CUTLASS 3.1

CUTLASS 3.1 - April 2023

CUTLASS is a collection of CUDA C++ template abstractions for implementing high-performance matrix-matrix multiplication (GEMM) and related computations at all levels and scales within CUDA. It incorporates strategies for hierarchical decomposition and data movement similar to those used to implement cuBLAS and cuDNN. CUTLASS decomposes these "moving parts" into reusable, modular software components abstracted by C++ template classes. Primitives for different levels of a conceptual parallelization hierarchy can be specialized and tuned via custom tiling sizes, data types, and other algorithmic policy. The resulting flexibility simplifies their use as building blocks within custom kernels and applications.

To support a wide variety of applications, CUTLASS provides extensive support for mixed-precision computations, providing specialized data-movement and multiply-accumulate abstractions for half-precision floating point (FP16), BFloat16 (BF16), Tensor Float 32 (TF32), single-precision floating point (FP32), FP32 emulation via tensor core instruction, double-precision floating point (FP64) types, integer data types (4b and 8b), and binary data types (1b). CUTLASS demonstrates warp-synchronous matrix multiply operations targeting the programmable, high-throughput Tensor Cores implemented by NVIDIA's Volta, Turing, Ampere, and Hopper architectures.

See the Quick Start Guide to get started quickly.

See the functionality listing for the list of operations supported at each level of the execution model hierarchy.

CUTLASS 3.0 introduced a new core library, CuTe, to describe and manipulate tensors of threads and data. CuTe is a collection of C++ CUDA template abstractions for defining and operating on hierarchically multidimensional layouts of threads and data. CuTe provides Layout and Tensor objects that compactly package the type, shape, memory space, and layout of data, while performing the complicated indexing for the user. This lets programmers focus on the logical descriptions of their algorithms while CuTe does the mechanical bookkeeping for them. With these tools, we can quickly design, implement, and modify all dense linear algebra operations.

The core abstractions of CuTe are hierarchically multidimensional layouts which can be composed with data arrays to represent tensors. The representation of layouts is powerful enough to represent nearly everything we need to implement efficient dense linear algebra. Layouts can also be combined and manipulated via functional composition, on which we build a large set of common operations such as tiling and partitioning.

CUTLASS 3.0 and beyond adopts CuTe throughout the GEMM hierarchy in its templates. This greatly simplifies the design and improves code composability and readability. More documentation specific to CuTe can be found in its dedicated documentation directory.

In addition to GEMMs, CUTLASS implements high-performance convolution via the implicit GEMM algorithm. Implicit GEMM is the formulation of a convolution operation as a GEMM thereby taking advantage of CUTLASS's modular GEMM pipeline. This allows CUTLASS to build convolutions by reusing highly-optimized GEMM components.

What's New in CUTLASS 3.1

CUTLASS 3.1 is an update to CUTLASS adding:

• New CUTLASS Python interface that aims to provide an ease-of-use interface for instantiating, emitting, compiling, and running CUTLASS kernels via Python. More details here and new examples.
• New efficient epilogues using TMA for Hopper.
• Support for fused epilogues, such Bias, ReLU and GELU, using the new efficient epilogues.
• New warp-specialized TensorFloat-32 (TF32) GEMM kernels targeting Hopper TMA.
• New warp-specialized persistent cooperative kernel design that improves performance on Hopper.
• An example showcasing GEMM-Like Tensor-Tensor Contraction (GETT) capability on Hopper.
• New Epilogue builders. Similar to mainloop builders (see example 49), epilogue builders aim to generate the best-possible epilogue while exposing incremental opt-ins for greater customization.
• Profiler support for overriding kernel and epilogue builder auto schedules for 3.x API kernels, allowing specific policies to be run in the CUTLASS profiler.
• Changes to the GEMM API 3.x, involving the host-facing arguments and the underlying Params structs.
• FMHA Backward Pass from Meta xFormers.
• Streamk GEMM with Broadcast enables epilogue broadcast with StreamK GEMM.
• Batched B2B GEMM now can run multiple Back-to-Back GEMM with the same problem size in parallel.
• Batched Strided GEMV support both row major and column major input matrix.
• Permute + GEMM fusion can fuse Permute with following GEMM now. Before, we only support fusing GEMM with Permute in the epilogue.

