StableHLO Interpreter

The main goal of the StableHLO interpreter is to provide a reference implementation to the semantics of StableHLO opset according to its specification. The secondary goal is for the implementation to closely follow the spec, favoring readability over performance, to provide additional clarity to the semantics of even the most involved operations like Convolution, Gather/Scatter, and DotGeneral.

At the moment, OpenXLA supports the interpretation of 91 out of 96 specced StableHLO ops. The remaining 5 ops (FftOp, RngOp, RngBitGeneratorOp, UniformDequantizeOp, and UniformQuantizeOp) have their semantics documented in, and have completed initial investigations on how to move forward (see for a complete list of ops and its latest status). These final enhancements will be implemented on an as-needed community basis.


We categorized the StableHLO opset into 11 categories consisting of 118 ops in total (see Appendix). Reference Implementation workstream organizes the work on implementing an interpreter for 100% of StableHLO ops as defined in the StableHLO specification. We are planning to complete all or almost all work in this workstream in StableHLO v1.0. Of the 96 ops that have a spec currently, we can interpret 91 ops through OpenXLA (see Special Cases for the remaining 5).


The main requirement for the interpreter is to have 1:1 correspondence with the spec. The spec allows standardization of the interpreter across similar ops that lead to modular, high quality implementation of the interpreter.

Special Cases


This category has decomposable ops whose future is unclear at the moment. There are three specced ops in this category that the interpreter does not support at the moment:

  • FftOp
  • RngOp
  • RngBitGeneratorOp

FftOp is categorized as Miscellaneous, but unlike other ops in this category, this op does not have an expander pass, and supporting this in StableHLO is a WIP.

RngOp and RngBitGeneratorOp can be decomposed into MHLO ops, but the decomposition introduces a XlaRngGetAndUpdateStateOp which is an MHLO specific op. Supporting interpretation of these two ops is a WIP.

The tool to convert remaining ops in this category to StableHLO ops that the interpreter supports resides in

Not in HLO

Apart from the specced ops, this category consists of 10 unspecced ops (see StableHLO Ops Categories) which are planed to be moved out of StableHLO. Some of these ops have existing passes in mhlo to convert them to StableHLO equivalent ops. There are three ops the interpreter does not support because there are no existing decompositions to StableHLO ops:

  • compute_reshape_shape
  • cstr_reshapable
  • trace

compute_reshape_shape and cstr_reshapable ops are part of the ongoing Dynamism work, and they are planned to be removed from StableHLO (see #1668).

trace op is private to XLA and there no no users in JAX, PyTorch or TensorFlow (see #604).

The tool to convert remaining ops in this category to equivalent StableHLO ops that the interpreter supports resides in


Quantization spec'ing is still WIP, and interpreter support for quantized ops (UniformDequantizeOp, UniformQuantizeOp) and type (QuantizedTensorType) is tracked by #1140, #1141, and #1691 respectively.

Usage Instructions

Building the Reference Interpreter

The interpreter can be built and tested via Bazel or CMake (preferred). For full instructions, see


bazel build //...


mkdir -p build && cd build

cmake .. -GNinja \

To run the interpreter, we have a translate tool to interpret StableHLO programs written in MLIR.

stablehlo-translate --interpret <path/to/program>

The Interpreter Dialect

The Interpreter dialect contains various utility ops related to the interpreter. Specifically, the interpreter.run_parallel (see for op semantics and example usage) op allows interpretation of Distribution ops, and more utilities plan to be added based on community needs.

The Check Dialect

The Check dialect is used to compare interpreter runtime values to expected values. StableHLO program outputs can be tested via various check ops (see for op semantics and example usage).

Writing Test Programs

We use LLVM's lit tool to run and compare against generated file to diff against the output of the interpreter (see stablehlo/tests/interpret for example tests).

Testing AddOp (sample from interpret_add.mlir):

// RUN: stablehlo-translate --interpret %s

func.func @add_op_scalar() {
  %0 = stablehlo.constant dense<2> : tensor<i4>
  %1 = stablehlo.constant dense<3> : tensor<i4>
  %2 = stablehlo.add %0, %1 : tensor<i4>
  check.expect_eq_const %2, dense<5> : tensor<i4>

Testing ops in the Distribution category requires running it via the interpreter.run_parallel utility op.

