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CUDA Templates for Linear Algebra Subroutines

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CUTLASS 2.4

CUTLASS 2.4 - November 2020

CUTLASS is a collection of CUDA C++ template abstractions for implementing high-performance matrix-multiplication (GEMM) at all levels and scales within CUDA. It incorporates strategies for hierarchical decomposition and data movement similar to those used to implement cuBLAS. CUTLASS decomposes these "moving parts" into reusable, modular software components abstracted by C++ template classes. These thread-wide, warp-wide, block-wide, and device-wide primitives 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), double-precision floating point (FP64) types, integer data types (4b and 8b), and binary data types (1b).

Furthermore, CUTLASS demonstrates warp-synchronous matrix multiply operations targeting the programmable, high-throughput Tensor Cores implemented by NVIDIA's Volta, Turing, and Ampere architectures.

Additionaly, CUTLASS implements high-performance convolution (implicit GEMM). Implicit GEMM is the formulation of a convolution operation as a GEMM. This allows CUTLASS to build convolutions by reusing highly optimized warp-wide GEMM components and below.

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.

What's New in CUTLASS 2.4

CUTLASS 2.4 is a significant update to CUTLASS adding:

  • 1-D, 2-D, and 3-D convolution targeting Tensor and CUDA cores for NVIDIA Ampere, Turing, and Volta GPU architectures
  • CUTLASS profiler support for convolution
  • Documentation describing Implicit GEMM Convolution algorithm and implementation
  • See the CHANGELOG for more details.

What's New in CUTLASS 2.3

CUTLASS 2.3 is a minor update to CUTLASS adding:

  • GEMMs targeting structured Sparse Tensor Cores in NVIDIA Ampere Architecture GPUs
  • Fast SGEMM kernels targeting GeForce RTX 30-series CUDA Cores
  • Intended to be compiled with CUDA 11.1 Toolkit
  • See the CHANGELOG for more details.

What's New in CUTLASS 2.2

CUTLASS 2.2 is a significant update to CUTLASS adding:

What's New in CUTLASS 2.1

CUTLASS 2.1 is a minor update to CUTLASS adding:

What's New in CUTLASS 2.0

CUTLASS 2.0 is a substantial refactoring from the previous version, intended to offer:

  • Better performance over 1.x, particularly for kernels targeting Turing Tensor Cores
  • Robust and durable templates that reliably span the design space
  • Encapsulated functionality that may be reusable in other contexts

See the CHANGELOG for more details.

Performance

CUTLASS primitives are very efficient. When used to construct device-wide GEMM kernels, they exhibit performance comparable to cuBLAS for scalar GEMM computations. The above figure shows CUTLASS performance relative to cuBLAS for large matrix dimensions on an NVIDIA GeForce 2080 Ti, an NVIDIA A100, and an NVIDIA TitanV using CUDA 11.0 Toolkit. Tensor Core operations are implemented using CUDA's mma instruction.

Compatibility

CUTLASS requires a C++11 host compiler and performs best when built with the CUDA 11.1 Toolkit. It is compatible with CUDA 9.2, CUDA 10.0, CUDA 10.1, CUDA 10.2, and CUDA 11.0.

We have tested the following environments.

Operating System Compiler
Windows 10 Microsoft Visual Studio 2015
Microsoft Visual Studio 2017
Ubuntu 16.04 GCC 5.4.0
Ubuntu 18.04 GCC 7.5.0

Additionally, CUTLASS may be built with clang. See these instructions for more details.

CUTLASS runs successfully on the following NVIDIA GPUs, and it is expected to be efficient on any Maxwell-, Pascal-, Volta-, Turing-, or NVIDIA Ampere- architecture NVIDIA GPU.

GPU CUDA Compute Capability Minimum CUDA Toolkit CUDA Toolkit Enabling Native Tensor Cores
NVIDIA Tesla P100 6.0 9.2
NVIDIA GeForce 1080 6.1 9.2
NVIDIA TitanXP 6.1 9.2
NVIDIA Tesla V100 7.0 9.2 10.1
NVIDIA TitanV 7.0 9.2 10.1
NVIDIA GeForce RTX 2080 TI, 2080, 2070 7.5 10.0 10.2
NVIDIA Tesla T4 7.5 10.0 10.2
NVIDIA A100 8.0 11.0 11.0
NVIDIA GeForce 3090 8.6 11.1 11.1

Documentation

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

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

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.

