Gemmlowp's public entry points

gemmlowp's public interface is defined in public/gemmlowp.h.


The primary public entry point is: GemmWithOutputPipeline.

A usage example is given in doc/

The high-level overview of how this specifies a low-precision matrix multiplication is explained in The rationale for a specific quantization paradigm is given in That specific quantization paradigm is implemented at two different stages of the computation: as pre-processing on the operands and as post-processing on the result:

  • Pre-processing on the LHS, RHS operands, in the form of adding constant lhs_offset, rhs_offset to them, is explained in

  • Post-processing on the result, in the form of a flexible “output pipeline”, is explained in

More details on this below as we discuss specific function parameters.

The prototype is:

template <typename InputScalar, typename OutputScalar, typename BitDepthParams,
          MapOrder LhsOrder, MapOrder RhsOrder, MapOrder ResultOrder,
          typename OutputPipelineType, typename GemmContextType>
void GemmWithOutputPipeline(GemmContextType* context,
                            const MatrixMap<const InputScalar, LhsOrder>& lhs,
                            const MatrixMap<const InputScalar, RhsOrder>& rhs,
                            MatrixMap<OutputScalar, ResultOrder>* result,
                            int lhs_offset, int rhs_offset,
                            const OutputPipelineType& output_pipeline);

A typical call looks like (from the usage example):

gemmlowp::GemmWithOutputPipeline<std::uint8_t, std::uint8_t,
    &gemm_context, uint8_lhs_matrix, uint8_rhs_matrix,
    &uint8_result_matrix, lhs_offset, rhs_offset, output_pipeline);

Template parameters

Typically only the 3 first template parameters need to be specified, the rest being automatically deduced from function parameters:

  • InputScalar: The scalar type of the LHS and RHS operands. At the moment, this must be std::uint8_t.
  • OutputScalar: The scalar type of the result. At the moment, this must be std::uint8_t.
  • BitDepthParams: Defines the bit format of the input and output matrices and the required accuracy of the computation. At the moment, the only non-deprecated valid value is gemmlowp::DefaultL8R8BitDepthParams. See for other values and the general idea of this, and how it may become more useful in the future.

The other template parameters, which typically do not need to be specified, are:

  • LhsOrder, RhsOrder, ResultOrder: the storage orders (row-major or column-major) of the LHS, RHS, result matrices. See public/map.h. See the below performance note: we recommend using respectively RowMajor, ColMajor, ColMajor for optimal performance.
  • OutputPipelineType: the actual std::tuple type of the output pipeline. See below explanation of the output_pipeline parameter, and
  • GemmContextType: the type of the context parameter. At the moment, this must be gemmlowp::GemmContext.

Function parameters

The function parameters taken by GemmWithOutputPipeline are:

  • context: The gemmlowp::GemmContext object holding state and resources to be used for this gemmlowp call.
  • lhs, rhs: The LHS and RHS operand matrices. Note that these are MatrixMap objects, mapping external buffers as matrices, not owning data. See public/map.h.
  • result: pointer to the destination MatrixMap object, which must be already constructed, wrapping the external destination buffer with the wanted destination matrix shape and storage layout. No memory allocation will be performed by gemmlowp for the destination buffer. See public/map.h.
  • lhs_offset, rhs_offset are constants added to each matrix entry in the LHS, RHS matrices respectively, as explained in This is only the part of the quantization paradigm explained in that needs to be implemented as operations on the operands; everything else is operations on the result, see output_pipeline.
  • output_pipeline is a std::tuple of output stages (see public/output_stages.h), specifying the output pipeline (see This is the part of the quantization paradigm explained in that needs to be implemented as operations on the result matrix.

Performance note on storage orders.

gemmlowp supports arbitrary combinations of storage orders for the LHS, RHS and result matrices. However, not all are equally optimized for.

Because gemmlowp is primarily aimed at neural network inference workloads, optimization focus is on this particular combination of storage orders:

  • LhsOrder=RowMajor
  • RhsOrder=ColMajor
  • ResultOrder=ColMajor

The rationale is that the LHS is typically the constant weights of a neural network layer (e.g. the weights of a Convolutional layer implemented as a matrix multiplication), while the RHS and result are neural network activations, respectively the input and output activations of the layer.

Because the RHS and result are activations, we want them to share the same storage order -- so that one layer‘s output activations can be readily used as the next layer’s input activations. Thus, we focus on RhsOrder=ResultOrder.

We also know from general considerations on matrix multiplication that it is slightly more efficient to have the direction of accumulation (the “depth” dimension) be the direction of contiguous storage in memory. That means that it is always going to be slightly easier and more efficient to have LhsOrder=RowMajor and RhsOrder=ColMajor.

Putting this together, we arrive at gemmlowp's focus on the above-described combination of storage orders.

Using other storage orders will typically mean taking less efficient paths in the packing and unpacking stages, see The compute kernel stage ( is unaffected.


This is a variant where lhs_offset and rhs_offset may be vectors instead of scalar. They are then broadcasted against LHS, RHS respectively.

This is useful for some flavors of neural network inference with “per-channel quantization”, whence the PC suffix. This has been useful in some settings where a neural network trained in float arithmetic was subsequently quantized. On the other hand, retraining neural networks for quantized inference tends to remove the need for per-channel quantization. For that reason, the long-term usefulness of this entry point is in question.


This is gemmlowp's original, now legacy and deprecated, entry point. See the section of on the legacy quantization paradigm. Avoid in new code.

The eight_bit_int_gemm directory

As explained in the top-level, this is entirely deprecated.