submission 914518
Deepon · python · License unknown
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submission.py
curl "https://kernelindex.com/api/v1/implementations/kernelbot-cholesky-914518?include=source"interfacepython
Compatibility
measured onNVIDIA B200
declared hardwareNVIDIA B200
architecturessm_100
dtypesfp32
Benchmark evidence
1 measurement across 1 GPU, fastest first.
Operation / workload
Hardware
Latency
Rank
Observed
Reported · How evidence levels are derived →
Source and license
sourceavailable
revision digestsha256:b36a00debfc5b74c14cdfdaa7d5e1f0a69544b16360a05b197be746f1505f5c1
license declaredunknown
license concludedunknown
authorsDeepon
imported2026-08-26
Techniques
Extracted from the mirrored source by pattern, never inferred. Each row cites its line.
mma
namespace wmma = nvcuda::wmma;num-warps = 8
num_warps=8,persistent-kernel
_PERSISTENT_WMMA_SOURCE = r"""shared-memory
__shared__ float tiles[kWarpsPerBlock][32 * 33];stages = 4
num_stages=4,tile-k = 32
BLOCK_K=32,Kernel source
submission.py2756 lines
import torch
import triton
import triton.language as tl
from functools import lru_cache
from torch.utils.cpp_extension import load_inline
from task import input_t, output_t
_CUDA32_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <vector>
namespace {
constexpr int kWarpsPerBlock = 4;
__global__ void cholesky32_warp_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
__shared__ float tiles[kWarpsPerBlock][32 * 33];
const int warp_in_block = threadIdx.x >> 5;
const int lane = threadIdx.x & 31;
const int matrix = blockIdx.x * kWarpsPerBlock + warp_in_block;
if (matrix >= batch) {
return;
}
float* tile = tiles[warp_in_block];
const float* matrix_input = input + static_cast<long long>(matrix) * 1024;
float* matrix_output = output + static_cast<long long>(matrix) * 1024;
#pragma unroll
for (int linear = lane; linear < 1024; linear += 32) {
const int row = linear >> 5;
const int col = linear & 31;
tile[row * 33 + col] =
row >= col ? matrix_input[linear] : 0.0f;
}
__syncwarp();
float row_values[32];
#pragma unroll
for (int col = 0; col < 32; ++col) {
row_values[col] = tile[lane * 33 + col];
}
constexpr unsigned kMask = 0xffffffffu;
#pragma unroll
for (int pivot = 0; pivot < 32; ++pivot) {
float dot = 0.0f;
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float pivot_value =
__shfl_sync(kMask, row_values[col], pivot);
dot = fmaf(row_values[col], pivot_value, dot);
}
float diagonal = 0.0f;
if (lane == pivot) {
diagonal = sqrtf(fmaxf(row_values[pivot] - dot, 0.0f));
}
diagonal = __shfl_sync(kMask, diagonal, pivot);
if (lane == pivot) {
row_values[pivot] = diagonal;
} else if (lane > pivot) {
row_values[pivot] =
(row_values[pivot] - dot) / diagonal;
}
}
#pragma unroll
for (int col = 0; col < 32; ++col) {
tile[lane * 33 + col] = row_values[col];
}
__syncwarp();
#pragma unroll
for (int linear = lane; linear < 1024; linear += 32) {
const int row = linear >> 5;
const int col = linear & 31;
matrix_output[linear] = tile[row * 33 + col];
}
}
} // namespace
torch::Tensor cholesky32_cuda(torch::Tensor input) {
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
const int blocks = (batch + kWarpsPerBlock - 1) / kWarpsPerBlock;
cholesky32_warp_kernel<<<
blocks,
kWarpsPerBlock * 32
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("cholesky32", &cholesky32_cuda);
}
"""
_CUDA64_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <vector>
namespace {
constexpr int kWarpsPerBlock = 2;
constexpr int kN = 64;
template <bool kMakeInverse>
__global__ void cholesky64_register_kernel(
const float* __restrict__ input,
float* __restrict__ output,
float* __restrict__ inverse,
int batch
) {
__shared__ float tiles[kWarpsPerBlock][kN * (kN + 1)];
const int warp_in_block = threadIdx.x >> 5;
const int lane = threadIdx.x & 31;
const int matrix = blockIdx.x * kWarpsPerBlock + warp_in_block;
if (matrix >= batch) {
return;
}
const float* matrix_input =
input + static_cast<long long>(matrix) * kN * kN;
float* matrix_output =
output + static_cast<long long>(matrix) * kN * kN;
float* matrix_inverse = kMakeInverse
? inverse + static_cast<long long>(matrix) * kN * kN
: nullptr;
float* tile = tiles[warp_in_block];
const int row0 = lane;
const int row1 = lane + 32;
#pragma unroll 4
for (int linear = lane; linear < kN * kN; linear += 32) {
const int row = linear >> 6;
const int col = linear & 63;
tile[row * (kN + 1) + col] =
row >= col ? matrix_input[linear] : 0.0f;
}
__syncwarp();
float values0[kN];
float values1[kN];
#pragma unroll
for (int col = 0; col < kN; ++col) {
values0[col] = tile[row0 * (kN + 1) + col];
values1[col] = tile[row1 * (kN + 1) + col];
}
constexpr unsigned kMask = 0xffffffffu;
#pragma unroll
for (int pivot = 0; pivot < kN; ++pivot) {
float dot0 = 0.0f;
float dot1 = 0.0f;
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float source =
pivot < 32 ? values0[col] : values1[col];
const float pivot_value =
__shfl_sync(kMask, source, pivot & 31);
dot0 = fmaf(values0[col], pivot_value, dot0);
dot1 = fmaf(values1[col], pivot_value, dot1);
}
float diagonal = 0.0f;
if (row0 == pivot) {
diagonal = sqrtf(
fmaxf(values0[pivot] - dot0, 0.0f)
);
} else if (row1 == pivot) {
diagonal = sqrtf(
fmaxf(values1[pivot] - dot1, 0.0f)
);
}
diagonal = __shfl_sync(kMask, diagonal, pivot & 31);
if (row0 == pivot) {
values0[pivot] = diagonal;
} else if (row0 > pivot) {
values0[pivot] = (values0[pivot] - dot0) / diagonal;
}
if (row1 == pivot) {
values1[pivot] = diagonal;
} else if (row1 > pivot) {
values1[pivot] = (values1[pivot] - dot1) / diagonal;
}
}
#pragma unroll
for (int col = 0; col < kN; ++col) {
tile[row0 * (kN + 1) + col] = values0[col];
tile[row1 * (kN + 1) + col] = values1[col];
}
__syncwarp();
#pragma unroll 4
for (int linear = lane; linear < kN * kN; linear += 32) {
const int row = linear >> 6;
const int col = linear & 63;
matrix_output[linear] = tile[row * (kN + 1) + col];
}
if constexpr (kMakeInverse) {
#pragma unroll
for (int which = 0; which < 2; ++which) {
const int row = which == 0 ? row0 : row1;
const float inverse_diagonal =
1.0f / tile[row * (kN + 1) + row];
#pragma unroll 1
for (int col = row - 1; col >= 0; --col) {
float value = 0.0f;
#pragma unroll 4
for (int inner = col + 1; inner <= row; ++inner) {
const float inverse_item =
inner == row
? inverse_diagonal
: tile[inner * (kN + 1) + row];
value = fmaf(
inverse_item,
tile[inner * (kN + 1) + col],
value
);
}
tile[col * (kN + 1) + row] =
-value / tile[col * (kN + 1) + col];
}
}
__syncwarp();
#pragma unroll 4
for (int linear = lane; linear < kN * kN; linear += 32) {
const int row = linear >> 6;
const int col = linear & 63;
matrix_inverse[linear] =
col < row
? tile[col * (kN + 1) + row]
: (
col == row
? 1.0f / tile[row * (kN + 1) + row]
: 0.0f
);
}
}
}
} // namespace
torch::Tensor cholesky64_cuda(torch::Tensor input) {
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
const int blocks = (batch + kWarpsPerBlock - 1) / kWarpsPerBlock;
cholesky64_register_kernel<false><<<
blocks,
kWarpsPerBlock * 32
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
nullptr,
batch
);
return output;
}
std::vector<torch::Tensor> cholesky64_inverse_cuda(torch::Tensor input) {
auto output = torch::empty_like(input);
auto inverse = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
const int blocks = (batch + kWarpsPerBlock - 1) / kWarpsPerBlock;
cholesky64_register_kernel<true><<<
blocks,
kWarpsPerBlock * 32
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
inverse.data_ptr<float>(),
batch
);
return {output, inverse};
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("cholesky64", &cholesky64_cuda);
module.def("cholesky64_inverse", &cholesky64_inverse_cuda);
}
"""
_CUDA128_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <c10/cuda/CUDAException.h>
namespace {
constexpr int kN = 128;
constexpr int kPitch = kN + 1;
constexpr int kThreads = 256;
constexpr int kSharedBytes = kN * kPitch * sizeof(float);
__global__ void cholesky128_panel_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
constexpr int kPanel = 32;
constexpr int kMatrixElements = kN * kN;
extern __shared__ float tile[];
const int matrix = static_cast<int>(blockIdx.x);
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
const long long matrix_offset =
static_cast<long long>(matrix) * kMatrixElements;
const float* matrix_input = input + matrix_offset;
float* matrix_output = output + matrix_offset;
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element / kN;
const int col = element - row * kN;
tile[row * kPitch + col] =
row >= col ? matrix_input[element] : 0.0f;
}
__syncthreads();
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
if (warp == 0) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
if (lane == local_col) {
const int diagonal = start + local_col;
float value = tile[diagonal * kPitch + diagonal];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = tile[
diagonal * kPitch + start + previous
];
value = fmaf(-item, item, value);
}
tile[diagonal * kPitch + diagonal] =
sqrtf(fmaxf(value, 0.0f));
}
__syncwarp();
if (lane > local_col) {
const int row = start + lane;
const int col = start + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] =
value / tile[col * kPitch + col];
}
__syncwarp();
}
}
__syncthreads();
const int panel_end = start + kPanel;
for (
int row = panel_end + thread;
row < kN;
row += kThreads
) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
const int col = start + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] =
value / tile[col * kPitch + col];
}
}
__syncthreads();
const int trailing = kN - panel_end;
const int trailing_elements = trailing * trailing;
for (
int local = thread;
local < trailing_elements;
local += kThreads
) {
const int local_row = local / trailing;
const int local_col = local - local_row * trailing;
if (local_row >= local_col) {
const int row = panel_end + local_row;
const int col = panel_end + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (int previous = 0; previous < kPanel; ++previous) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] = value;
}
}
__syncthreads();
}
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element / kN;
const int col = element - row * kN;
matrix_output[element] =
row >= col ? tile[row * kPitch + col] : 0.0f;
}
}
bool configure_cholesky128() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky128_panel_kernel,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky128_panel_kernel,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
torch::Tensor cholesky128_cuda(torch::Tensor input) {
static const bool configured = configure_cholesky128();
TORCH_CHECK(configured, "failed to configure shared memory");
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
cholesky128_panel_kernel<<<
batch,
kThreads,
kSharedBytes
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("cholesky128", &cholesky128_cuda);
}
"""
_CUDA128_INVERSE_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <c10/cuda/CUDAException.h>
#include <vector>
namespace {
constexpr int kN = 128;
constexpr int kPitch = kN + 1;
constexpr int kPanel = 32;
constexpr int kThreads = 256;
constexpr int kMatrixElements = kN * kN;
constexpr int kSharedBytes = kN * kPitch * sizeof(float);
__global__ void cholesky128_inverse_kernel(
const float* __restrict__ input,
float* __restrict__ factor_output,
float* __restrict__ inverse_output,
int batch
) {
extern __shared__ float tile[];
const int matrix = static_cast<int>(blockIdx.x);
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
const long long matrix_offset =
static_cast<long long>(matrix) * kMatrixElements;
const float* matrix_input = input + matrix_offset;
float* matrix_factor = factor_output + matrix_offset;
float* matrix_inverse = inverse_output + matrix_offset;
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element / kN;
const int col = element - row * kN;
tile[row * kPitch + col] =
row >= col ? matrix_input[element] : 0.0f;
}
__syncthreads();
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
if (warp == 0) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
if (lane == local_col) {
const int diagonal = start + local_col;
float value =
tile[diagonal * kPitch + diagonal];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = tile[
diagonal * kPitch + start + previous
];
value = fmaf(-item, item, value);
}
tile[diagonal * kPitch + diagonal] =
sqrtf(fmaxf(value, 0.0f));
}
__syncwarp();
if (lane > local_col) {
const int row = start + lane;
const int col = start + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] =
value / tile[col * kPitch + col];
}
__syncwarp();
}
}
__syncthreads();
const int panel_end = start + kPanel;
for (
int row = panel_end + thread;
row < kN;
row += kThreads
) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
const int col = start + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] =
value / tile[col * kPitch + col];
}
}
__syncthreads();
const int trailing = kN - panel_end;
const int trailing_elements = trailing * trailing;
for (
int local = thread;
local < trailing_elements;
local += kThreads
) {
const int local_row = local / trailing;
const int local_col = local - local_row * trailing;
if (local_row >= local_col) {
const int row = panel_end + local_row;
const int col = panel_end + local_col;
float value = tile[row * kPitch + col];
#pragma unroll
for (int previous = 0; previous < kPanel; ++previous) {
value = fmaf(
-tile[row * kPitch + start + previous],
tile[col * kPitch + start + previous],
value
);
}
tile[row * kPitch + col] = value;
}
}
__syncthreads();
}
if (thread < kN) {
const int row = thread;
const float inverse_diagonal =
1.0f / tile[row * kPitch + row];
#pragma unroll 1
for (int col = row - 1; col >= 0; --col) {
float value = 0.0f;
#pragma unroll 4
for (int inner = col + 1; inner <= row; ++inner) {
const float inverse_item =
inner == row
? inverse_diagonal
: tile[inner * kPitch + row];
value = fmaf(
inverse_item,
tile[inner * kPitch + col],
value
);
}
tile[col * kPitch + row] =
-value / tile[col * kPitch + col];
}
}
__syncthreads();
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element / kN;
const int col = element - row * kN;
matrix_factor[element] =
row >= col ? tile[row * kPitch + col] : 0.0f;
matrix_inverse[element] =
col < row
? tile[col * kPitch + row]
: (
col == row
? 1.0f / tile[row * kPitch + row]
: 0.0f
);
}
}
bool configure_cholesky128_inverse() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky128_inverse_kernel,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky128_inverse_kernel,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
std::vector<torch::Tensor> cholesky128_inverse_cuda(torch::Tensor input) {
TORCH_CHECK(input.is_cuda(), "input must be CUDA");
TORCH_CHECK(input.scalar_type() == at::kFloat, "input must be FP32");
TORCH_CHECK(input.dim() == 3, "input rank must be three");
TORCH_CHECK(
input.size(1) == kN && input.size(2) == kN,
"matrix dimensions must be 128x128"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
static const bool configured = configure_cholesky128_inverse();
TORCH_CHECK(configured, "failed to configure shared memory");
auto factor = torch::empty_like(input);
auto inverse = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
cholesky128_inverse_kernel<<<
batch,
kThreads,
kSharedBytes
>>>(
input.data_ptr<float>(),
factor.data_ptr<float>(),
inverse.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return {factor, inverse};
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("cholesky128_inverse", &cholesky128_inverse_cuda);
}
"""
_CUDA256_PACKED_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <c10/cuda/CUDAException.h>
namespace {
constexpr int kN = 256;
constexpr int kPanel = 32;
constexpr int kThreads = 256;
constexpr int kMatrixElements = kN * kN;
constexpr int kPackedElements = kN * (kN + 1) / 2;
constexpr int kSharedBytes = kPackedElements * sizeof(float);
__device__ __forceinline__ int packed_offset(int row, int col) {
return row * (row + 1) / 2 + col;
}
__global__ void cholesky256_packed_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
extern __shared__ float packed[];
const int matrix = static_cast<int>(blockIdx.x);
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
const long long matrix_offset =
static_cast<long long>(matrix) * kMatrixElements;
const float* matrix_input = input + matrix_offset;
float* matrix_output = output + matrix_offset;
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element >> 8;
const int col = element & (kN - 1);
if (row >= col) {
packed[packed_offset(row, col)] = matrix_input[element];
}
}
__syncthreads();
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
if (warp == 0) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
if (lane == local_col) {
const int diagonal = start + local_col;
float value =
packed[packed_offset(diagonal, diagonal)];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = packed[
packed_offset(
diagonal,
start + previous
)
];
value = fmaf(-item, item, value);
}
packed[packed_offset(diagonal, diagonal)] =
sqrtf(fmaxf(value, 0.0f));
}
__syncwarp();
if (lane > local_col) {
const int row = start + lane;
const int col = start + local_col;
float value = packed[packed_offset(row, col)];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-packed[
packed_offset(
row,
start + previous
)
],
packed[
packed_offset(
col,
start + previous
)
],
value
);
}
packed[packed_offset(row, col)] =
value / packed[packed_offset(col, col)];
}
__syncwarp();
}
}
__syncthreads();
const int panel_end = start + kPanel;
for (
int row = panel_end + thread;
row < kN;
row += kThreads
) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
const int col = start + local_col;
float value = packed[packed_offset(row, col)];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-packed[
packed_offset(
row,
start + previous
)
],
packed[
packed_offset(
col,
start + previous
)
],
value
);
}
packed[packed_offset(row, col)] =
value / packed[packed_offset(col, col)];
}
}
__syncthreads();
const int trailing = kN - panel_end;
const int trailing_elements = trailing * trailing;
for (
int local = thread;
local < trailing_elements;
local += kThreads
) {
const int local_row = local / trailing;
const int local_col = local - local_row * trailing;
if (local_row >= local_col) {
const int row = panel_end + local_row;
const int col = panel_end + local_col;
float value = packed[packed_offset(row, col)];
#pragma unroll
for (int previous = 0; previous < kPanel; ++previous) {
value = fmaf(
-packed[
packed_offset(
row,
start + previous
)
],
packed[
packed_offset(
col,
start + previous
)
],
value
);
}
packed[packed_offset(row, col)] = value;
}
}
__syncthreads();
}
for (
int element = thread;
element < kMatrixElements;
element += kThreads
) {
const int row = element >> 8;
const int col = element & (kN - 1);
matrix_output[element] =
row >= col ? packed[packed_offset(row, col)] : 0.0f;
}
}
bool configure_cholesky256_packed() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky256_packed_kernel,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky256_packed_kernel,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
torch::Tensor cholesky256_packed_cuda(torch::Tensor input) {
TORCH_CHECK(input.is_cuda(), "input must be CUDA");
TORCH_CHECK(input.scalar_type() == at::kFloat, "input must be FP32");
TORCH_CHECK(input.dim() == 3, "input rank must be three");
TORCH_CHECK(
input.size(1) == kN && input.size(2) == kN,
"matrix dimensions must be 256x256"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
static const bool configured = configure_cholesky256_packed();
TORCH_CHECK(configured, "failed to configure shared memory");
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
cholesky256_packed_kernel<<<
batch,
kThreads,
kSharedBytes
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("cholesky256_packed", &cholesky256_packed_cuda);
}
"""
_PERSISTENT_WMMA_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_fp16.h>
#include <cuda_runtime.h>
#include <mma.h>
#include <c10/cuda/CUDAException.h>
namespace {
namespace wmma = nvcuda::wmma;
constexpr int kPanel = 32;
constexpr int kThreads = 256;
constexpr int kWarps = kThreads / 32;
template <int N>
__global__ void persistent_wmma_cholesky_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ output,
int batch
) {
extern __shared__ float panel[];
const int matrix = static_cast<int>(blockIdx.x);
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
const long long matrix_offset =
static_cast<long long>(matrix) * N * N;
const float* matrix_input = input + matrix_offset;
half* matrix_history = history + matrix_offset;
float* matrix_output = output + matrix_offset;
#pragma unroll 1
for (int start = 0; start < N; start += kPanel) {
const int row_tiles = (N - start) / 16;
const int tile_jobs = row_tiles * 2;
for (int job = warp; job < tile_jobs; job += kWarps) {
const int row_tile = job >> 1;
const int col_tile = job & 1;
const int row_relative = row_tile * 16;
const int row_global = start + row_relative;
const int col_relative = col_tile * 16;
wmma::fragment<
wmma::accumulator,
16,
16,
16,
float
> accumulator;
wmma::load_matrix_sync(
accumulator,
matrix_input
+ static_cast<long long>(row_global) * N
+ start
+ col_relative,
N,
wmma::mem_row_major
);
#pragma unroll
for (
int element = 0;
element < accumulator.num_elements;
++element
) {
accumulator.x[element] = -accumulator.x[element];
}
for (int inner = 0; inner < start; inner += 16) {
wmma::fragment<
wmma::matrix_a,
16,
16,
16,
half,
wmma::row_major
> left_fragment;
wmma::fragment<
wmma::matrix_b,
16,
16,
16,
half,
wmma::col_major
> right_fragment;
wmma::load_matrix_sync(
left_fragment,
matrix_history
+ static_cast<long long>(row_global) * N
+ inner,
N
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * N
+ inner,
N
);
wmma::mma_sync(
accumulator,
left_fragment,
right_fragment,
accumulator
);
}
#pragma unroll
for (
int element = 0;
element < accumulator.num_elements;
++element
) {
accumulator.x[element] = -accumulator.x[element];
}
wmma::store_matrix_sync(
panel + row_relative * kPanel + col_relative,
accumulator,
kPanel,
wmma::mem_row_major
);
}
__syncthreads();
if (warp == 0) {
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
if (lane == local_col) {
float value =
panel[local_col * kPanel + local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item =
panel[local_col * kPanel + previous];
value = fmaf(-item, item, value);
}
const float diagonal = sqrtf(fmaxf(value, 0.0f));
const half quantized = __float2half_rn(diagonal);
panel[local_col * kPanel + local_col] =
__half2float(quantized);
matrix_history[
static_cast<long long>(start + local_col) * N
+ start
+ local_col
] = quantized;
}
__syncwarp();
if (lane > local_col) {
float value = panel[lane * kPanel + local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-panel[lane * kPanel + previous],
panel[local_col * kPanel + previous],
value
);
}
value /= panel[
local_col * kPanel + local_col
];
const half quantized = __float2half_rn(value);
panel[lane * kPanel + local_col] =
__half2float(quantized);
matrix_history[
static_cast<long long>(start + lane) * N
+ start
+ local_col
] = quantized;
}
__syncwarp();
}
for (int local_col = 0; local_col <= lane; ++local_col) {
matrix_output[
static_cast<long long>(start + lane) * N
+ start
+ local_col
] = panel[lane * kPanel + local_col];
}
}
__syncthreads();
for (
int row = start + kPanel + thread;
row < N;
row += kThreads
) {
const int row_relative = row - start;
float* row_values = panel + row_relative * kPanel;
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
float value = row_values[local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-row_values[previous],
panel[local_col * kPanel + previous],
value
);
}
value /= panel[local_col * kPanel + local_col];
const half quantized = __float2half_rn(value);
const float quantized_float = __half2float(quantized);
row_values[local_col] = quantized_float;
matrix_history[
static_cast<long long>(row) * N
+ start
+ local_col
] = quantized;
matrix_output[
static_cast<long long>(row) * N
+ start
+ local_col
] = quantized_float;
}
}
__syncthreads();
}
for (
int element = thread;
element < N * N;
element += kThreads
) {
const int row = element / N;
const int col = element - row * N;
if (col > row) {
matrix_output[element] = 0.0f;
}
}
}
template <int N>
bool configure_persistent_kernel() {
constexpr int kSharedBytes = N * kPanel * sizeof(float);
const cudaError_t shared_result = cudaFuncSetAttribute(
persistent_wmma_cholesky_kernel<N>,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
persistent_wmma_cholesky_kernel<N>,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
torch::Tensor persistent_wmma_cholesky_cuda(torch::Tensor input) {
TORCH_CHECK(input.is_cuda(), "input must be CUDA");
TORCH_CHECK(input.scalar_type() == at::kFloat, "input must be FP32");
TORCH_CHECK(input.dim() == 3, "input rank must be three");
TORCH_CHECK(input.size(1) == input.size(2), "input must be square");
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
const int batch = static_cast<int>(input.size(0));
const int n = static_cast<int>(input.size(1));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
if (n == 512) {
static const bool configured = configure_persistent_kernel<512>();
TORCH_CHECK(configured, "failed to configure n=512 kernel");
constexpr int shared_bytes = 512 * kPanel * sizeof(float);
persistent_wmma_cholesky_kernel<512><<<
batch,
kThreads,
shared_bytes
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(history.data_ptr<at::Half>()),
output.data_ptr<float>(),
batch
);
} else if (n == 1024) {
static const bool configured = configure_persistent_kernel<1024>();
TORCH_CHECK(configured, "failed to configure n=1024 kernel");
constexpr int shared_bytes = 1024 * kPanel * sizeof(float);
persistent_wmma_cholesky_kernel<1024><<<
batch,
kThreads,
shared_bytes
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(history.data_ptr<at::Half>()),
output.data_ptr<float>(),
batch
);
} else {
TORCH_CHECK(false, "matrix dimension must be 512 or 1024");
}
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"persistent_wmma_cholesky",
&persistent_wmma_cholesky_cuda
);
}
"""
_FAST_UPDATE_SOURCE = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContextLight.h>
#include <cublas_v2.h>
torch::Tensor bf16_update_cuda(
torch::Tensor left,
torch::Tensor right,
torch::Tensor output
) {
TORCH_CHECK(left.is_cuda(), "left must be CUDA");
TORCH_CHECK(right.is_cuda(), "right must be CUDA");
TORCH_CHECK(output.is_cuda(), "output must be CUDA");
TORCH_CHECK(left.scalar_type() == at::kFloat, "left must be FP32");
TORCH_CHECK(right.scalar_type() == at::kFloat, "right must be FP32");
TORCH_CHECK(output.scalar_type() == at::kFloat, "output must be FP32");
TORCH_CHECK(left.dim() == right.dim(), "rank mismatch");
TORCH_CHECK(left.dim() == output.dim(), "rank mismatch");
TORCH_CHECK(left.dim() == 2 || left.dim() == 3, "rank must be 2 or 3");
TORCH_CHECK(left.stride(-1) == 1, "left inner stride");
TORCH_CHECK(right.stride(-1) == 1, "right inner stride");
TORCH_CHECK(output.stride(-1) == 1, "output inner stride");
const int m = static_cast<int>(left.size(-2));
const int n = static_cast<int>(right.size(-2));
const int k = static_cast<int>(left.size(-1));
TORCH_CHECK(right.size(-1) == k, "contracting dimension mismatch");
TORCH_CHECK(output.size(-2) == m, "output row mismatch");
TORCH_CHECK(output.size(-1) == n, "output column mismatch");
const int batches = left.dim() == 3
? static_cast<int>(left.size(0))
: 1;
TORCH_CHECK(
right.dim() == 2 || right.size(0) == batches,
"right batch mismatch"
);
TORCH_CHECK(
output.dim() == 2 || output.size(0) == batches,
"output batch mismatch"
);
const long long left_batch = left.dim() == 3 ? left.stride(0) : 0;
const long long right_batch = right.dim() == 3 ? right.stride(0) : 0;
const long long output_batch = output.dim() == 3 ? output.stride(0) : 0;
const int left_leading = static_cast<int>(left.stride(-2));
const int right_leading = static_cast<int>(right.stride(-2));
const int output_leading = static_cast<int>(output.stride(-2));
const float alpha = -1.0f;
const float beta = 1.0f;
cublasHandle_t handle = at::cuda::getCurrentCUDABlasHandle();
const cublasStatus_t status = cublasGemmStridedBatchedEx(
handle,
CUBLAS_OP_T,
CUBLAS_OP_N,
n,
m,
k,
&alpha,
right.data_ptr<float>(),
CUDA_R_32F,
right_leading,
right_batch,
left.data_ptr<float>(),
CUDA_R_32F,
left_leading,
left_batch,
&beta,
output.data_ptr<float>(),
CUDA_R_32F,
output_leading,
output_batch,
batches,
CUBLAS_COMPUTE_32F_FAST_16F,
CUBLAS_GEMM_DEFAULT_TENSOR_OP
);
TORCH_CHECK(status == CUBLAS_STATUS_SUCCESS, "cuBLAS update failed");
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("bf16_update", &bf16_update_cuda);
}
"""
_LOWER_CUBLAS_SOURCE = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContextLight.h>
#include <cublas_v2.h>
#include <algorithm>
#include <cstdint>
#include <limits>
namespace {
void check_status(cublasStatus_t status, const char* operation) {
TORCH_CHECK(
status == CUBLAS_STATUS_SUCCESS,
operation,
" failed with cuBLAS status ",
static_cast<int>(status)
);
}
int checked_int(int64_t value, const char* name) {
TORCH_CHECK(
value >= 0
&& value <= static_cast<int64_t>(
std::numeric_limits<int>::max()
),
name,
" is outside the cuBLAS integer range"
);
return static_cast<int>(value);
}
void validate_inputs(
const torch::Tensor& c,
const torch::Tensor& a
) {
TORCH_CHECK(c.is_cuda(), "c must be a CUDA tensor");
TORCH_CHECK(a.is_cuda(), "a must be a CUDA tensor");
TORCH_CHECK(
c.scalar_type() == at::kFloat,
"c must have dtype torch.float32"
);
TORCH_CHECK(
a.scalar_type() == at::kFloat,
"a must have dtype torch.float32"
);
TORCH_CHECK(c.dim() == 2, "c must be two-dimensional");
TORCH_CHECK(a.dim() == 2, "a must be two-dimensional");
TORCH_CHECK(
c.device() == a.device(),
"c and a must be on the same device"
);
TORCH_CHECK(
c.size(0) == c.size(1),
"c must be square"
);
TORCH_CHECK(
c.size(0) == a.size(0),
"c and a must have the same row count"
);
TORCH_CHECK(
c.stride(1) == 1,
"c must have unit column stride"
);
TORCH_CHECK(
a.stride(1) == 1,
"a must have unit column stride"
);
TORCH_CHECK(
c.stride(0) >= c.size(1),
"c rows must not overlap"
);
TORCH_CHECK(
a.stride(0) >= a.size(1),
"a rows must not overlap"
);
}
class HandleModeGuard {
public:
explicit HandleModeGuard(cublasHandle_t handle)
: handle_(handle) {
check_status(
cublasGetMathMode(handle_, &previous_),
"cublasGetMathMode"
);
check_status(
cublasSetMathMode(
handle_,
CUBLAS_TF32_TENSOR_OP_MATH
),
"cublasSetMathMode"
);
check_status(
cublasGetPointerMode(
handle_,
&previous_pointer_
),
"cublasGetPointerMode"
);
check_status(
cublasSetPointerMode(
handle_,
CUBLAS_POINTER_MODE_HOST
),
"cublasSetPointerMode"
);
}
HandleModeGuard(const HandleModeGuard&) = delete;
HandleModeGuard& operator=(const HandleModeGuard&) = delete;
~HandleModeGuard() {
cublasSetPointerMode(handle_, previous_pointer_);
cublasSetMathMode(handle_, previous_);
}
private:
cublasHandle_t handle_;
cublasMath_t previous_;
cublasPointerMode_t previous_pointer_;
};
} // namespace
torch::Tensor syrk_lower_in_place(
torch::Tensor c,
torch::Tensor a
) {
validate_inputs(c, a);
const int size = checked_int(c.size(0), "size");
const int rank = checked_int(a.size(1), "rank");
const int lda = checked_int(a.stride(0), "a row stride");
const int ldc = checked_int(c.stride(0), "c row stride");
if (size == 0 || rank == 0) {
return c;
}
cublasHandle_t handle =
at::cuda::getCurrentCUDABlasHandle();
HandleModeGuard mode_guard(handle);
const float alpha = -1.0f;
const float beta = 1.0f;
check_status(
cublasSsyrk(
handle,
CUBLAS_FILL_MODE_UPPER,
CUBLAS_OP_T,
size,
rank,
&alpha,
a.data_ptr<float>(),
lda,
&beta,
c.data_ptr<float>(),
ldc
),
"cublasSsyrk"
);
return c;
}
torch::Tensor gemm_lower_blocks_in_place(
torch::Tensor c,
torch::Tensor a,
int64_t row_block
) {
validate_inputs(c, a);
TORCH_CHECK(row_block > 0, "row_block must be positive");
const int size = checked_int(c.size(0), "size");
const int rank = checked_int(a.size(1), "rank");
const int lda = checked_int(a.stride(0), "a row stride");
const int ldc = checked_int(c.stride(0), "c row stride");
const int block = checked_int(row_block, "row_block");
if (size == 0 || rank == 0) {
return c;
}
cublasHandle_t handle =
at::cuda::getCurrentCUDABlasHandle();
HandleModeGuard mode_guard(handle);
const float alpha = -1.0f;
const float beta = 1.0f;
for (int row_begin = 0; row_begin < size; row_begin += block) {
const int rows =
std::min(block, size - row_begin);
const int columns = row_begin + rows;
const float* left =
a.data_ptr<float>()
+ static_cast<int64_t>(row_begin) * lda;
float* destination =
c.data_ptr<float>()
+ static_cast<int64_t>(row_begin) * ldc;
check_status(
cublasGemmEx(
handle,
CUBLAS_OP_T,
CUBLAS_OP_N,
columns,
rows,
rank,
&alpha,
a.data_ptr<float>(),
CUDA_R_32F,
lda,
left,
CUDA_R_32F,
lda,
&beta,
destination,
CUDA_R_32F,
ldc,
CUBLAS_COMPUTE_32F_FAST_TF32,
CUBLAS_GEMM_DEFAULT
),
"cublasGemmEx"
);
}
return c;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"syrk_lower_in_place",
&syrk_lower_in_place
);
module.def(
"gemm_lower_blocks_in_place",
&gemm_lower_blocks_in_place
);
}
"""
@lru_cache(maxsize=1)
def _cuda32_extension():
return load_inline(
name="b200_cholesky32_padded_v3",
cpp_sources="",
cuda_sources=_CUDA32_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda64_extension():
return load_inline(
name="b200_cholesky64_inverse_v3",
cpp_sources="",
cuda_sources=_CUDA64_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda128_extension():
return load_inline(
name="b200_cholesky128_panel32_v2",
cpp_sources="",
cuda_sources=_CUDA128_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda128_inverse_extension():
return load_inline(
name="b200_cholesky128_inverse_panel32_v1",
cpp_sources="",
cuda_sources=_CUDA128_INVERSE_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda256_packed_extension():
return load_inline(
name="b200_cholesky256_packed_panel32_v1",
cpp_sources="",
cuda_sources=_CUDA256_PACKED_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma_extension():
return load_inline(
name="b200_persistent_wmma_cholesky_v1",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _fast_update_extension():
return load_inline(
name="b200_bf16_update_v1",
cpp_sources="",
cuda_sources=_FAST_UPDATE_SOURCE,
functions=None,
extra_cuda_cflags=["-O3"],
extra_ldflags=["-lcublas"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _lower_cublas_extension():
return load_inline(
name="b200_cublas_lower_v1",
cpp_sources="",
cuda_sources=_LOWER_CUBLAS_SOURCE,
functions=None,
extra_cuda_cflags=["-O3"],
extra_ldflags=["-lcublas"],
with_cuda=True,
verbose=False,
)
def _cuda_cholesky32(data: torch.Tensor) -> torch.Tensor:
try:
return _cuda32_extension().cholesky32(data)
except Exception:
return _triton_cholesky32(data)
def _cuda_cholesky64(data: torch.Tensor) -> torch.Tensor:
try:
return _cuda64_extension().cholesky64(data)
except Exception:
return torch.linalg.cholesky_ex(data, check_errors=False).L
def _cuda_cholesky64_inverse(
data: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor]:
try:
factor, inverse = _cuda64_extension().cholesky64_inverse(data)
return factor, inverse
except Exception:
factor = torch.linalg.cholesky_ex(
data,
check_errors=False,
).L
identity = torch.eye(
64,
device=data.device,
dtype=data.dtype,
).expand(data.shape[0], -1, -1)
inverse = torch.linalg.solve_triangular(
factor,
identity,
upper=False,
left=True,
)
return factor, inverse
def _cuda_cholesky128(data: torch.Tensor) -> torch.Tensor:
try:
return _cuda128_extension().cholesky128(data)
except Exception:
return _blocked_cholesky128(data)
_cuda128_inverse_failed = False
def _cuda_cholesky128_inverse(
data: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor]:
global _cuda128_inverse_failed
if not _cuda128_inverse_failed:
try:
factor, inverse = (
_cuda128_inverse_extension()
.cholesky128_inverse(data)
)
return factor, inverse
except Exception:
_cuda128_inverse_failed = True
factor = torch.linalg.cholesky_ex(
data,
check_errors=False,
).L
identity = torch.eye(
128,
dtype=data.dtype,
device=data.device,
).expand(data.shape[0], 128, 128)
inverse = torch.linalg.solve_triangular(
factor,
identity,
upper=False,
left=True,
)
return factor, inverse
def _cuda_cholesky256_packed(data: torch.Tensor) -> torch.Tensor:
try:
return _cuda256_packed_extension().cholesky256_packed(data)
except Exception:
return torch.linalg.cholesky_ex(
data,
check_errors=False,
).L
def _persistent_wmma_cholesky(data: torch.Tensor) -> torch.Tensor:
return (
_persistent_wmma_extension()
.persistent_wmma_cholesky(data)
)
def _syrk_lower_update(
output: torch.Tensor,
panel: torch.Tensor,
) -> torch.Tensor:
return _lower_cublas_extension().syrk_lower_in_place(
output,
panel,
)
def _gemm_lower_update(
output: torch.Tensor,
panel: torch.Tensor,
row_block: int,
) -> torch.Tensor:
return _lower_cublas_extension().gemm_lower_blocks_in_place(
output,
panel,
row_block,
)
def _bf16_update(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
return _fast_update_extension().bf16_update(
left,
right,
output,
)
@triton.jit
def _bf16_update_kernel(
output_ptr,
left_ptr,
right_ptr,
m_size: tl.constexpr,
n_size: tl.constexpr,
k_size: tl.constexpr,
output_row_stride: tl.constexpr,
left_row_stride: tl.constexpr,
right_row_stride: tl.constexpr,
output_batch_stride: tl.constexpr,
left_batch_stride: tl.constexpr,
right_batch_stride: tl.constexpr,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
GROUP_M: tl.constexpr,
):
program = tl.program_id(0)
batch = tl.program_id(1)
output_ptr += batch * output_batch_stride
left_ptr += batch * left_batch_stride
right_ptr += batch * right_batch_stride
programs_m = tl.cdiv(m_size, BLOCK_M)
programs_n = tl.cdiv(n_size, BLOCK_N)
programs_per_group = GROUP_M * programs_n
group = program // programs_per_group
first_m = group * GROUP_M
group_m = tl.minimum(programs_m - first_m, GROUP_M)
local = program % programs_per_group
program_m = first_m + (local % group_m)
program_n = local // group_m
rows = program_m * BLOCK_M + tl.arange(0, BLOCK_M)
cols = program_n * BLOCK_N + tl.arange(0, BLOCK_N)
inner = tl.arange(0, BLOCK_K)
accumulator = tl.zeros((BLOCK_M, BLOCK_N), tl.float32)
for start in range(0, k_size, BLOCK_K):
inner_offsets = start + inner
left_values = tl.load(
left_ptr
+ rows[:, None] * left_row_stride
+ inner_offsets[None, :],
mask=(rows[:, None] < m_size)
& (inner_offsets[None, :] < k_size),
other=0.0,
).to(tl.bfloat16)
right_values = tl.load(
right_ptr
+ cols[:, None] * right_row_stride
+ inner_offsets[None, :],
mask=(cols[:, None] < n_size)
& (inner_offsets[None, :] < k_size),
other=0.0,
).to(tl.bfloat16)
accumulator += tl.dot(
left_values,
tl.trans(right_values),
out_dtype=tl.float32,
)
output_offsets = (
rows[:, None] * output_row_stride + cols[None, :]
)
output_mask = (rows[:, None] < m_size) & (cols[None, :] < n_size)
previous = tl.load(
output_ptr + output_offsets,
mask=output_mask,
other=0.0,
)
tl.store(
output_ptr + output_offsets,
previous - accumulator,
mask=output_mask,
)
def _triton_bf16_update(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
m_size = output.shape[-2]
n_size = output.shape[-1]
k_size = left.shape[-1]
block = 128
grid = (
triton.cdiv(m_size, block) * triton.cdiv(n_size, block),
output.shape[0] if output.dim() == 3 else 1,
)
output_batch_stride = output.stride(0) if output.dim() == 3 else 0
left_batch_stride = left.stride(0) if left.dim() == 3 else 0
right_batch_stride = right.stride(0) if right.dim() == 3 else 0
_bf16_update_kernel[grid](
output,
left,
right,
m_size,
n_size,
k_size,
output.stride(-2),
left.stride(-2),
right.stride(-2),
output_batch_stride,
left_batch_stride,
right_batch_stride,
BLOCK_M=block,
BLOCK_N=block,
BLOCK_K=32,
GROUP_M=8,
num_warps=8,
num_stages=4,
)
return output
@triton.jit
def _cholesky32_kernel(
input_ptr,
output_ptr,
matrix_stride: tl.constexpr,
):
matrix = tl.program_id(0)
row_ids = tl.arange(0, 32)
col_ids = tl.arange(0, 32)
rows = row_ids[:, None]
cols = col_ids[None, :]
offsets = matrix * matrix_stride + rows * 32 + cols
values = tl.where(rows >= cols, tl.load(input_ptr + offsets), 0.0)
for k in range(32):
pivot_row = tl.sum(tl.where(rows == k, values, 0.0), axis=0)
diagonal = tl.sum(
tl.where(col_ids == k, pivot_row, 0.0),
axis=0,
)
diagonal -= tl.sum(
tl.where(col_ids < k, pivot_row * pivot_row, 0.0),
axis=0,
)
diagonal = tl.sqrt(tl.maximum(diagonal, 0.0))
column = tl.sum(tl.where(cols == k, values, 0.0), axis=1)
products = tl.where(
cols < k,
values * pivot_row[None, :],
0.0,
)
column = (column - tl.sum(products, axis=1)) / diagonal
values = tl.where(
(rows == k) & (cols == k),
diagonal,
values,
)
values = tl.where(
(rows > k) & (cols == k),
column[:, None],
values,
)
tl.store(output_ptr + offsets, values)
def _triton_cholesky32(data: torch.Tensor) -> torch.Tensor:
output = torch.empty_like(data)
_cholesky32_kernel[(data.shape[0],)](
data,
output,
32 * 32,
num_warps=1,
)
return output
def _individual_cholesky(data: torch.Tensor) -> torch.Tensor:
"""Avoid cuSOLVER's slow batched path for a few large matrices."""
output = torch.empty_like(data)
info = torch.empty((data.shape[0],), device=data.device, dtype=torch.int32)
for matrix in range(data.shape[0]):
torch.linalg.cholesky_ex(
data[matrix],
check_errors=False,
out=(output[matrix], info[matrix]),
)
return output
def _blocked_cholesky128(data: torch.Tensor) -> torch.Tensor:
"""Two 64-wide panels, using the register kernel on both diagonals."""
output = torch.empty_like(data)
output[:, :64, 64:].zero_()
diagonal0 = _cuda_cholesky64(data[:, :64, :64].contiguous())
output[:, :64, :64].copy_(diagonal0)
right_hand_side = data[:, 64:, :64].transpose(-1, -2)
solved = torch.linalg.solve_triangular(
diagonal0,
right_hand_side,
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
output[:, 64:, :64].copy_(panel)
trailing = data[:, 64:, 64:].clone()
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
torch.baddbmm(
trailing,
panel,
panel.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=trailing,
)
finally:
torch.set_float32_matmul_precision(previous_precision)
diagonal1 = _cuda_cholesky64(trailing)
output[:, 64:, 64:].copy_(diagonal1)
return output
def _blocked_custom64(data: torch.Tensor) -> torch.Tensor:
"""Blocked factorization with register-resident 64x64 diagonals."""
work = data.clone()
n = data.shape[-1]
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, 64):
end = start + 64
diagonal = _cuda_cholesky64(
work[:, start:end, start:end].contiguous()
)
work[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
work[:, start:end, end:].zero_()
right_hand_side = work[:, end:, start:end].transpose(-1, -2)
solved = torch.linalg.solve_triangular(
diagonal,
right_hand_side,
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
work[:, end:, start:end].copy_(panel)
trailing = work[:, end:, end:]
torch.baddbmm(
trailing,
panel,
panel.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=trailing,
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return work
def _blocked_batched_cholesky(
data: torch.Tensor,
block_size: int,
) -> torch.Tensor:
"""Use exact panels and tensor-core trailing updates for medium matrices."""
work = data.clone()
n = data.shape[-1]
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, block_size):
end = min(start + block_size, n)
diagonal = torch.linalg.cholesky_ex(
work[:, start:end, start:end],
check_errors=False,
).L
work[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
right_hand_side = work[:, end:, start:end].transpose(-1, -2)
solved = torch.linalg.solve_triangular(
diagonal,
right_hand_side,
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
work[:, end:, start:end].copy_(panel)
trailing = work[:, end:, end:]
torch.baddbmm(
trailing,
panel,
panel.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=trailing,
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return torch.tril(work)
def _left_blocked_batched_cholesky(
data: torch.Tensor,
block_size: int,
custom64: bool = False,
fast_updates: bool = False,
inverse_panels: bool = False,
) -> torch.Tensor:
"""Batched left-looking factorization with lower-panel updates only."""
factor = torch.zeros_like(data)
n = data.shape[-1]
identity = (
torch.eye(
block_size,
device=data.device,
dtype=data.dtype,
).expand(data.shape[0], -1, -1)
if inverse_panels
else None
)
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, block_size):
end = min(start + block_size, n)
diagonal_input = data[:, start:end, start:end].clone()
if start:
if fast_updates:
_bf16_update(
diagonal_input,
factor[:, start:end, :start],
factor[:, start:end, :start],
)
else:
torch.baddbmm(
diagonal_input,
factor[:, start:end, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=diagonal_input,
)
if custom64:
diagonal = _cuda_cholesky64(diagonal_input)
else:
diagonal = torch.linalg.cholesky_ex(
diagonal_input,
check_errors=False,
).L
factor[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
panel_input = data[:, end:, start:end].clone()
if start:
if fast_updates:
_bf16_update(
panel_input,
factor[:, end:, :start],
factor[:, start:end, :start],
)
else:
torch.baddbmm(
panel_input,
factor[:, end:, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=panel_input,
)
if inverse_panels:
diagonal_inverse = torch.linalg.solve_triangular(
diagonal,
identity,
upper=False,
left=True,
)
panel = torch.bmm(
panel_input,
diagonal_inverse.transpose(-1, -2),
)
else:
solved = torch.linalg.solve_triangular(
diagonal,
panel_input.transpose(-1, -2),
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
factor[:, end:, start:end].copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _left_blocked_batched128(data: torch.Tensor) -> torch.Tensor:
"""Two or four 128-wide panels with a fused factor-and-inverse base."""
factor = torch.zeros_like(data)
n = data.shape[-1]
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, 128):
end = start + 128
diagonal_input = data[:, start:end, start:end].clone()
if start:
previous_row = factor[:, start:end, :start]
torch.baddbmm(
diagonal_input,
previous_row,
previous_row.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=diagonal_input,
)
diagonal, diagonal_inverse = _cuda_cholesky128_inverse(
diagonal_input
)
factor[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
panel_input = data[:, end:, start:end].clone()
if start:
torch.baddbmm(
panel_input,
factor[:, end:, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=panel_input,
)
torch.bmm(
panel_input,
diagonal_inverse.transpose(-1, -2),
out=factor[:, end:, start:end],
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _left_blocked_batched64_inverse(data: torch.Tensor) -> torch.Tensor:
"""Left-looking 64-wide panels with fused factor and inverse."""
factor = torch.zeros_like(data)
n = data.shape[-1]
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, 64):
end = start + 64
diagonal_input = data[:, start:end, start:end].clone()
if start:
previous_row = factor[:, start:end, :start]
torch.baddbmm(
diagonal_input,
previous_row,
previous_row.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=diagonal_input,
)
diagonal, diagonal_inverse = _cuda_cholesky64_inverse(
diagonal_input
)
factor[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
panel_input = data[:, end:, start:end].clone()
if start:
torch.baddbmm(
panel_input,
factor[:, end:, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=panel_input,
)
torch.bmm(
panel_input,
diagonal_inverse.transpose(-1, -2),
out=factor[:, end:, start:end],
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _column_blocked_batched_cholesky(
data: torch.Tensor,
block_size: int,
fast_updates: bool = False,
custom64_inverse: bool = False,
) -> torch.Tensor:
"""Left-looking factorization updating each complete block column once."""
factor = torch.zeros_like(data)
batch = data.shape[0]
n = data.shape[-1]
identity = (
torch.eye(
block_size,
device=data.device,
dtype=data.dtype,
).expand(batch, -1, -1)
if not custom64_inverse
else None
)
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, block_size):
end = start + block_size
column = data[:, start:, start:end].clone()
if start:
if fast_updates:
_bf16_update(
column,
factor[:, start:, :start],
factor[:, start:end, :start],
)
else:
torch.baddbmm(
column,
factor[:, start:, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=column,
)
diagonal_input = column[:, :block_size, :]
if custom64_inverse:
diagonal, diagonal_inverse = _cuda_cholesky64_inverse(
diagonal_input.contiguous()
)
else:
diagonal = torch.linalg.cholesky_ex(
diagonal_input,
check_errors=False,
).L
diagonal_inverse = torch.linalg.solve_triangular(
diagonal,
identity,
upper=False,
left=True,
)
factor[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
torch.bmm(
column[:, block_size:, :],
diagonal_inverse.transpose(-1, -2),
out=factor[:, end:, start:end],
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _blocked_cholesky(
data: torch.Tensor,
block_size: int,
inverse_panels: bool = False,
) -> torch.Tensor:
# All routed shapes have batch one. Squeezing the batch dimension makes
# PyTorch select the ordinary cuSOLVER/cuBLAS paths instead of their
# strided-batched variants.
work = data[0].clone()
n = data.shape[-1]
identity = (
torch.eye(
block_size,
device=data.device,
dtype=data.dtype,
)
if inverse_panels
else None
)
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, block_size):
end = min(start + block_size, n)
diagonal = torch.linalg.cholesky_ex(
work[start:end, start:end],
check_errors=False,
).L
work[start:end, start:end].copy_(diagonal)
if end == n:
continue
if inverse_panels:
diagonal_inverse = torch.linalg.solve_triangular(
diagonal,
identity,
upper=False,
left=True,
)
panel = torch.mm(
work[end:, start:end],
diagonal_inverse.transpose(-1, -2),
)
else:
right_hand_side = work[end:, start:end].transpose(-1, -2)
solved = torch.linalg.solve_triangular(
diagonal,
right_hand_side,
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
work[end:, start:end].copy_(panel)
trailing = work[end:, end:]
torch.addmm(
trailing,
panel,
panel.transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=trailing,
)
finally:
torch.set_float32_matmul_precision(previous_precision)
return torch.tril(work).unsqueeze(0)
def _left_blocked_cholesky(
data: torch.Tensor,
block_size: int,
inverse_panels: bool = False,
fast_updates: bool = False,
) -> torch.Tensor:
"""Left-looking factorization that never updates the unused upper half."""
source = data[0]
factor = torch.zeros_like(source)
n = source.shape[-1]
identity = (
torch.eye(
block_size,
device=data.device,
dtype=data.dtype,
)
if inverse_panels
else None
)
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, block_size):
end = min(start + block_size, n)
diagonal_input = source[start:end, start:end].clone()
if start:
if fast_updates:
_bf16_update(
diagonal_input,
factor[start:end, :start],
factor[start:end, :start],
)
else:
torch.addmm(
diagonal_input,
factor[start:end, :start],
factor[start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=diagonal_input,
)
diagonal = torch.linalg.cholesky_ex(
diagonal_input,
check_errors=False,
).L
factor[start:end, start:end].copy_(diagonal)
if end == n:
continue
panel_input = source[end:, start:end].clone()
if start:
if fast_updates:
_bf16_update(
panel_input,
factor[end:, :start],
factor[start:end, :start],
)
else:
torch.addmm(
panel_input,
factor[end:, :start],
factor[start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=panel_input,
)
if inverse_panels:
diagonal_inverse = torch.linalg.solve_triangular(
diagonal,
identity,
upper=False,
left=True,
)
panel = torch.mm(
panel_input,
diagonal_inverse.transpose(-1, -2),
)
else:
solved = torch.linalg.solve_triangular(
diagonal,
panel_input.transpose(-1, -2),
upper=False,
left=True,
)
panel = solved.transpose(-1, -2)
factor[end:, start:end].copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor.unsqueeze(0)
def _dispatch_eager(data: torch.Tensor) -> torch.Tensor:
shape = tuple(data.shape)
if shape == (4, 512, 512):
return _persistent_wmma_cholesky(data)
if shape == (4096, 32, 32):
return _cuda_cholesky32(data)
if shape == (1024, 64, 64):
return _cuda_cholesky64(data)
if shape == (256, 128, 128):
return _cuda_cholesky128(data)
if shape == (64, 256, 256):
return _cuda_cholesky256_packed(data)
if shape == (16, 512, 512):
return _blocked_custom64(data)
if shape == (640, 512, 512):
return _persistent_wmma_cholesky(data)
if shape == (60, 1024, 1024):
return _left_blocked_batched_cholesky(
data,
256,
fast_updates=True,
inverse_panels=True,
)
if shape in {
(2, 2048, 2048),
(2, 4096, 4096),
}:
return _individual_cholesky(data)
if shape == (1, 8192, 8192):
return _left_blocked_cholesky(
data,
2048,
fast_updates=True,
)
if shape == (1, 16384, 16384):
return _left_blocked_cholesky(
data,
4096,
inverse_panels=True,
fast_updates=True,
)
if shape == (1, 32768, 32768):
return _left_blocked_cholesky(
data,
4096,
inverse_panels=True,
fast_updates=True,
)
return torch.linalg.cholesky_ex(data, check_errors=False).L
_graph_shape = None
_graph_position = 0
_graph_slots = []
_graph_disabled = set()
def _capture_graph_slot(data: torch.Tensor):
fixed = data.clone()
warm = _dispatch_eager(fixed)
torch.cuda.synchronize()
graph = torch.cuda.CUDAGraph()
with torch.cuda.graph(graph):
answer = _dispatch_eager(fixed)
warm = None
graph.replay()
return fixed, answer, graph
def _run_graphed(data: torch.Tensor, width: int) -> torch.Tensor:
global _graph_shape, _graph_position, _graph_slots
shape = tuple(data.shape)
if shape in _graph_disabled:
return _dispatch_eager(data)
if _graph_shape != shape:
_graph_shape = shape
_graph_position = 0
_graph_slots = []
position = _graph_position
if position == len(_graph_slots):
try:
slot = _capture_graph_slot(data)
except Exception:
_graph_disabled.add(shape)
return _dispatch_eager(data)
_graph_slots.append(slot)
answer = slot[1]
else:
fixed, answer, graph = _graph_slots[position]
fixed.copy_(data)
graph.replay()
_graph_position = (position + 1) % width
return answer
def custom_kernel(data: input_t) -> output_t:
shape = tuple(data.shape)
graph_widths = {
(60, 1024, 1024): 1,
}
width = graph_widths.get(shape)
if width is not None:
return _run_graphed(data, width)
return _dispatch_eager(data)
scrolls · 2756 lines total
Source code from GPU Mode and the KernelBot dataset · June 9 Researcher Reciprocity License v1.0
Best evidence level for this revision: reported
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