$ 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, and 8.6. To reduce compile time you can specify the architectures to build CUTLASS for by changing the CMake configuration setting CUTLASS_NVCC_ARCHS.

$ mkdir build && cd build

$ cmake .. -DCUTLASS_NVCC_ARCHS=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.

$ 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

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

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

CUTLASS SDK Examples

CUTLASS SDK examples apply CUTLASS templates to implement basic computations.

examples/
  00_basic_gemm/                   # launches a basic GEMM with single precision inputs and outputs

  01_cutlass_utilities/            # demonstrates CUTLASS Utilities for allocating and initializing tensors
  
  02_dump_reg_smem/                # debugging utilities for printing register and shared memory contents
  
  03_visualize_layout/             # utility for visualizing all layout functions in CUTLASS

  04_tile_iterator/                # example demonstrating an iterator over tiles in memory

  05_batched_gemm/                 # example demonstrating CUTLASS's batched strided GEMM operation

  06_splitK_gemm/                  # exmaple demonstrating CUTLASS's Split-K parallel reduction kernel

  07_volta_tensorop_gemm/          # example demonstrating mixed precision GEMM using Volta Tensor Cores

  08_turing_tensorop_gemm/         # example demonstrating integer GEMM using Turing Tensor Cores

  09_turing_tensorop_conv2dfprop/  # example demonstrating integer implicit GEMM convolution (forward propagation) using Turing Tensor Cores

  10_planar_complex/               # example demonstrating planar complex GEMM kernels

  11_planar_complex_array/         # example demonstrating planar complex kernels with batch-specific problem sizes

  12_gemm_bias_relu/               # example demonstrating GEMM fused with bias and relu

  13_fused_two_gemms/              # example demonstrating two GEMms fused in one kernel

  22_ampere_tensorop_conv2dfprop/  # example demonstrating integer implicit GEMM convolution (forward propagation) using Ampere Tensor Cores

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:

$ 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 thousands of kernels and long build times.

$ cmake .. -DCUTLASS_NVCC_ARCHS=75 -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 targetting NVIDIA Ampere and Turing architecture, use the below cmake command line:

$ 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:

./tools/profiler/cutlass_profiler --kernels=cutlass_tensorop_s*gemm_f16_*_nt_align8 --m=3456 --n=4096 --k=4096

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

        Provider: CUTLASS
   OperationKind: gemm
       Operation: cutlass_tensorop_s1688gemm_f16_256x128_32x2_nt_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 targetting NVIDIA Ampere and Turing architecture, use the below cmake command line:

$ 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:

$ ./tools/profiler/cutlass_profiler --kernels=sgemm --m=3456 --n=4096 --k=4096

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

        Provider: CUTLASS
   OperationKind: gemm
       Operation: cutlass_simt_sgemm_128x128_8x2_nn_align1

          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 targetting NVIDIA Ampere and Turing architecture, use the below cmake command line:

$ 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:

$ ./tools/profiler/cutlass_profiler --kernels=cutlass_tensorop_s*fprop_optimized_f16 --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3

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

        Provider: CUTLASS
   OperationKind: conv2d
       Operation: cutlass_tensorop_s16816fprop_optimized_f16_128x128_32x5_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 targetting NVIDIA Ampere and Turing architecture, use the below cmake command line:

$ 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:

$ ./tools/profiler/cutlass_profiler --kernels=cutlass_simt_sfprop_optimized_128x128_8x2_nhwc --n=8 --h=224 --w=224 --c=128 --k=128 --r=3 --s=3


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

        Provider: CUTLASS
   OperationKind: conv2d
       Operation: cutlass_simt_sfprop_optimized_128x128_8x2_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=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

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) 2017-2021, NVIDIA CORPORATION. All rights reserved.

  Redistribution and use in source and binary forms, with or without modification, are permitted
  provided that the following conditions are met:
      * Redistributions of source code must retain the above copyright notice, this list of
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      * Redistributions in binary form must reproduce the above copyright notice, this list of
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CUDA Templates for Linear Algebra Subroutines

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