5, 6]]
+// %result@(2, 0): [[5, 6]]
+// %result@(3, 0): [[0, 0]]
+```