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#include
#include
#include
#include
#include
#include
#include
#include
#include
#include <cuda_runtime.h>
#define CHECK_CUDA_ERROR(val) check((val), #val, __FILE__, __LINE__)
void check(cudaError_t err, char const* func, char const* file, int line)
{
if (err != cudaSuccess)
{
std::cerr << "CUDA Runtime Error at: " << file << ":" << line
<< std::endl;
std::cerr << cudaGetErrorString(err) << " " << func << std::endl;
std::exit(EXIT_FAILURE);
}
}
#define CHECK_LAST_CUDA_ERROR() check_last(__FILE__, __LINE__)
void check_last(char const* file, int line)
{
cudaError_t const err{cudaGetLastError()};
if (err != cudaSuccess)
{
std::cerr << "CUDA Runtime Error at: " << file << ":" << line
<< std::endl;
std::cerr << cudaGetErrorString(err) << std::endl;
std::exit(EXIT_FAILURE);
}
}
template <class T>
float measure_performance(std::function<T(cudaStream_t)> bound_function,
cudaStream_t stream, size_t num_repeats = 10,
size_t num_warmups = 10)
{
cudaEvent_t start, stop;
float time;
CHECK\_CUDA\_ERROR(cudaEventCreate(&start));
CHECK\_CUDA\_ERROR(cudaEventCreate(&stop));
for (size\_t i{0}; i < num\_warmups; ++i)
{
bound\_function(stream);
}
CHECK\_CUDA\_ERROR(cudaStreamSynchronize(stream));
CHECK\_CUDA\_ERROR(cudaEventRecord(start, stream));
for (size\_t i{0}; i < num\_repeats; ++i)
{
bound\_function(stream);
}
CHECK\_CUDA\_ERROR(cudaEventRecord(stop, stream));
CHECK\_CUDA\_ERROR(cudaEventSynchronize(stop));
CHECK\_LAST\_CUDA\_ERROR();
CHECK\_CUDA\_ERROR(cudaEventElapsedTime(&time, start, stop));
CHECK\_CUDA\_ERROR(cudaEventDestroy(start));
CHECK\_CUDA\_ERROR(cudaEventDestroy(stop));
float const latency{time / num\_repeats};
return latency;
}
constexpr size_t div_up(size_t a, size_t b) { return (a + b - 1) / b; }
template <typename T, size_t BLOCK_TILE_SIZE_X = 32,
size_t BLOCK_TILE_SIZE_Y = 32, size_t BLOCK_TILE_SKEW_SIZE_X = 0>
__global__ void transpose(T* output_matrix, T const* input_matrix, size_t M,
size_t N)
{
\_\_shared\_\_ T
shm\[BLOCK\_TILE\_SIZE\_Y\]\[BLOCK\_TILE\_SIZE\_X + BLOCK\_TILE\_SKEW\_SIZE\_X\];
size\_t const input\_matrix\_from\_idx\_x{threadIdx.x + blockIdx.x \* blockDim.x};
size\_t const input\_matrix\_from\_idx\_y{threadIdx.y + blockIdx.y \* blockDim.y};
size\_t const input\_matrix\_from\_idx{input\_matrix\_from\_idx\_x +
input\_matrix\_from\_idx\_y \* N};
size\_t const shm\_to\_idx\_x{threadIdx.x};
size\_t const shm\_to\_idx\_y{threadIdx.y};
if ((input\_matrix\_from\_idx\_y < M) && (input\_matrix\_from\_idx\_x < N))
{
shm\[shm\_to\_idx\_y\]\[shm\_to\_idx\_x\] = input\_matrix\[input\_matrix\_from\_idx\];
}
\_\_syncthreads();
size\_t const block\_thread\_idx{threadIdx.x + threadIdx.y \* blockDim.x};
size\_t const shm\_from\_idx\_x{block\_thread\_idx / BLOCK\_TILE\_SIZE\_Y};
size\_t const shm\_from\_idx\_y{block\_thread\_idx % BLOCK\_TILE\_SIZE\_Y};