• Row Broadcast can be fused in the epilogue.

• Announcement:

  • The GitHub branch is renamed from master to main in this release.
  • A slight modification has been made to the ordering of arguments passed in to epilogues in 3.x kernels. Existing CUTLASS 3.x kernel invocations will need to be modified to reflect this change. 2.x kernels remain unaffected. See #890 for additional information.
  • The CUTLASS Python interface supersedes PyCUTLASS. PyCUTLASS has been moved to /python/cutlass/backend. Backward compatibility between the Python interface and PyCUTLASS will not be maintained moving forward.

Minimum requirements:

• Architecture: Volta
• Compiler: Must support at least C++17
• CUDA Toolkit version: 11.4

Starting from CUTLASS 3.0, CUTLASS removed support for the following:

• Maxwell and Pascal GPU architectures
• Ubuntu 16.04
• CUDA 10.2
• C++ language versions less than 17.

See the CHANGELOG for a detailed listing of releases and updates.

Performance

CUTLASS primitives are very efficient. When used to construct device-wide GEMM kernels, they exhibit peak performance comparable to cuBLAS for scalar GEMM computations. The above figure shows CUTLASS performance relative to cuBLAS for large matrix dimensions on an NVIDIA H100 (NVIDIA Hopper architecture), an NVIDIA L40 (NVIDIA Ada architecture), an NVIDIA A100 (NVIDIA Ampere architecture),
and an NVIDIA A40 (NVIDIA Ampere architecture). CUTLASS 3.0 was compiled with the CUDA 12.0 Toolkit. Tensor Core operations are implemented using CUDA's mma and wgmma instructions.

When using CUTLASS building blocks to construct device-wide implicit gemm (Fprop, Dgrad, and Wgrad) kernels, CUTLASS performance is also comparable to cuDNN when running Resnet-50 layers on an NVIDIA A100 as shown in the above figure. Tensor Core operations are implemented using CUDA's mma instruction.

Compatibility

CUTLASS requires a C++17 host compiler and performs best when built with the CUDA 12.1 Toolkit. It is also compatible with CUDA 11.4, CUDA 11.5, CUDA 11.6, CUDA 11.7, CUDA 11.8, and CUDA 12.0.

Operating Systems

We have tested the following environments.

|Operating System | Compiler | |-----------------|----------| | Ubuntu 18.04 | GCC 7.5.0 | | Ubuntu 20.04 | GCC 10.3.0 | | Ubuntu 22.04 | GCC 11.2.0 |

Note: We plan to add Windows (MSVC) & Clang compiler support soon. Note: GCC 8.5.0 has known regressions regarding fold expressions and overloaded operators. Using GCC 7.5.0 or (preferred) GCC >= 9 is recommended.

Hardware

CUTLASS runs successfully on the following NVIDIA GPUs, and it is expected to be efficient on Volta, Turing, Ampere, Ada, and Hopper architecture based NVIDIA GPUs.

|GPU|CUDA Compute Capability|Minimum CUDA Toolkit Required by CUTLASS-3| |---|---|---| |NVIDIA V100 Tensor Core GPU |7.0|11.4| |NVIDIA TitanV |7.0|11.4| |NVIDIA GeForce RTX 2080 TI, 2080, 2070 |7.5|11.4| |NVIDIA T4 |7.5|11.4| |NVIDIA A100 Tensor Core GPU |8.0|11.4| |NVIDIA A10 |8.6|11.4| |NVIDIA GeForce RTX 3090 |8.6|11.4| |NVIDIA GeForce RTX 4090 |8.9|11.8| |NVIDIA L40 |8.9|11.8| |NVIDIA H100 Tensor Core GPU |9.0|11.8|

Target Architecture

In general, PTX code generated for one target architecture can be run on future architectures (i.e., it is forward compatible). However, CUDA 12.0 introduced the concept of "architecture-accelerated features" whose PTX does not have forward compatibility guarantees. Several Hopper PTX instructions fall under this category of architecture-accelerated features, and thus require a sm_90a target architecture (note the "a" appended). For more details on this and other architecture-accelerated instructions, please refer to the CUDA Documentation.