Testing AllReduceOp (sample from all_reduce.mlir):

// RUN: stablehlo-translate --interpret %s

module @cross_replica {
  func.func public @all_reduce(%operand : tensor<4xi64>) -> tensor<4xi64> {
    %result = "stablehlo.all_reduce"(%operand) ({
      ^bb0(%arg0: tensor<i64>, %arg1: tensor<i64>):
        %0 = stablehlo.add %arg0, %arg1 : tensor<i64>
        stablehlo.return %0 : tensor<i64>
    }) {
      replica_groups = dense<[[0, 1]]> : tensor<1x2xi64>,
      channel_handle = #stablehlo.channel_handle<handle = 0, type = 0>
    } : (tensor<4xi64>) -> tensor<4xi64>
    return %result : tensor<4xi64>
  func.func public @main() {
    %inputs0 = stablehlo.constant dense<[1, 2, 3, 4]> : tensor<4xi64>
    %inputs1 = stablehlo.constant dense<[5, 6, 7, 8]> : tensor<4xi64>
    %results:2 = "interpreter.run_parallel"(%inputs0, %inputs1) {
      programs=[[@all_reduce], [@all_reduce]]
    } : (tensor<4xi64>, tensor<4xi64>) -> (tensor<4xi64>, tensor<4xi64>)
    check.expect_eq_const %results#0, dense<[6, 8, 10, 12]> : tensor<4xi64>
    check.expect_eq_const %results#1, dense<[6, 8, 10, 12]> : tensor<4xi64>

Debugging StableHLO

Following the StableHLO build steps, the StableHLO binaries for tools in stablehlo/tools should reside in /build/bin. Common debugging tools like GDB can be used to step through the code:

gdb --args ./build/bin/stablehlo-translate -allow-unregistered-dialect --interpret ./stablehlo/tests/interpret/<test>.mlir


Convert Miscellaneous Ops

# batch_norm_grad
hlo-expand --batch_norm_grad_expander <path/to/hlo_module>

# batch_norm_inference
hlo-expand --batch_norm_inference_expander <path/to/hlo_module>

# batch_norm_training
hlo-expand --batch_norm_training_expander <path/to/hlo_module>

# cholesky
hlo-expand --cholesky_expander <path/to/hlo_module>

# constant
# Supported in StableHLO interpreter.

# fft

# iota
# Supported in StableHLO interpreter.

# rng

# rng_bit_generator

# triangular_solve
hlo-expand --triangular_solve_expander <path/to/hlo_module>

Convert Not In HLO Ops

# broadcast
mlir-hlo-opt -mhlo-legalize-broadcast-to-broadcast-in-dim <path/to/input>

# compute_reshape_shape
# This op will be removed from StableHLO as part of Dynamism work (see #1668).

# create_token
mlir-hlo-opt -mhlo-legalize-create-token-to-after-all <path/to/input>

# cross-replica-sum
mlir-hlo-opt -mhlo-legalize-cross-replica-sum-to-all-reduce <path/to/input>

# cstr_reshapable
# This op will be removed from StableHLO as part of Dynamism work (see #1668).

# dot
mlir-hlo-opt -mhlo-legalize-dot-to-dot-general <path/to/input>

# einsum
mlir-hlo-opt -mhlo-legalize-einsum-to-dot-general <path/to/input>

# torch_index_select
mlir-hlo-opt -mhlo-legalize-torch-index-select-to-gather <path/to/input>

# trace
# There are no current users of trace (see #604).

# unary_einsum
mlir-hlo-opt --canonicalize -mhlo-legalize-einsum-to-dot-general <path/to/input>

StableHLO Ops Categories

Categories Mnemonics Total
Control Flow after_all, case, if, optimization_barrier, while 5
Data Movement broadcast_in_dim, concatenate, dynamic_slice, dynamic_update_slice, gather, pad, reshape, reverse, scatter, slice, sort, transpose 12
Distribution all_gather, all_reduce, all_to_all, collective_permute, infeed, outfeed, partition_id, recv, reduce_scatter, replica_id, send 11
Dynamism dynamic_broadcast_in_dim, dynamic_conv, dynamic_gather, dynamic_iota, dynamic_pad, dynamic_reshape, get_dimension_size, real_dynamic_slice, set_dimension_size 9
Elementwise abs, add, and, atan2, bitcast_convert, cbrt, ceil, clamp, compare, complex, convert, cosine, count_leading_zeros, divide, exponential, exponential_minus_one, floor, imag, is_finite, log, log_plus_one, logistic, map, maximum, minimum, multiply, negate, not, or, popcnt, power, real, reduce_precision, remainder, round_nearest_afz, round_nearest_even, rsqrt, select, shift_left, shift_right_arithmetic, shift_right_logical, sign, sine, sqrt, subtract, tanh, xor 47
Extensibility custom_call, get_tuple_element, tuple 3
Miscellaneous batch_norm_grad, batch_norm_inference, batch_norm_training, cholesky, constant, fft, iota, rng, rng_bit_generator, triangular_solve 10
Modularity call, func, module, return 4
Not In HLO broadcast, compute_reshape_shape, create_token, cross-replica-sum, cstr_reshapable, dot, einsum, torch_index_select, trace, unary_einsum 10
Quantization uniform_dequantize, uniform_quantize 2
Reduction convolution, dot_general, reduce, reduce_window, select_and_scatter 5