size\_t const output\_matrix\_to\_idx\_x{shm\_from\_idx\_y +
blockIdx.y \* blockDim.y};
size\_t const output\_matrix\_to\_idx\_y{shm\_from\_idx\_x +
blockIdx.x \* blockDim.x};
size\_t const output\_matrix\_to\_idx{output\_matrix\_to\_idx\_x +
output\_matrix\_to\_idx\_y \* M};
if ((output\_matrix\_to\_idx\_y < N) && (output\_matrix\_to\_idx\_x < M))
{
output\_matrix\[output\_matrix\_to\_idx\] =
shm\[shm\_from\_idx\_y\]\[shm\_from\_idx\_x\];
}
}
template <typename T, size_t BLOCK_TILE_SIZE_X = 32,
size_t BLOCK_TILE_SIZE_Y = 32>
__global__ void transpose_swizzling(T* output_matrix, T const* input_matrix,
size_t M, size_t N)
{
__shared__ T shm[BLOCK_TILE_SIZE_Y][BLOCK_TILE_SIZE_X];
size\_t const input\_matrix\_from\_idx\_x{threadIdx.x + blockIdx.x \* blockDim.x};
size\_t const input\_matrix\_from\_idx\_y{threadIdx.y + blockIdx.y \* blockDim.y};
size\_t const input\_matrix\_from\_idx{input\_matrix\_from\_idx\_x +
input\_matrix\_from\_idx\_y \* N};
size\_t const shm\_to\_idx\_x{threadIdx.x};
size\_t const shm\_to\_idx\_y{threadIdx.y};
size\_t const shm\_to\_idx\_x\_swizzled{(shm\_to\_idx\_x ^ shm\_to\_idx\_y) %
BLOCK\_TILE\_SIZE\_X};
if ((input\_matrix\_from\_idx\_y < M) && (input\_matrix\_from\_idx\_x < N))
{
shm\[shm\_to\_idx\_y\]\[shm\_to\_idx\_x\_swizzled\] =
input\_matrix\[input\_matrix\_from\_idx\];
}
\_\_syncthreads();
size\_t const block\_thread\_idx{threadIdx.x + threadIdx.y \* blockDim.x};
size\_t const shm\_from\_idx\_x{block\_thread\_idx / BLOCK\_TILE\_SIZE\_Y};
size\_t const shm\_from\_idx\_y{block\_thread\_idx % BLOCK\_TILE\_SIZE\_Y};
size\_t const shm\_from\_idx\_x\_swizzled{(shm\_from\_idx\_x ^ shm\_from\_idx\_y) %
BLOCK\_TILE\_SIZE\_X};
size\_t const output\_matrix\_to\_idx\_x{shm\_from\_idx\_y +
blockIdx.y \* blockDim.y};
size\_t const output\_matrix\_to\_idx\_y{shm\_from\_idx\_x +
blockIdx.x \* blockDim.x};
size\_t const output\_matrix\_to\_idx{output\_matrix\_to\_idx\_x +
output\_matrix\_to\_idx\_y \* M};
if ((output\_matrix\_to\_idx\_y < N) && (output\_matrix\_to\_idx\_x < M))
{
output\_matrix\[output\_matrix\_to\_idx\] =
shm\[shm\_from\_idx\_y\]\[shm\_from\_idx\_x\_swizzled\];
}
}
template
void launch_transpose_with_shm_bank_conflict(T* d_output_matrix,
T const* d_input_matrix, size_t M,
size_t N, cudaStream_t stream)
{
constexpr size_t BLOCK_TILE_SIZE_X{32};
constexpr size_t BLOCK_TILE_SIZE_Y{32};
constexpr size_t BLOCK_TILE_SKEW_SIZE_X{0};
dim3 const block_size{BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y};
dim3 const grid_size{static_cast<unsigned int>(div_up(N, block_size.x)),
static_cast<unsigned int>(div_up(M, block_size.y))};
transpose<T, BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y, BLOCK_TILE_SKEW_SIZE_X>
<<<grid_size, block_size, 0, stream>>>(d_output_matrix, d_input_matrix,
M, N);
CHECK_LAST_CUDA_ERROR();
}
template
void launch_transpose_without_shm_bank_conflict_via_padding(
T* d_output_matrix, T const* d_input_matrix, size_t M, size_t N,
cudaStream_t stream)
{
constexpr size_t BLOCK_TILE_SIZE_X{32};
constexpr size_t BLOCK_TILE_SIZE_Y{32};
constexpr size_t BLOCK_TILE_SKEW_SIZE_X{1};
dim3 const block_size{BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y};
dim3 const grid_size{static_cast<unsigned int>(div_up(N, block_size.x)),
static_cast<unsigned int>(div_up(M, block_size.y))};
transpose<T, BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y, BLOCK_TILE_SKEW_SIZE_X>
<<<grid_size, block_size, 0, stream>>>(d_output_matrix, d_input_matrix,
M, N);
CHECK_LAST_CUDA_ERROR();
}
template
void launch_transpose_without_shm_bank_conflict_via_swizzling(
T* d_output_matrix, T const* d_input_matrix, size_t M, size_t N,
cudaStream_t stream)
{
constexpr size_t BLOCK_TILE_SIZE_X{32};
constexpr size_t BLOCK_TILE_SIZE_Y{32};
dim3 const block_size{BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y};
dim3 const grid_size{static_cast<unsigned int>(div_up(N, block_size.x)),
static_cast<unsigned int>(div_up(M, block_size.y))};
transpose_swizzling<T, BLOCK_TILE_SIZE_X, BLOCK_TILE_SIZE_Y><<<grid_size, block_size, 0, stream>>>(
d_output_matrix, d_input_matrix, M, N);
CHECK_LAST_CUDA_ERROR();
}
template
bool is_equal(T const* data_1, T const* data_2, size_t size)
{
for (size_t i{0}; i < size; ++i)
{
if (data_1[i] != data_2[i])
{
return false;
}
}
return true;
}
template
bool verify_transpose_implementation(
std::function<void(T*, T const*, size_t, size_t, cudaStream_t)>
transpose_function,
size_t M, size_t N)
{
std::mt19937 gen{0};
cudaStream\_t stream;
size\_t const matrix\_size{M \* N};
std::vector<T> matrix(matrix\_size, 0.0f);
std::vector<T> matrix\_transposed(matrix\_size, 1.0f);
std::vector<T> matrix\_transposed\_reference(matrix\_size, 2.0f);
std::uniform\_real\_distribution<T> uniform\_dist(\-256, 256);
for (size\_t i{0}; i < matrix\_size; ++i)
{
matrix\[i\] = uniform\_dist(gen);
}
for (size\_t i{0}; i < M; ++i)
{
for (size\_t j{0}; j < N; ++j)
{
size\_t const from\_idx{i \* N + j};
size\_t const to\_idx{j \* M + i};
matrix\_transposed\_reference\[to\_idx\] = matrix\[from\_idx\];
}
}
T\* d\_matrix;
T\* d\_matrix\_transposed;
CHECK\_CUDA\_ERROR(cudaMalloc(&d\_matrix, matrix\_size \* sizeof(T)));
CHECK\_CUDA\_ERROR(cudaMalloc(&d\_matrix\_transposed, matrix\_size \* sizeof(T)));
CHECK\_CUDA\_ERROR(cudaStreamCreate(&stream));
CHECK\_CUDA\_ERROR(cudaMemcpy(d\_matrix, matrix.data(),
matrix\_size \* sizeof(T),
cudaMemcpyHostToDevice));
transpose\_function(d\_matrix\_transposed, d\_matrix, M, N, stream);
CHECK\_CUDA\_ERROR(cudaStreamSynchronize(stream));
CHECK\_CUDA\_ERROR(cudaMemcpy(matrix\_transposed.data(), d\_matrix\_transposed,
matrix\_size \* sizeof(T),
cudaMemcpyDeviceToHost));
bool const correctness{is\_equal(matrix\_transposed.data(),
matrix\_transposed\_reference.data(),
matrix\_size)};
CHECK\_CUDA\_ERROR(cudaFree(d\_matrix));
CHECK\_CUDA\_ERROR(cudaFree(d\_matrix\_transposed));
CHECK\_CUDA\_ERROR(cudaStreamDestroy(stream));
return correctness;
}
template
float profile_transpose_implementation(
std::function<void(T*, T const*, size_t, size_t, cudaStream_t)>
transpose_function,
size_t M, size_t N)
{
constexpr int num_repeats{100};
constexpr int num_warmups{10};
cudaStream_t stream;
size_t const matrix_size{M * N};
T* d_matrix;
T* d_matrix_transposed;
CHECK_CUDA_ERROR(cudaMalloc(&d_matrix, matrix_size * sizeof(T)));
CHECK_CUDA_ERROR(cudaMalloc(&d_matrix_transposed, matrix_size * sizeof(T)));
CHECK_CUDA_ERROR(cudaStreamCreate(&stream));
std::function<void(cudaStream\_t)> const transpose\_function\_wrapped{
std::bind(transpose\_function, d\_matrix\_transposed, d\_matrix, M, N,
std::placeholders::\_1)};
float const transpose\_function\_latency{measure\_performance(
transpose\_function\_wrapped, stream, num\_repeats, num\_warmups)};
CHECK\_CUDA\_ERROR(cudaFree(d\_matrix));
CHECK\_CUDA\_ERROR(cudaFree(d\_matrix\_transposed));
CHECK\_CUDA\_ERROR(cudaStreamDestroy(stream));
return transpose\_function\_latency;
}
void print_latencty(std::string const& kernel_name, float latency)
{
std::cout << kernel_name << ": " << std::fixed << std::setprecision(2)
<< latency << " ms" << std::endl;
}
int main()
{
for (size\_t m{1}; m <= 64; ++m)
{
for (size\_t n{1}; n <= 64; ++n)
{
assert(verify\_transpose\_implementation<float\>(
&launch\_transpose\_with\_shm\_bank\_conflict<float\>, m, n));
assert(verify\_transpose\_implementation<float\>(
&launch\_transpose\_without\_shm\_bank\_conflict\_via\_padding<float\>,
m, n));
assert(verify\_transpose\_implementation<float\>(
&launch\_transpose\_without\_shm\_bank\_conflict\_via\_swizzling<
float\>,
m, n));
}
}
size\_t const M{8192};
size\_t const N{8192};
std::cout << M << " x " << N << " Matrix" << std::endl;
float const latency\_with\_shm\_bank\_conflict{
profile\_transpose\_implementation<float\>(
&launch\_transpose\_with\_shm\_bank\_conflict<float\>, M, N)};
print\_latencty("Transpose with Shared Memory Bank Conflict",
latency\_with\_shm\_bank\_conflict);
float const latency\_without\_shm\_bank\_conflict\_via\_padding{
profile\_transpose\_implementation<float\>(
&launch\_transpose\_without\_shm\_bank\_conflict\_via\_padding<float\>, M,
N)};
print\_latencty("Transpose without Shared Memory Bank Conflict via Padding",
latency\_without\_shm\_bank\_conflict\_via\_padding);
float const latency\_without\_shm\_bank\_conflict\_via\_swizzling{
profile\_transpose\_implementation<float\>(
&launch\_transpose\_without\_shm\_bank\_conflict\_via\_swizzling<float\>, M,
N)};
print\_latencty(
"Transpose without Shared Memory Bank Conflict via Swizzling",
latency\_without\_shm\_bank\_conflict\_via\_swizzling);
return 0;
}