The target architecture information is passed on to CUTLASS via the cmake flag CUTLASS_NVCC_ARCHS. In order to maximize performance on Hopper GH100, users are required to build CUTLASS with 90a as the target architecture. If a user accidentally builds a kernel which uses SM90a features (e.g. Hopper Tensor Core Instructions), using the SM90 target (note the lack of "a"), with either CTK 12 or 11.8, the kernel is expected to fail with a runtime error.

cmake .. -DCUTLASS_NVCC_ARCHS="90a"

Please refer to the functionality documentation for details on which kernels require which target architectures.

Documentation

CUTLASS is described in the following documents and the accompanying Doxygen documentation.

• Quick Start Guide - build and run CUTLASS
• Functionality - summarizes functionality available in CUTLASS
• Efficient GEMM in CUDA - describes how GEMM kernels may be implemented efficiently in CUDA
• CUTLASS 3.x Design - describes the CUTLASS 3.x design, its benefits, and how CuTe enables us to write much more composable components
• GEMM API 3.x - describes the CUTLASS 3.x GEMM model and C++ template concepts
• GEMM API 2.x - describes the CUTLASS 2.x GEMM model and C++ template concepts
• Implicit GEMM Convolution - describes 2-D and 3-D convolution in CUTLASS
• Code Organization - describes the organization and contents of the CUTLASS project
• Terminology - describes terms used in the code
• Programming Guidelines - guidelines for writing efficient modern CUDA C++
• Fundamental types - describes basic C++ classes used in CUTLASS to represent numeric quantities and arrays
• Layouts - describes layouts of matrices and tensors in memory
• Tile Iterators - describes C++ concepts for iterating over tiles of matrices in memory
• CUTLASS Profiler - command-line driven profiling application
• CUTLASS Utilities - additional templates used to facilate rapid development

Resources

We have also described the structure of an efficient GEMM in our talk at the GPU Technology Conference 2018.

• CUTLASS: Software Primitives for Dense Linear Algebra at All Levels and Scales within CUDA
• Developing CUDA Kernels to Push Tensor Cores to the Absolute Limit on NVIDIA A100
• Accelerating Convolution with Tensor Cores in CUTLASS
• Accelerating Backward Data Gradient by Increasing Tensor Core Utilization in CUTLASS
• CUTLASS: Python API, Enhancements, and NVIDIA Hopper

Building CUTLASS

CUTLASS is a header-only template library and does not need to be built to be used by other projects. Client applications should target CUTLASS's include/ directory in their include paths.

CUTLASS unit tests, examples, and utilities can be build with CMake starting version 3.12. Make sure the CUDACXX environment variable points to NVCC in the CUDA Toolkit installed on your system.

bash $ export CUDACXX=${CUDA_INSTALL_PATH}/bin/nvcc

Create a build directory within the CUTLASS project, then run CMake. By default CUTLASS will build kernels for CUDA architecture versions 5.0, 6.0, 6.1, 7.0, 7.5, 8.0, 8.6, 8.9, and 9.0. To reduce compile time you can specify the architectures to build CUTLASS for by changing the CMake configuration setting CUTLASS_NVCC_ARCHS.

```bash $ mkdir build && cd build

$ cmake .. -DCUTLASSNVCCARCHS=80 # compiles for NVIDIA's Ampere Architecture ```

From the build/ directory, compile and run the CUTLASS unit tests by building the target test_unit with make.

The unit tests are organized as several binaries mirroring the top-level namespaces of CUTLASS, and they may be executed in parallel via make's -j command line argument.

bash $ make test_unit -j ... ... ... [----------] Global test environment tear-down [==========] 946 tests from 57 test cases ran. (10812 ms total) [ PASSED ] 946 tests.

All tests should pass on supported platforms, though the exact number of tests may vary over time.

Project Structure

CUTLASS is arranged as a header-only library along with Utilities, Tools, Examples, and unit tests. Doxygen documentation provides a complete list of files, classes, and template concepts defined in the CUTLASS project.

A detailed explanation of the source code organization may be found in the CUTLASS documentation, but several main components are summarized below.

CUTLASS Template Library

``` include/ # client applications should target this directory in their build's include paths

cutlass/ # CUDA Templates for Linear Algebra Subroutines and Solvers - headers only

arch/                    # direct exposure of architecture features (including instruction-level GEMMs)

conv/                    # code specialized for convolution

epilogue/                # code specialized for the epilogue of gemm/convolution

gemm/                    # code specialized for general matrix product computations

layout/                  # layout definitions for matrices, tensors, and other mathematical objects in memory

platform/                # CUDA-capable Standard Library components

reduction/               # bandwidth-limited reduction kernels that do not fit the "gemm" model

thread/                  # simt code that can be performed within a CUDA thread

transform/               # code specialized for layout, type, and domain transformations

*                        # core vocabulary types, containers, and basic numeric operations

cute/ # CuTe Layout, layout algebra, MMA/Copy atoms, tiled MMA/Copy

algorithm/               # Definitions of core operations such as copy, gemm, and operations on cute::tuples

arch/                    # Bare bones PTX wrapper structs for copy and math instructions

atom/                    # Meta-information either link to or built from arch/ operators

  mma_atom.hpp           # cute::Mma_Atom and cute::TiledMma

  copy_atom.hpp          # cute::Copy_Atom and cute::TiledCopy

  *sm*.hpp               # Arch specific meta-information for copy and math operations

*                        # Core library types such as Shape, Stride, Layout, Tensor, and associated operations

```

CUTLASS SDK Examples

CUTLASS SDK examples apply CUTLASS templates to implement basic computations.

Tools

``` tools/ library/ # CUTLASS Instance Library - contains instantiations of all supported CUTLASS templates include/ cutlass/ library/

profiler/ # CUTLASS Profiler - command-line utility for executing operations in the # CUTLASS Library

util/ # CUTLASS Utilities - contains numerous helper classes for include/ # manging tensors in device memory, reference cutlass/ # implementations for GEMM, random initialization util/ # of tensors, and I/O. ```

Test

The test/unit/ directory consist of unit tests implemented with Google Test that demonstrate basic usage of Core API components and complete tests of the CUTLASS GEMM computations.

Instructions for building and running the Unit tests are described in the Quickstart guide.

Performance Profiling

The tools/profiler/ directory contains a command-line utility for launching each of the GEMM kernels. It can be built as follows:

bash $ make cutlass_profiler -j16

Building all GEMM and Convolution kernels (long build times)

By default, only one tile size is instantiated for each data type, math instruction, and layout. To instantiate all, set the following environment variable when running CMake from an empty build/ directory. Beware, this results in tens of thousands of kernels and long build times. This would also result in a large binary size and on some platforms linker to fail on building the library. Therefore, it's highly recommended to generate only a subset of kernels as demonstrated in the sub-section below. bash $ cmake .. -DCUTLASS_NVCC_ARCHS=90a -DCUTLASS_LIBRARY_KERNELS=all ... $ make cutlass_profiler -j16

Building a subset of GEMM and Convolution kernels (reduced build times)

To compile strictly one kernel or a small set of kernels, a comma-delimited list of kernel names with wildcard characters may be used to reduce the set of kernels. The following examples show building exactly one or a subset of kernels for NVIDIA Ampere and Turing architecture:

Building a subset Tensor Core GEMM kernels

To compile a subset of Tensor Core GEMM kernels with FP32 accumulation and FP16 input targeting NVIDIA Ampere and Turing architecture, use the below cmake command line: bash $ cmake .. -DCUTLASS_NVCC_ARCHS='75;80' -DCUTLASS_LIBRARY_KERNELS=cutlass_tensorop_s*gemm_f16_*_nt_align8 ... $ make cutlass_profiler -j16

Example command line for profiling a subset of Tensor Core GEMM kernels is as follows: ```bash ./tools/profiler/cutlassprofiler --kernels=cutlasstensorops*gemmf16*nt_align8 --m=3456 --n=4096 --k=4096

...

Problem ID: 1

    Provider: CUTLASS

OperationKind: gemm Operation: cutlasstensorops1688gemmf16256x12832x2nt_align8

      Status: Success
Verification: ON
 Disposition: Passed

reference_device: Passed cuBLAS: Passed

   Arguments: --gemm_kind=universal --m=3456 --n=4096 --k=4096 --A=f16:column --B=f16:row --C=f32:column --alpha=1  \
              --beta=0 --split_k_slices=1 --batch_count=1 --op_class=tensorop --accum=f32 --cta_m=256 --cta_n=128  \
              --cta_k=32 --stages=2 --warps_m=4 --warps_n=2 --warps_k=1 --inst_m=16 --inst_n=8 --inst_k=8 --min_cc=75  \
              --max_cc=1024

       Bytes: 118489088  bytes
       FLOPs: 115992428544  flops

     Runtime: 1.55948  ms
      Memory: 70.7616 GiB/s

        Math: 74378.8 GFLOP/s

============================= ... ```

Building one CUDA Core GEMM kernel

To compile one SGEMM kernel targeting NVIDIA Ampere and Turing architecture, use the below cmake command line: bash $ cmake .. -DCUTLASS_NVCC_ARCHS='75;80' -DCUTLASS_LIBRARY_KERNELS=cutlass_simt_sgemm_128x128_8x2_nn_align1 ... $ make cutlass_profiler -j16

Example command line for profiling single SGEMM CUDA kernel is as follows: ```bash $ ./tools/profiler/cutlass_profiler --kernels=sgemm --m=3456 --n=4096 --k=4096

============================= Problem ID: 1

    Provider: CUTLASS

OperationKind: gemm Operation: cutlasssimtsgemm128x1288x2nnalign1

      Status: Success
Verification: ON
 Disposition: Passed

      cuBLAS: Passed

   Arguments: --m=3456 --n=4096 --k=4096 --A=f32:column --B=f32:column --C=f32:column --alpha=1 --beta=0 --split_k_slices=1  \
              --batch_count=1 --op_class=simt --accum=f32 --cta_m=128 --cta_n=128 --cta_k=8 --stages=2 --warps_m=4  \
              --warps_n=2 --warps_k=1 --inst_m=1 --inst_n=1 --inst_k=1 --min_cc=50 --max_cc=1024

       Bytes: 180355072  bytes
       FLOPs: 115992428544  flops

     Runtime: 6.73655  ms
      Memory: 24.934 GiB/s

        Math: 17218.4 GFLOP/s

============================= ```

Building a subset of Tensor Core Convolution kernels

To compile a subset of Tensor core convolution kernels implementing forward propagation (fprop) with FP32 accumulation and FP16 input targeting NVIDIA Ampere and Turing architecture, use the below cmake command line: bash $ cmake .. -DCUTLASS_NVCC_ARCHS='75;80' -DCUTLASS_LIBRARY_KERNELS=cutlass_tensorop_s*fprop_optimized_f16 ... $ make cutlass_profiler -j16

Example command line for profiling a subset of Tensor Core convolution kernels is as follows:

```bash $ ./tools/profiler/cutlassprofiler --kernels=cutlasstensorops*fpropoptimized_f16 --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3

...

Problem ID: 1

    Provider: CUTLASS

OperationKind: conv2d Operation: cutlasstensorops16816fpropoptimizedf16128x12832x5_nhwc

      Status: Success
Verification: ON
 Disposition: Passed

reference_device: Passed

   Arguments: --conv_kind=fprop --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3 --p=224 --q=224 --pad_h=1 --pad_w=1  \
              --stride_h=1 --stride_w=1 --dilation_h=1 --dilation_w=1 --Activation=f16:nhwc --Filter=f16:nhwc --Output=f32:nhwc  \
              --conv_mode=cross --iterator_algorithm=optimized --alpha=1 --beta=0 --split_k_mode=serial --split_k_slices=1  \
              --eq_gemm_provider=none --op_class=tensorop --accum=f32 --cta_m=128 --cta_n=128 --cta_k=32 --stages=5  \
              --warps_m=2 --warps_n=2 --warps_k=1 --inst_m=16 --inst_n=8 --inst_k=16 --min_cc=80 --max_cc=1024

       Bytes: 1130659840  bytes
       FLOPs: 118482796544  flops

     Runtime: 0.711496  ms
      Memory: 1479.99 GiB/s

        Math: 166526 GFLOP/s

============================= ... ```

Building one Convolution CUDA kernel

To compile and run one CUDA Core convolution kernel implementing forward propagation (fprop) with F32 accumulation and FP32 input targeting NVIDIA Ampere and Turing architecture, use the below cmake command line: bash $ cmake .. -DCUTLASS_NVCC_ARCHS='75;80' -DCUTLASS_LIBRARY_KERNELS=cutlass_simt_sfprop_optimized_128x128_8x2_nhwc ... $ make cutlass_profiler -j16

Example command line for profiling one CUDA Core convolution kernel:

```bash $ ./tools/profiler/cutlassprofiler --kernels=cutlasssimtsfpropoptimized128x1288x2_nhwc --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3

============================= Problem ID: 1

    Provider: CUTLASS

OperationKind: conv2d Operation: cutlasssimtsfpropoptimized128x1288x2nhwc

      Status: Success
Verification: ON
 Disposition: Passed

reference_device: Passed

   Arguments: --conv_kind=fprop --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3 --p=224 --q=224 --pad_h=1 --pad_w=1  \
              --stride_h=1 --stride_w=1 --dilation_h=1 --dilation_w=1 --Activation=f32:nhwc --Filter=f32:nhwc --Output=f32:nhwc  \
              --conv_mode=cross --iterator_algorithm=optimized --alpha=1 --beta=0 --split_k_mode=serial --split_k_slices=1  \
              --eq_gemm_provider=none --op_class=simt --accum=f32 --cta_m=128 --cta_n=128 --cta_k=8 --stages=2 --warps_m=4  \
              --warps_n=2 --warps_k=1 --inst_m=1 --inst_n=1 --inst_k=1 --min_cc=50 --max_cc=1024

       Bytes: 2055798784  bytes
       FLOPs: 118482796544  flops

     Runtime: 7.34266  ms
      Memory: 260.752 GiB/s

        Math: 16136.2 GFLOP/s

=============================

```

More Details on Compiling CUTLASS Kernels and CUTLASS Profiler

• Please follow the links for more CMake examples on selectively compiling CUTLASS kernels:
  • GEMM CMake Examples
  • Implicit GEMM conovlution CMake Examples
• Further details about the CUTLASS Profiler are described here.

About

CUTLASS is released by NVIDIA Corporation as Open Source software under the 3-clause "New" BSD license.

Contributors

The official list of CUTLASS developers and contributors is available here: CONTRIBUTORS.

Copyright

Copyright (c) 2017 - 2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved. SPDX-License-Identifier: BSD-3-Clause

``` Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ```