submission 914977
neuralnetworking · python · License unknown
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Vendorable · source mirrored · license unknownView source →
No package. Vendor the mirrored source: 7800 lines, June 9 Researcher Reciprocity License v1.0.
submission.py
curl "https://kernelindex.com/api/v1/implementations/kernelbot-cholesky-914977?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:ee98e83c67d00e2ea559a66195033debd9f535ba6ee7befc3e2798fdb226cd0b
license declaredunknown
license concludedunknown
authorsneuralnetworking
imported2026-08-26
Techniques
Extracted from the mirrored source by pattern, never inferred. Each row cites its line.
cluster
void __cluster_dims__(kClusterBlocks, 1, 1) cholesky256_cluster2_kernel(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.py7800 lines
import base64
import hashlib
import zlib
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);
}
"""
_CUDA64_STRIDED_ENCODED = (
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'Hq>dd$s)#k1pvQ({`KmUfA#75>SqavFcbQm0qTii<|+qFJQ8&E?ZdmCbWY`y!B!b1q<3)^Nzio)gzx6%@C|T;Q=h'
')9iS4jff$3<p{K#@yv;X6lv(payyG0ouwaF?x+GUsSW4knt;&3HooS}n*658b=$a@OOb5=@AalGVnbJAs@Ccrdkm'
'x!`*xLgFB1h7n5K9$R54*1NskbZH#xj662geh5FS47L4>?ga-Ox<i{Lo-~DNrz;mkTQ1F+#$oXD50w`Td^N|$<VA'
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'YMbecK5Ou)_qIBJ>3FZZVfU&K9qiHCiy&>Se*i;w<~0'
)
_CUDA64_STRIDED_SOURCE = zlib.decompress(
base64.b85decode(_CUDA64_STRIDED_ENCODED)
).decode("utf-8")
_CUDA64_STRIDED_SOURCE_HASH = (
"539e7b7b0c51c10d79479dbcc87510c3fc2c700b77c1ed7f33bde54e6a2cb44d"
)
if (
hashlib.sha256(_CUDA64_STRIDED_SOURCE.encode()).hexdigest()
!= _CUDA64_STRIDED_SOURCE_HASH
):
raise RuntimeError("embedded strided inverse source is corrupt")
_PHASED_SMALL_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
namespace {
constexpr int kN32 = 32;
constexpr int kN64 = 64;
template <int GroupWidth>
__device__ __forceinline__ unsigned subgroup_mask() {
constexpr unsigned base =
(1u << GroupWidth) - 1u;
const int group_in_warp =
(static_cast<int>(threadIdx.x) & 31) / GroupWidth;
return base << (group_in_warp * GroupWidth);
}
template <int GroupsPerBlock>
__global__ void cholesky32_phased_halfwarp_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
constexpr int group_width = 16;
constexpr int half = 16;
constexpr int pitch = half + 1;
constexpr int tile_elements = kN32 * pitch;
// 560 mod 32 is 16, so the two half-warp tiles use complementary
// shared-memory banks.
constexpr int tile_stride = tile_elements + 16;
extern __shared__ float storage[];
const int thread = static_cast<int>(threadIdx.x);
const int group = thread / group_width;
const int local_lane = thread - group * group_width;
const int matrix =
static_cast<int>(blockIdx.x) * GroupsPerBlock + group;
if (matrix >= batch) {
return;
}
const unsigned mask = subgroup_mask<group_width>();
const long long matrix_offset =
static_cast<long long>(matrix) * kN32 * kN32;
const float* matrix_input = input + matrix_offset;
float* matrix_output = output + matrix_offset;
float* tile = storage + group * tile_stride;
float top[half];
float bottom[half];
// Stage the complete left half. Both 16-lane groups in a warp issue
// naturally aligned 64-byte global transactions.
#pragma unroll 4
for (
int linear = local_lane;
linear < kN32 * half;
linear += group_width
) {
const int row = linear >> 4;
const int col = linear & 15;
tile[row * pitch + col] =
row >= col
? matrix_input[row * kN32 + col]
: 0.0f;
}
__syncwarp(mask);
#pragma unroll
for (int col = 0; col < half; ++col) {
top[col] = tile[local_lane * pitch + col];
bottom[col] =
tile[(local_lane + half) * pitch + col];
}
// Factor L11 and solve L21. The ordering matches the active scalar
// recurrence, but each warp advances two independent matrices.
#pragma unroll
for (int pivot = 0; pivot < half; ++pivot) {
float dot_top = 0.0f;
float dot_bottom = 0.0f;
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float pivot_value = __shfl_sync(
mask,
top[col],
pivot,
group_width
);
dot_top = fmaf(top[col], pivot_value, dot_top);
dot_bottom = fmaf(
bottom[col],
pivot_value,
dot_bottom
);
}
float diagonal = 0.0f;
if (local_lane == pivot) {
diagonal = sqrtf(
fmaxf(top[pivot] - dot_top, 0.0f)
);
}
diagonal = __shfl_sync(
mask,
diagonal,
pivot,
group_width
);
if (local_lane == pivot) {
top[pivot] = diagonal;
} else if (local_lane > pivot) {
top[pivot] =
(top[pivot] - dot_top) / diagonal;
}
bottom[pivot] =
(bottom[pivot] - dot_bottom) / diagonal;
}
#pragma unroll
for (int col = 0; col < half; ++col) {
tile[local_lane * pitch + col] = top[col];
tile[(local_lane + half) * pitch + col] =
bottom[col];
}
__syncwarp(mask);
#pragma unroll 4
for (
int linear = local_lane;
linear < kN32 * half;
linear += group_width
) {
const int row = linear >> 4;
const int col = linear & 15;
matrix_output[row * kN32 + col] =
tile[row * pitch + col];
}
// Reuse top[] and the same tile for A22/L22. The old top state is no
// longer live; bottom[] retains exactly the 16-column L21 history.
#pragma unroll
for (
int linear = local_lane;
linear < half * half;
linear += group_width
) {
const int row = linear >> 4;
const int col = linear & 15;
tile[row * pitch + col] =
row >= col
? matrix_input[
(row + half) * kN32 + col + half
]
: 0.0f;
matrix_output[row * kN32 + col + half] = 0.0f;
}
__syncwarp(mask);
#pragma unroll
for (int col = 0; col < half; ++col) {
top[col] = tile[local_lane * pitch + col];
}
#pragma unroll
for (int pivot = 0; pivot < half; ++pivot) {
float dot = 0.0f;
#pragma unroll
for (int col = 0; col < half; ++col) {
const float pivot_value = __shfl_sync(
mask,
bottom[col],
pivot,
group_width
);
dot = fmaf(bottom[col], pivot_value, dot);
}
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float pivot_value = __shfl_sync(
mask,
top[col],
pivot,
group_width
);
dot = fmaf(top[col], pivot_value, dot);
}
float diagonal = 0.0f;
if (local_lane == pivot) {
diagonal = sqrtf(
fmaxf(top[pivot] - dot, 0.0f)
);
}
diagonal = __shfl_sync(
mask,
diagonal,
pivot,
group_width
);
if (local_lane == pivot) {
top[pivot] = diagonal;
} else if (local_lane > pivot) {
top[pivot] = (top[pivot] - dot) / diagonal;
}
}
#pragma unroll
for (int col = 0; col < half; ++col) {
tile[local_lane * pitch + col] = top[col];
}
__syncwarp(mask);
#pragma unroll
for (
int linear = local_lane;
linear < half * half;
linear += group_width
) {
const int row = linear >> 4;
const int col = linear & 15;
matrix_output[
(row + half) * kN32 + col + half
] = tile[row * pitch + col];
}
}
template <int WarpsPerBlock>
__global__ void cholesky64_phased_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
constexpr int half = 32;
constexpr int pitch = half + 1;
constexpr int tile_stride = kN64 * pitch;
extern __shared__ float storage[];
const int thread = static_cast<int>(threadIdx.x);
const int warp = thread >> 5;
const int lane = thread & 31;
const int matrix =
static_cast<int>(blockIdx.x) * WarpsPerBlock + warp;
if (matrix >= batch) {
return;
}
const long long matrix_offset =
static_cast<long long>(matrix) * kN64 * kN64;
const float* matrix_input = input + matrix_offset;
float* matrix_output = output + matrix_offset;
float* tile = storage + warp * tile_stride;
float top[half];
float bottom[half];
#pragma unroll 4
for (
int linear = lane;
linear < kN64 * half;
linear += 32
) {
const int row = linear >> 5;
const int col = linear & 31;
tile[row * pitch + col] =
row >= col
? matrix_input[row * kN64 + col]
: 0.0f;
}
__syncwarp();
#pragma unroll
for (int col = 0; col < half; ++col) {
top[col] = tile[lane * pitch + col];
bottom[col] = tile[(lane + half) * pitch + col];
}
constexpr unsigned mask = 0xffffffffu;
#pragma unroll
for (int pivot = 0; pivot < half; ++pivot) {
float dot_top = 0.0f;
float dot_bottom = 0.0f;
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float pivot_value = __shfl_sync(
mask,
top[col],
pivot
);
dot_top = fmaf(top[col], pivot_value, dot_top);
dot_bottom = fmaf(
bottom[col],
pivot_value,
dot_bottom
);
}
float diagonal = 0.0f;
if (lane == pivot) {
diagonal = sqrtf(
fmaxf(top[pivot] - dot_top, 0.0f)
);
}
diagonal = __shfl_sync(mask, diagonal, pivot);
if (lane == pivot) {
top[pivot] = diagonal;
} else if (lane > pivot) {
top[pivot] =
(top[pivot] - dot_top) / diagonal;
}
bottom[pivot] =
(bottom[pivot] - dot_bottom) / diagonal;
}
#pragma unroll
for (int col = 0; col < half; ++col) {
tile[lane * pitch + col] = top[col];
tile[(lane + half) * pitch + col] = bottom[col];
}
__syncwarp();
#pragma unroll 4
for (
int linear = lane;
linear < kN64 * half;
linear += 32
) {
const int row = linear >> 5;
const int col = linear & 31;
matrix_output[row * kN64 + col] =
tile[row * pitch + col];
}
#pragma unroll
for (int linear = lane; linear < half * half; linear += 32) {
const int row = linear >> 5;
const int col = linear & 31;
tile[row * pitch + col] =
row >= col
? matrix_input[
(row + half) * kN64 + col + half
]
: 0.0f;
matrix_output[row * kN64 + col + half] = 0.0f;
}
__syncwarp();
#pragma unroll
for (int col = 0; col < half; ++col) {
top[col] = tile[lane * pitch + col];
}
#pragma unroll
for (int pivot = 0; pivot < half; ++pivot) {
float dot = 0.0f;
#pragma unroll
for (int col = 0; col < half; ++col) {
const float pivot_value = __shfl_sync(
mask,
bottom[col],
pivot
);
dot = fmaf(bottom[col], pivot_value, dot);
}
#pragma unroll
for (int col = 0; col < pivot; ++col) {
const float pivot_value = __shfl_sync(
mask,
top[col],
pivot
);
dot = fmaf(top[col], pivot_value, dot);
}
float diagonal = 0.0f;
if (lane == pivot) {
diagonal = sqrtf(
fmaxf(top[pivot] - dot, 0.0f)
);
}
diagonal = __shfl_sync(mask, diagonal, pivot);
if (lane == pivot) {
top[pivot] = diagonal;
} else if (lane > pivot) {
top[pivot] = (top[pivot] - dot) / diagonal;
}
}
#pragma unroll
for (int col = 0; col < half; ++col) {
tile[lane * pitch + col] = top[col];
}
__syncwarp();
#pragma unroll
for (int linear = lane; linear < half * half; linear += 32) {
const int row = linear >> 5;
const int col = linear & 31;
matrix_output[
(row + half) * kN64 + col + half
] = tile[row * pitch + col];
}
}
void check_input(
const torch::Tensor& input,
int expected_n
) {
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 must be rank three");
TORCH_CHECK(
input.size(1) == expected_n && input.size(2) == expected_n,
"unexpected matrix dimension"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
}
torch::Tensor cholesky32_phased_half_cuda(torch::Tensor input) {
constexpr int groups = 8;
constexpr int group_width = 16;
constexpr int tile_stride = kN32 * 17 + 16;
check_input(input, kN32);
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
const int blocks = (batch + groups - 1) / groups;
cholesky32_phased_halfwarp_kernel<groups><<<
blocks,
groups * group_width,
groups * tile_stride * sizeof(float)
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
return output;
}
torch::Tensor cholesky64_phased2_cuda(torch::Tensor input) {
constexpr int warps = 2;
constexpr int tile_stride = kN64 * 33;
constexpr int shared_bytes =
warps * tile_stride * sizeof(float);
check_input(input, kN64);
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
const int blocks = (batch + warps - 1) / warps;
cholesky64_phased_kernel<warps><<<
blocks,
warps * 32,
shared_bytes
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
return output;
}
} // namespace
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cholesky32_phased_half",
&cholesky32_phased_half_cuda
);
module.def(
"cholesky64_phased2",
&cholesky64_phased2_cuda
);
}
"""
_REGISTER_PANEL128_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 kPanel = 32;
constexpr int kMatrixElements = kN * kN;
constexpr int kSharedBytes = kN * kPitch * sizeof(float);
template <int Threads>
__global__ __launch_bounds__(Threads, 2)
void cholesky128_register_panel_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
static_assert(Threads == 256 || Threads == 384);
constexpr int warps = Threads / 32;
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 += Threads
) {
const int row = element >> 7;
const int col = element & 127;
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) {
float row_values[kPanel];
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
row_values[local_col] = tile[
(start + lane) * kPitch + start + local_col
];
}
constexpr unsigned mask = 0xffffffffu;
#pragma unroll
for (int pivot = 0; pivot < kPanel; ++pivot) {
float value = row_values[pivot];
#pragma unroll
for (int previous = 0; previous < pivot; ++previous) {
const float pivot_value = __shfl_sync(
mask,
row_values[previous],
pivot
);
value = fmaf(
-row_values[previous],
pivot_value,
value
);
}
float diagonal = 0.0f;
if (lane == pivot) {
diagonal = sqrtf(fmaxf(value, 0.0f));
}
diagonal = __shfl_sync(mask, diagonal, pivot);
if (lane == pivot) {
row_values[pivot] = diagonal;
} else if (lane > pivot) {
row_values[pivot] = value / diagonal;
}
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
tile[
(start + lane) * kPitch + start + local_col
] = row_values[local_col];
}
}
__syncthreads();
const int panel_end = start + kPanel;
const int remaining_rows = kN - panel_end;
if (thread < remaining_rows) {
const int row = panel_end + thread;
float row_values[kPanel];
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
row_values[local_col] =
tile[row * kPitch + start + local_col];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
const int col = start + local_col;
float value = row_values[local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-row_values[previous],
tile[col * kPitch + start + previous],
value
);
}
row_values[local_col] =
value / tile[col * kPitch + col];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
tile[row * kPitch + start + local_col] =
row_values[local_col];
}
}
__syncthreads();
const int trailing = kN - panel_end;
for (
int local_row = warp;
local_row < trailing;
local_row += warps
) {
const int row = panel_end + local_row;
for (
int local_col = lane;
local_col <= local_row;
local_col += 32
) {
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 += Threads
) {
const int row = element >> 7;
const int col = element & 127;
matrix_output[element] =
row >= col ? tile[row * kPitch + col] : 0.0f;
}
}
template <int Threads>
bool configure_kernel() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky128_register_panel_kernel<Threads>,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky128_register_panel_kernel<Threads>,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
void check_input(const 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");
}
template <int Threads>
torch::Tensor launch_kernel(torch::Tensor input) {
check_input(input);
static const bool configured = configure_kernel<Threads>();
TORCH_CHECK(configured, "failed to configure shared memory");
auto output = torch::empty_like(input);
const int batch = static_cast<int>(input.size(0));
cholesky128_register_panel_kernel<Threads><<<
batch,
Threads,
kSharedBytes
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
torch::Tensor cholesky128_register256_cuda(torch::Tensor input) {
return launch_kernel<256>(input);
}
torch::Tensor cholesky128_register384_cuda(torch::Tensor input) {
return launch_kernel<384>(input);
}
} // namespace
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cholesky128_register256",
&cholesky128_register256_cuda
);
module.def(
"cholesky128_register384",
&cholesky128_register384_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);
}
"""
_CUDA256_PACKED_WIDE_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 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;
}
template <int Threads>
__global__ __launch_bounds__(Threads, 1)
void cholesky256_packed_wide_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
extern __shared__ __align__(32) float packed[];
constexpr int kWarps = Threads / 32;
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 row = warp; row < kN; row += kWarps) {
const int input_row = row * kN;
const int packed_row = packed_offset(row, 0);
for (int col = lane; col <= row; col += 32) {
packed[packed_row + col] = matrix_input[input_row + col];
}
}
__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 += Threads
) {
#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;
for (
int local_row = warp;
local_row < trailing;
local_row += kWarps
) {
const int row = panel_end + local_row;
const int row_offset = packed_offset(row, 0);
for (
int local_col = lane;
local_col <= local_row;
local_col += 32
) {
const int col = panel_end + local_col;
float value = packed[row_offset + col];
#pragma unroll
for (int previous = 0; previous < kPanel; ++previous) {
value = fmaf(
-packed[
row_offset
+ start
+ previous
],
packed[
packed_offset(
col,
start + previous
)
],
value
);
}
packed[row_offset + col] = value;
}
}
__syncthreads();
}
for (
int element = thread;
element < kMatrixElements;
element += Threads
) {
const int row = element >> 8;
const int col = element & (kN - 1);
matrix_output[element] =
row >= col ? packed[packed_offset(row, col)] : 0.0f;
}
}
template <int Threads>
bool configure_cholesky256_packed_wide() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky256_packed_wide_kernel<Threads>,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky256_packed_wide_kernel<Threads>,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
template <int Threads>
torch::Tensor launch_cholesky256_packed_wide(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_wide<Threads>();
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_wide_kernel<Threads><<<
batch,
Threads,
kSharedBytes
>>>(
input.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
} // namespace
torch::Tensor cholesky256_packed_512_cuda(torch::Tensor input) {
return launch_cholesky256_packed_wide<512>(input);
}
torch::Tensor cholesky256_packed_1024_cuda(torch::Tensor input) {
return launch_cholesky256_packed_wide<1024>(input);
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cholesky256_packed_512",
&cholesky256_packed_512_cuda
);
module.def(
"cholesky256_packed_1024",
&cholesky256_packed_1024_cuda
);
}
"""
_CUDA256_CLUSTER2_SOURCE = r"""
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cooperative_groups.h>
#include <c10/cuda/CUDAException.h>
namespace {
namespace cg = cooperative_groups;
constexpr int kN = 256;
constexpr int kPanel = 32;
constexpr int kDiagonalPitch = kPanel + 1;
constexpr int kThreads = 512;
constexpr int kWarps = kThreads / 32;
constexpr int kClusterBlocks = 2;
constexpr int kClusterWarps = kWarps * kClusterBlocks;
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__ __launch_bounds__(kThreads, 1)
void __cluster_dims__(kClusterBlocks, 1, 1) cholesky256_cluster2_kernel(
const float* __restrict__ input,
float* __restrict__ output,
int batch
) {
extern __shared__ __align__(32) float local_packed[];
__shared__ float diagonal_tile[kPanel * kDiagonalPitch];
cg::cluster_group cluster = cg::this_cluster();
const int cluster_block = static_cast<int>(cluster.block_rank());
const int matrix =
static_cast<int>(blockIdx.x) / kClusterBlocks;
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
// Interleave ranks so each CTA owns alternating lower rows. Contiguous
// rank ranges skew toward longer rows and leave CTA one with ~55% work.
// Give the slightly heavier parity to CTA zero because CTA one also fills
// its local factor cache before every trailing update.
const int cluster_warp =
warp * kClusterBlocks + (kClusterBlocks - 1 - cluster_block);
const long long matrix_offset =
static_cast<long long>(matrix) * kMatrixElements;
const float* matrix_input = input + matrix_offset;
float* matrix_output = output + matrix_offset;
// Every CTA must be resident before distributed shared-memory access.
cluster.sync();
float* packed = cluster.map_shared_rank(local_packed, 0);
// Thirty-two cluster warps load complete lower rows into CTA zero's
// packed shared allocation. Lanes write contiguous row segments.
for (
int row = cluster_warp;
row < kN;
row += kClusterWarps
) {
const int input_row = row * kN;
const int packed_row = packed_offset(row, 0);
for (int col = lane; col <= row; col += 32) {
packed[packed_row + col] = matrix_input[input_row + col];
}
}
cluster.sync();
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
// CTA zero stages and factors the diagonal tile with the baseline's
// FP32 fmaf ordering. Padding rotates shared banks across rows.
if (cluster_block == 0) {
for (
int local_row = warp;
local_row < kPanel;
local_row += kWarps
) {
if (lane <= local_row) {
diagonal_tile[
local_row * kDiagonalPitch + lane
] = packed[
packed_offset(start + local_row, start + lane)
];
}
}
__syncthreads();
if (warp == 0) {
#pragma unroll
for (
int local_col = 0;
local_col < kPanel;
++local_col
) {
if (lane == local_col) {
float value = diagonal_tile[
local_col * kDiagonalPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = diagonal_tile[
local_col * kDiagonalPitch + previous
];
value = fmaf(-item, item, value);
}
diagonal_tile[
local_col * kDiagonalPitch + local_col
] = sqrtf(fmaxf(value, 0.0f));
}
__syncwarp();
if (lane > local_col) {
float value = diagonal_tile[
lane * kDiagonalPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-diagonal_tile[
lane * kDiagonalPitch + previous
],
diagonal_tile[
local_col * kDiagonalPitch + previous
],
value
);
}
diagonal_tile[
lane * kDiagonalPitch + local_col
] = value / diagonal_tile[
local_col * kDiagonalPitch + local_col
];
}
__syncwarp();
}
}
__syncthreads();
// Publish the factored lower diagonal tile back to packed DSM.
for (
int local_row = warp;
local_row < kPanel;
local_row += kWarps
) {
if (lane <= local_row) {
packed[
packed_offset(start + local_row, start + lane)
] = diagonal_tile[
local_row * kDiagonalPitch + lane
];
}
}
}
cluster.sync();
// CTA one replicates the completed diagonal tile locally. CTA zero
// already owns the source tile. The local barrier is CTA-scoped.
if (cluster_block != 0) {
float* leader_diagonal =
cluster.map_shared_rank(diagonal_tile, 0);
for (
int local_row = warp;
local_row < kPanel;
local_row += kWarps
) {
if (lane <= local_row) {
diagonal_tile[
local_row * kDiagonalPitch + lane
] = leader_diagonal[
local_row * kDiagonalPitch + lane
];
}
}
}
__syncthreads();
// Alternating rows give each CTA half of the independent triangular
// solves. Register rows sharply reduce remote DSM traffic.
const int panel_end = start + kPanel;
const int row = panel_end + thread * kClusterBlocks + cluster_block;
if (row < kN) {
float values[kPanel];
const int row_offset = packed_offset(row, 0);
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
values[local_col] = packed[
row_offset + start + local_col
];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
float value = values[local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-values[previous],
diagonal_tile[
local_col * kDiagonalPitch + previous
],
value
);
}
values[local_col] = value / diagonal_tile[
local_col * kDiagonalPitch + local_col
];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
packed[row_offset + start + local_col] =
values[local_col];
}
}
cluster.sync();
// CTA one's dynamic allocation is otherwise idle. Cache the immutable
// solved panel columns locally once, replacing repeated remote factor
// reads during the Schur update with ordinary shared-memory loads.
const int trailing = kN - panel_end;
if (cluster_block != 0) {
const int factor_elements = trailing * kPanel;
for (
int element = thread;
element < factor_elements;
element += kThreads
) {
const int local_row = element / kPanel;
const int previous = element - local_row * kPanel;
const int factor_row = panel_end + local_row;
const int factor_offset = packed_offset(
factor_row,
start + previous
);
local_packed[factor_offset] = packed[factor_offset];
}
}
__syncthreads();
// Cluster warps own disjoint trailing rows. Lanes update contiguous
// lower columns and preserve the exact previous=0..31 fmaf order.
for (
int local_row = cluster_warp;
local_row < trailing;
local_row += kClusterWarps
) {
const int trailing_row = panel_end + local_row;
const int row_offset = packed_offset(trailing_row, 0);
for (
int local_col = lane;
local_col <= local_row;
local_col += 32
) {
const int col = panel_end + local_col;
float value = packed[row_offset + col];
#pragma unroll
for (int previous = 0; previous < kPanel; ++previous) {
value = fmaf(
-local_packed[
row_offset + start + previous
],
local_packed[
packed_offset(
col,
start + previous
)
],
value
);
}
packed[row_offset + col] = value;
}
}
cluster.sync();
}
// Cluster warps expand the packed factor and explicitly zero the upper
// triangle. Each warp writes contiguous 32-column row segments.
for (
int row = cluster_warp;
row < kN;
row += kClusterWarps
) {
const int output_row = row * kN;
const int packed_row = packed_offset(row, 0);
for (int col = lane; col < kN; col += 32) {
matrix_output[output_row + col] =
col <= row ? packed[packed_row + col] : 0.0f;
}
}
// CTA one reads CTA zero's distributed shared allocation above. Both
// blocks must finish those remote reads before the owning CTA exits.
cluster.sync();
}
bool configure_cholesky256_cluster2() {
const cudaError_t shared_result = cudaFuncSetAttribute(
cholesky256_cluster2_kernel,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
cholesky256_cluster2_kernel,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
torch::Tensor cholesky256_cluster2_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_cluster2();
TORCH_CHECK(configured, "failed to configure clustered kernel");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
cholesky256_cluster2_kernel<<<
batch * kClusterBlocks,
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_cluster2",
&cholesky256_cluster2_cuda
);
}
"""
_CUDA256_CLUSTER_WMMA_T512_ENCODED = (
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'p=7^|NAd$(w#6cNjLf*01<;k2Qy=?gThBOzKC5D?h?9A6?rg}jf=Qwa@;^#kPiX^;TYf*0&qC$JUuGRUG(L2v>ho3div|44BJrIi'
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'k4ax|Kv{jn$;*Fu^Yr=GW*FM(j3)I;m=WcO!0s3}h;M4HSo@Cq2dn<s8_hG^tgPWhI!ZLfNAbu=b@t|-fxte84$*XKQp{O4?r-'
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'8K#l-'
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'vN>N)S+s@<$u5Z_Bp;@pLSST#Y90bIcLjf|jicC0v30V(b2EO%;m=fCtTx|u4&Ecn-rW&(OwF*g@c81F>Jb==6V;n2+8cnR%h^(1'
'K!ft|inc5Xod`if1wV-'
'B<ZnwZ`NW5PfNyyt(LB{6WX~U|KwR~}<G_S6(j_I6E+kIrNN5o$~(y?RTTSvZ!rQyCP7RX0js?8SSx*X^T;oT%^ua$QCSCUQJAd='
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'V~}Ux75yJUpiD}BA&204I+5$&JXX1V^@8BN)sZy55!dnB#p`#qN4V`_fUJI+SXAdK5MFZrcF=-'
'7)jVQ8D7TVD!^{)R;QHk6h^gxpLi5+=+AyK)bj|XQ8k6-'
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'-L0t9k)<P)4ZXdlZF~AfpRE~|kuYw5SMQ<st4z{B{9$_}`4L3fGK`^9q*at3F9TAGlBBTSEsi(ZBjo?`9*o*aRf4%FNm;7A4Vs_k'
'#%J@UXS;@HO|#R~=xpBP^d(6Z)2*rbzuyK)ueE#Mu~qrIZLhIIpJA~+qoHox7HrWHY*E&)k5oUB-'
';T+T$75eG)Euxk$%`8%F=^5*bD5l|zf$gX9?(k~4`2!9+7Dpi__#cKFF$?I$tyYCVdvj)zDbn4MK@}R{Q9K;aS|TR{`hQVu$6VEo'
'y&69sg)QxM`NBP*H-'
'x2NwC6#Y(}o8;mr)x_@;6jE2_WjzmUaeYZlDW(@I*9)G3R#YF2G(>DE(Hk5b#*168Q)Y@m79ELHO&qMhJ{Zs(pKk1X%dwOTEH|8F'
'$<05>AQ*P8Ee;YB;)jVhKntyZw};qCj=SMKSnv(w+&d}M&Pln}MkBYWaP%6y4i5scuy!o8eT8LwJ8CxBNnD74#m3)b%7D>s^rM%O'
'P<l~uu@k$(B^_-L;s<-'
's~%aGgz%J1!Z+ji{0Y<}<bld%@qVeaI<khw0&PvIH{ZAlm5;733%fk(LE__TYL7TrPpVvIQgUlgB;0(#ZdG)~paEAH&_4t0h!k2K'
'iTmdqvo-LIJ<1Wx9E#tU8~YF0+`FmwIyhVDm+G=Z3*G6F4$#b>m0|Hi;G)*B;0GA}S0Fd~Oun9$tY{cVv0+dE`q<=9#|mh4xVDxq'
'IDP=PSs!l;heBHy+31>hPKnsGfPMxs+;WGMVVY@M%WfMV5?t5Sz$iNf>B`B~WB%LQ(v7mv*2j7kNbo#fDOww5tkIB3g>BX=b7GCJ'
'1rGQqs%m@X$ricYiy3e}4AHee?X|d1<&gjJOn-Q+F_Swch>v*VpGShC}!Fw=X`vIcp1ZKl|5*v-'
'3Y*zdd))pZ|W=BXGZ9S=~(%zXm>&nxef%z3o+uKUyCSi)G!n{sW;CfUE'
)
_CUDA256_CLUSTER_WMMA_T512_SOURCE = zlib.decompress(
base64.b85decode(_CUDA256_CLUSTER_WMMA_T512_ENCODED)
).decode("utf-8")
if hashlib.sha256(
_CUDA256_CLUSTER_WMMA_T512_SOURCE.encode()
).hexdigest() != (
"9363da4ef287f84689ea056ce9e1dbcf6ff12f5d3263ba4f0178fc138f4d2b98"
):
raise RuntimeError("embedded n256 cluster WMMA source is corrupt")
_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) {
constexpr float kJitter =
N == 1024 ? 0.00390625f : 0.0f;
float value =
panel[local_col * kPanel + local_col]
+ kJitter;
#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
);
}
"""
_PERSISTENT_WMMA512_OPT_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 kN = 512;
constexpr int kPanel = 32;
constexpr int kThreads = 256;
constexpr int kWarps = kThreads / 32;
constexpr int kSharedBytes = kN * kPanel * sizeof(float);
__global__ void persistent_wmma512_opt_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ output,
int batch
) {
extern __shared__ __align__(32) 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) * kN * kN;
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 < kN; start += kPanel) {
const int row_tiles = (kN - 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) * kN
+ start
+ col_relative,
kN,
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) * kN
+ inner,
kN
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);
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);
}
__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);
}
__syncwarp();
}
}
__syncthreads();
for (
int row = start + kPanel + thread;
row < kN;
row += kThreads
) {
const int row_relative = row - start;
float values[kPanel];
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
values[local_col] =
panel[row_relative * kPanel + local_col];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
float value = values[local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-values[previous],
panel[local_col * kPanel + previous],
value
);
}
value /= panel[local_col * kPanel + local_col];
const half quantized = __float2half_rn(value);
values[local_col] = __half2float(quantized);
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
panel[row_relative * kPanel + local_col] =
values[local_col];
}
}
__syncthreads();
const int panel_elements = (kN - start) * kPanel;
for (
int element = thread;
element < panel_elements;
element += kThreads
) {
const int row_relative = element / kPanel;
const int local_col = element - row_relative * kPanel;
if (local_col <= row_relative) {
const int row = start + row_relative;
const long long output_index =
static_cast<long long>(row) * kN
+ start
+ local_col;
const float value = panel[element];
matrix_history[output_index] = __float2half_rn(value);
matrix_output[output_index] = value;
}
}
__syncthreads();
}
for (
int element = thread;
element < kN * kN;
element += kThreads
) {
const int row = element / kN;
const int col = element - row * kN;
if (col > row) {
matrix_output[element] = 0.0f;
}
}
}
bool configure_persistent_wmma512_opt() {
const cudaError_t shared_result = cudaFuncSetAttribute(
persistent_wmma512_opt_kernel,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
persistent_wmma512_opt_kernel,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
} // namespace
torch::Tensor persistent_wmma512_opt_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 dimension must be 512"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
static const bool configured = configure_persistent_wmma512_opt();
TORCH_CHECK(configured, "failed to configure n=512 kernel");
persistent_wmma512_opt_kernel<<<
batch,
kThreads,
kSharedBytes
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(history.data_ptr<at::Half>()),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"persistent_wmma512_opt",
&persistent_wmma512_opt_cuda
);
}
"""
_PERSISTENT_WMMA512_OPT_512T_SOURCE = (
_PERSISTENT_WMMA512_OPT_SOURCE.replace(
"constexpr int kThreads = 256;",
"constexpr int kThreads = 512;",
).replace(
"persistent_wmma512_opt",
"persistent_wmma512_opt_512t",
)
)
_PERSISTENT_WMMA512_OPT_1024T_SOURCE = (
_PERSISTENT_WMMA512_OPT_SOURCE.replace(
"constexpr int kThreads = 256;",
"constexpr int kThreads = 1024;",
)
.replace(
"persistent_wmma512_opt",
"persistent_wmma512_opt_1024t",
)
.replace(
"__global__ void persistent_wmma512_opt_1024t_kernel(",
"__global__ __launch_bounds__(kThreads, 1)\n"
"void persistent_wmma512_opt_1024t_kernel(",
)
)
def _make_persistent_wmma512_multi2_source() -> str:
source = _PERSISTENT_WMMA512_OPT_SOURCE
comment_insertions = (
(
" for (int job = warp; job < tile_jobs; job += kWarps) {",
"""\
// Produce A[:, panel] - H[:, history] @ H[panel, history].T.
// Each warp owns complete 16x16 WMMA tiles.
for (int job = warp; job < tile_jobs; job += kWarps) {""",
),
(
" if (warp == 0) {",
"""\
// Warp zero factors the 32x32 diagonal tile. Every produced value is
// rounded to half before it can influence a later scalar operation.
if (warp == 0) {""",
),
(
"""\
for (
int row = start + kPanel + thread;""",
"""\
// Each below-diagonal row is independent. Keeping its 32 entries in
// a scalarized register array removes the repeated pitch-32 shared
// accesses from the dependency chain. Quantization occurs at exactly
// the same point as in the baseline kernel.
for (
int row = start + kPanel + thread;""",
),
(
" const int panel_elements = (kN - start) * kPanel;",
"""\
// Publish the completed block column only after every row solve has
// finished. Linear panel indexing maps each warp to one contiguous
// 32-value row for coalesced history and output stores.
const int panel_elements = (kN - start) * kPanel;""",
),
(
"""\
for (
int element = thread;
element < kN * kN;""",
"""\
// Every lower entry was emitted panel by panel. Initialize only the
// unused upper half of the FP32 result.
for (
int element = thread;
element < kN * kN;""",
),
)
for anchor, replacement in comment_insertions:
if source.count(anchor) != 1:
raise RuntimeError("unexpected comment insertion layout")
source = source.replace(anchor, replacement)
include_anchor = "#include <mma.h>"
constants = """\
constexpr int kThreads = 256;
constexpr int kWarps = kThreads / 32;
constexpr int kSharedBytes = kN * kPanel * sizeof(float);"""
new_constants = """\
constexpr int kThreads = 512;
constexpr int kMatricesPerBlock = 2;
constexpr int kBlockThreads = kThreads * kMatricesPerBlock;
constexpr int kWarps = kThreads / 32;
constexpr int kSharedBytesPerMatrix =
kN * kPanel * sizeof(float);
constexpr int kSharedBytes =
kMatricesPerBlock * kSharedBytesPerMatrix;"""
old_kernel_start = """\
extern __shared__ __align__(32) 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;"""
new_kernel_start = """\
extern __shared__ __align__(32) float shared_panel[];
const int block_thread = static_cast<int>(threadIdx.x);
const int matrix_group = block_thread / kThreads;
auto group = cg::tiled_partition<kThreads>(
cg::this_thread_block()
);
const int matrix =
static_cast<int>(blockIdx.x) * kMatricesPerBlock
+ matrix_group;
if (matrix >= batch) {
return;
}
const int thread = block_thread - matrix_group * kThreads;
const int lane = thread & 31;
const int warp = thread >> 5;
float* panel =
shared_panel + matrix_group * kN * kPanel;"""
old_declaration = "__global__ void persistent_wmma512_opt_multi2_kernel("
new_declaration = (
"__global__ __launch_bounds__(kBlockThreads, 1)\n"
"void persistent_wmma512_opt_multi2_kernel("
)
old_launch = """\
persistent_wmma512_opt_multi2_kernel<<<
batch,
kThreads,
kSharedBytes
>>>("""
new_launch = """\
const int blocks =
(batch + kMatricesPerBlock - 1) / kMatricesPerBlock;
persistent_wmma512_opt_multi2_kernel<<<
blocks,
kBlockThreads,
kSharedBytes
>>>("""
required = {
"include": source.count(include_anchor) == 1,
"constants": source.count(constants) == 1,
"kernel start": source.count(old_kernel_start) == 1,
}
if not all(required.values()):
raise RuntimeError(f"unexpected base source layout: {required}")
source = (
source.replace(
include_anchor,
include_anchor + "\n#include <cooperative_groups.h>",
)
.replace(
"namespace wmma = nvcuda::wmma;",
"namespace wmma = nvcuda::wmma;\nnamespace cg = cooperative_groups;",
)
.replace(
constants,
new_constants,
)
.replace(
"persistent_wmma512_opt",
"persistent_wmma512_opt_multi2",
)
)
if source.count(old_declaration) != 1:
raise RuntimeError("unexpected kernel declaration")
source = (
source.replace(
old_declaration,
new_declaration,
)
.replace(
old_kernel_start,
new_kernel_start,
)
.replace(
"__syncthreads();",
"group.sync();",
)
)
if source.count(old_launch) != 1:
raise RuntimeError("unexpected launch source layout")
return source.replace(old_launch, new_launch)
_PERSISTENT_WMMA512_MULTI2_SOURCE = (
_make_persistent_wmma512_multi2_source()
)
def _make_persistent_wmma512_multi2_stageright_source() -> str:
"""Build the repaired two-matrix CTA with a shared right operand."""
source = _PERSISTENT_WMMA512_OPT_SOURCE
constants = """\
constexpr int kThreads = 256;
constexpr int kWarps = kThreads / 32;
constexpr int kSharedBytes = kN * kPanel * sizeof(float);"""
new_constants = """\
constexpr int kThreads = 512;
constexpr int kMatricesPerBlock = 2;
constexpr int kBlockThreads = kThreads * kMatricesPerBlock;
constexpr int kWarps = kThreads / 32;
constexpr int kSharedBytesPerMatrix =
kN * kPanel * sizeof(float);
constexpr int kSharedBytes =
kMatricesPerBlock * kSharedBytesPerMatrix;"""
kernel_start = """\
extern __shared__ __align__(32) 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;"""
new_kernel_start = """\
extern __shared__ __align__(32) float shared_panel[];
const int block_thread = static_cast<int>(threadIdx.x);
const int matrix_group = block_thread / kThreads;
const int matrix =
static_cast<int>(blockIdx.x) * kMatricesPerBlock
+ matrix_group;
const int thread = block_thread - matrix_group * kThreads;
const int lane = thread & 31;
const int warp = thread >> 5;
float* panel =
shared_panel + matrix_group * kN * kPanel;"""
panel_loop = """\
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
const int row_tiles = (kN - start) / 16;"""
staged_panel_loop = """\
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
// The live FP32 residual occupies only
// (kN - start) * kPanel entries. Reuse the untouched tail for a
// compact row-major copy of H[start:start + kPanel, :start].
half* staged_right = reinterpret_cast<half*>(
panel + (kN - start) * kPanel
);
if (start != 0) {
for (
int staged_row = warp;
staged_row < kPanel;
staged_row += kWarps
) {
for (
int history_col = lane;
history_col < start;
history_col += 32
) {
staged_right[staged_row * start + history_col] =
matrix_history[
static_cast<long long>(
start + staged_row
) * kN
+ history_col
];
}
}
}
__syncthreads();
const int row_tiles = (kN - start) / 16;"""
right_load = """\
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);"""
staged_right_load = """\
wmma::load_matrix_sync(
right_fragment,
staged_right
+ col_relative * start
+ inner,
start
);"""
batch_setup = """\
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);"""
even_batch_setup = """\
const int batch = static_cast<int>(input.size(0));
TORCH_CHECK(
batch % kMatricesPerBlock == 0,
"multi2 stageright requires an even batch"
);
auto output = torch::empty_like(input);"""
old_declaration = (
"__global__ void "
"persistent_wmma512_opt_multi2_stageright_kernel("
)
new_declaration = """\
__global__ __launch_bounds__(kBlockThreads, 1)
void persistent_wmma512_opt_multi2_stageright_kernel("""
old_launch = """\
persistent_wmma512_opt_multi2_stageright_kernel<<<
batch,
kThreads,
kSharedBytes
>>>("""
new_launch = """\
const int blocks = batch / kMatricesPerBlock;
persistent_wmma512_opt_multi2_stageright_kernel<<<
blocks,
kBlockThreads,
kSharedBytes
>>>("""
required = {
"constants": source.count(constants),
"kernel start": source.count(kernel_start),
"panel loop": source.count(panel_loop),
"right load": source.count(right_load),
"batch setup": source.count(batch_setup),
}
if required != {
"constants": 1,
"kernel start": 1,
"panel loop": 1,
"right load": 1,
"batch setup": 1,
}:
raise RuntimeError(
f"unexpected staged multi2 source layout: {required}"
)
source = (
source.replace(
"persistent_wmma512_opt",
"persistent_wmma512_opt_multi2_stageright",
)
.replace(constants, new_constants)
)
if source.count(old_declaration) != 1:
raise RuntimeError("unexpected staged multi2 declaration")
source = (
source.replace(old_declaration, new_declaration)
.replace(kernel_start, new_kernel_start)
.replace(panel_loop, staged_panel_loop)
.replace(right_load, staged_right_load)
.replace(batch_setup, even_batch_setup)
)
if source.count(old_launch) != 1:
raise RuntimeError("unexpected staged multi2 launch")
return source.replace(old_launch, new_launch)
_PERSISTENT_WMMA512_MULTI2_STAGERIGHT_SOURCE = (
_make_persistent_wmma512_multi2_stageright_source()
)
_PERSISTENT_WMMA512_PANEL16_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 kN = 512;
constexpr int kPanel = 16;
constexpr int kColumnTiles = kPanel / 16;
constexpr int kSharedBytes = kN * kPanel * sizeof(float);
template <int Threads>
__global__ __launch_bounds__(Threads, 1)
void persistent_wmma512_panel16_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ output,
int batch
) {
extern __shared__ __align__(32) float panel[];
constexpr int kWarps = Threads / 32;
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) * kN * kN;
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 < kN; start += kPanel) {
const int row_tiles = (kN - start) / 16;
const int tile_jobs = row_tiles * kColumnTiles;
for (int job = warp; job < tile_jobs; job += kWarps) {
const int row_tile = job / kColumnTiles;
const int col_tile = job - row_tile * kColumnTiles;
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) * kN
+ start
+ col_relative,
kN,
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) * kN
+ inner,
kN
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);
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);
}
__syncwarp();
if (lane < kPanel && 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);
}
__syncwarp();
}
}
__syncthreads();
for (
int row = start + kPanel + thread;
row < kN;
row += Threads
) {
const int row_relative = row - start;
float values[kPanel];
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
values[local_col] =
panel[row_relative * kPanel + local_col];
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
float value = values[local_col];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-values[previous],
panel[local_col * kPanel + previous],
value
);
}
value /= panel[local_col * kPanel + local_col];
const half quantized = __float2half_rn(value);
values[local_col] = __half2float(quantized);
}
#pragma unroll
for (int local_col = 0; local_col < kPanel; ++local_col) {
panel[row_relative * kPanel + local_col] =
values[local_col];
}
}
__syncthreads();
const int panel_elements = (kN - start) * kPanel;
for (
int element = thread;
element < panel_elements;
element += Threads
) {
const int row_relative = element / kPanel;
const int local_col = element - row_relative * kPanel;
if (local_col <= row_relative) {
const int row = start + row_relative;
const long long output_index =
static_cast<long long>(row) * kN
+ start
+ local_col;
const float value = panel[element];
matrix_history[output_index] = __float2half_rn(value);
matrix_output[output_index] = value;
}
}
__syncthreads();
}
for (
int element = thread;
element < kN * kN;
element += Threads
) {
const int row = element / kN;
const int col = element - row * kN;
if (col > row) {
matrix_output[element] = 0.0f;
}
}
}
template <int Threads>
bool configure_persistent_wmma512_panel16() {
const cudaError_t shared_result = cudaFuncSetAttribute(
persistent_wmma512_panel16_kernel<Threads>,
cudaFuncAttributeMaxDynamicSharedMemorySize,
kSharedBytes
);
const cudaError_t carveout_result = cudaFuncSetAttribute(
persistent_wmma512_panel16_kernel<Threads>,
cudaFuncAttributePreferredSharedMemoryCarveout,
100
);
return shared_result == cudaSuccess && carveout_result == cudaSuccess;
}
template <int Threads>
torch::Tensor launch_persistent_wmma512_panel16(
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 dimension must be 512"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
static const bool configured =
configure_persistent_wmma512_panel16<Threads>();
TORCH_CHECK(configured, "failed to configure n=512 kernel");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
persistent_wmma512_panel16_kernel<Threads><<<
batch,
Threads,
kSharedBytes
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(history.data_ptr<at::Half>()),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
} // namespace
torch::Tensor persistent_wmma512_panel16_256_cuda(
torch::Tensor input
) {
return launch_persistent_wmma512_panel16<256>(input);
}
torch::Tensor persistent_wmma512_panel16_512_cuda(
torch::Tensor input
) {
return launch_persistent_wmma512_panel16<512>(input);
}
torch::Tensor persistent_wmma512_panel16_1024_cuda(
torch::Tensor input
) {
return launch_persistent_wmma512_panel16<1024>(input);
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"persistent_wmma512_panel16_256",
&persistent_wmma512_panel16_256_cuda
);
module.def(
"persistent_wmma512_panel16_512",
&persistent_wmma512_panel16_512_cuda
);
module.def(
"persistent_wmma512_panel16_1024",
&persistent_wmma512_panel16_1024_cuda
);
}
"""
_CLUSTER_WMMA512_SOURCE = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_fp16.h>
#include <cooperative_groups.h>
#include <mma.h>
namespace {
namespace cg = cooperative_groups;
namespace wmma = nvcuda::wmma;
constexpr int kN = 512;
constexpr int kPanel = 32;
constexpr int kPitch = kPanel + 1;
constexpr int kThreads = 512;
constexpr int kWarps = kThreads / 32;
constexpr int kClusterBlocks = 8;
constexpr int kSolveRows = kN / kClusterBlocks;
__global__ void __cluster_dims__(kClusterBlocks, 1, 1)
cluster_wmma_cholesky512_t512_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ workspace,
float* __restrict__ output,
int batch
) {
__shared__ float diagonal_tile[kPanel * kPitch];
__shared__ float solve_rows[kSolveRows * kPitch];
cg::cluster_group cluster = cg::this_cluster();
const int cluster_block = static_cast<int>(cluster.block_rank());
const int matrix =
static_cast<int>(blockIdx.x) / kClusterBlocks;
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
int cluster_warp;
if (cluster_block == 0 && warp < 4) {
cluster_warp = warp;
} else if (warp < 4) {
cluster_warp =
4
+ warp * (kClusterBlocks - 1)
+ cluster_block - 1;
} else {
cluster_warp =
4
+ 4 * (kClusterBlocks - 1)
+ (warp - 4) * kClusterBlocks
+ cluster_block;
}
const long long matrix_offset =
static_cast<long long>(matrix) * kN * kN;
const long long workspace_offset =
static_cast<long long>(matrix) * kN * kPanel;
const float* matrix_input = input + matrix_offset;
half* matrix_history = history + matrix_offset;
float* matrix_workspace = workspace + workspace_offset;
float* matrix_output = output + matrix_offset;
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
const int row_tiles = (kN - start) / 16;
const int tile_jobs = row_tiles * 2;
for (
int job = cluster_warp;
job < tile_jobs;
job += kWarps * kClusterBlocks
) {
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) * kN
+ start
+ col_relative,
kN,
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) * kN
+ inner,
kN
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);
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(
matrix_workspace
+ row_relative * kPanel
+ col_relative,
accumulator,
kPanel,
wmma::mem_row_major
);
}
if (cluster_block == 0) {
__syncthreads();
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
diagonal_tile[row * kPitch + column] =
matrix_workspace[element];
}
__syncthreads();
if (warp == 0) {
#pragma unroll
for (
int local_col = 0;
local_col < kPanel;
++local_col
) {
if (lane == local_col) {
float value = diagonal_tile[
local_col * kPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = diagonal_tile[
local_col * kPitch + previous
];
value = fmaf(-item, item, value);
}
diagonal_tile[
local_col * kPitch + local_col
] = __half2float(
__float2half_rn(
sqrtf(fmaxf(value, 0.0f))
)
);
}
__syncwarp();
if (lane > local_col) {
float value = diagonal_tile[
lane * kPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-diagonal_tile[
lane * kPitch + previous
],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
diagonal_tile[
lane * kPitch + local_col
] = __half2float(
__float2half_rn(value)
);
}
__syncwarp();
}
}
}
cluster.sync();
float* leader_tile =
cluster.map_shared_rank(diagonal_tile, 0);
const int solve_row_begin =
start + kPanel + cluster_block * kSolveRows;
const int remaining_rows = kN - solve_row_begin;
const int owned_rows = remaining_rows <= 0
? 0
: (remaining_rows < kSolveRows
? remaining_rows
: kSolveRows);
const bool owns_solve_rows = owned_rows != 0;
if (cluster_block != 0) {
if (owns_solve_rows) {
for (
int element = thread;
element < kPanel * kPitch;
element += kThreads
) {
diagonal_tile[element] = leader_tile[element];
}
}
} else {
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
matrix_workspace[element] =
diagonal_tile[row * kPitch + column];
}
}
if (owns_solve_rows) {
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int row = solve_row_begin + local_row;
solve_rows[
local_row * kPitch + local_col
] = matrix_workspace[
(row - start) * kPanel + local_col
];
}
__syncthreads();
if (thread < owned_rows) {
float* row_values =
solve_rows + thread * kPitch;
#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],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
row_values[local_col] = __half2float(
__float2half_rn(value)
);
}
}
__syncthreads();
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int solved_row =
solve_row_begin + local_row;
matrix_workspace[
(solved_row - start) * kPanel + local_col
] = solve_rows[
local_row * kPitch + local_col
];
}
}
cluster.sync();
for (
int row = cluster_warp;
row < kN;
row += kWarps * kClusterBlocks
) {
const int local_col = lane;
const int column = start + local_col;
const long long output_index =
static_cast<long long>(row) * kN + column;
if (column <= row) {
const int row_relative = row - start;
const float value = matrix_workspace[
row_relative * kPanel + local_col
];
matrix_history[output_index] =
__float2half_rn(value);
matrix_output[output_index] = value;
} else {
matrix_output[output_index] = 0.0f;
}
}
if (start + kPanel < kN) {
cluster.sync();
}
}
}
} // namespace
torch::Tensor cluster_wmma_cholesky512_t512_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(0) == 16
&& input.size(1) == kN
&& input.size(2) == kN,
"expected shape (16, 512, 512)"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
auto workspace = torch::empty(
{batch, kN, kPanel},
input.options()
);
cluster_wmma_cholesky512_t512_kernel<<<
batch * kClusterBlocks,
kThreads
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(
history.data_ptr<at::Half>()
),
workspace.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cluster_wmma_cholesky512_t512",
&cluster_wmma_cholesky512_t512_cuda
);
}
"""
_CLUSTER_WMMA1024_SOURCE = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_fp16.h>
#include <cooperative_groups.h>
#include <mma.h>
namespace {
namespace cg = cooperative_groups;
namespace wmma = nvcuda::wmma;
constexpr int kN = 1024;
constexpr int kPanel = 32;
constexpr int kPitch = kPanel + 1;
constexpr int kThreads = 512;
constexpr int kSolveRows = 256;
constexpr int kWarps = kThreads / 32;
constexpr int kClusterBlocks = 4;
constexpr float kDiagonalJitter = 0.00390625f;
__global__ void __cluster_dims__(kClusterBlocks, 1, 1)
cluster_wmma_cholesky1024_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ workspace,
float* __restrict__ output,
int batch
) {
__shared__ float diagonal_tile[kPanel * kPitch];
__shared__ float solve_rows[kSolveRows * kPitch];
cg::cluster_group cluster = cg::this_cluster();
const int cluster_block = static_cast<int>(cluster.block_rank());
const int matrix =
static_cast<int>(blockIdx.x) / kClusterBlocks;
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
int cluster_warp;
if (cluster_block == 0 && warp < 4) {
cluster_warp = warp;
} else if (warp < 4) {
cluster_warp =
4
+ warp * (kClusterBlocks - 1)
+ cluster_block - 1;
} else {
cluster_warp =
4
+ 4 * (kClusterBlocks - 1)
+ (warp - 4) * kClusterBlocks
+ cluster_block;
}
const long long matrix_offset =
static_cast<long long>(matrix) * kN * kN;
const long long workspace_offset =
static_cast<long long>(matrix) * kN * kPanel;
const float* matrix_input = input + matrix_offset;
half* matrix_history = history + matrix_offset;
float* matrix_workspace = workspace + workspace_offset;
float* matrix_output = output + matrix_offset;
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
const int row_tiles = (kN - start) / 16;
const int tile_jobs = row_tiles * 2;
// Thirty-two warps across the cluster form the complete residual
// column. Each warp owns disjoint 16x16 tiles.
for (
int job = cluster_warp;
job < tile_jobs;
job += kWarps * kClusterBlocks
) {
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) * kN
+ start
+ col_relative,
kN,
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) * kN
+ inner,
kN
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);
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(
matrix_workspace
+ row_relative * kPanel
+ col_relative,
accumulator,
kPanel,
wmma::mem_row_major
);
}
// The four diagonal-tile jobs belong to warps zero through three of
// CTA zero. A local barrier is sufficient before that CTA starts the
// factorization; the later cluster barrier publishes every CTA's
// residual rows before any triangular solve.
if (cluster_block == 0) {
__syncthreads();
// Values are quantized before they can affect another pivot,
// matching the persistent history.
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
diagonal_tile[row * kPitch + column] =
matrix_workspace[element];
}
__syncthreads();
if (warp == 0) {
#pragma unroll
for (
int local_col = 0;
local_col < kPanel;
++local_col
) {
if (lane == local_col) {
float value =
diagonal_tile[
local_col * kPitch + local_col
]
+ kDiagonalJitter;
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = diagonal_tile[
local_col * kPitch + previous
];
value = fmaf(-item, item, value);
}
const float diagonal =
sqrtf(fmaxf(value, 0.0f));
const half quantized =
__float2half_rn(diagonal);
const float quantized_float =
__half2float(quantized);
diagonal_tile[
local_col * kPitch + local_col
] = quantized_float;
}
__syncwarp();
if (lane > local_col) {
float value = diagonal_tile[
lane * kPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-diagonal_tile[
lane * kPitch + previous
],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
const half quantized =
__float2half_rn(value);
const float quantized_float =
__half2float(quantized);
diagonal_tile[
lane * kPitch + local_col
] = quantized_float;
}
__syncwarp();
}
}
}
cluster.sync();
// Non-leaders copy the factored diagonal tile from distributed
// shared memory. The leader simultaneously stages that tile into
// the compact workspace for the deferred row-major emitter.
float* leader_tile =
cluster.map_shared_rank(diagonal_tile, 0);
const int solve_row_begin =
start + kPanel + cluster_block * kSolveRows;
const int remaining_rows = kN - solve_row_begin;
const int owned_rows = remaining_rows <= 0
? 0
: (remaining_rows < kSolveRows
? remaining_rows
: kSolveRows);
const bool owns_solve_rows = owned_rows != 0;
if (cluster_block != 0) {
if (owns_solve_rows) {
for (
int element = thread;
element < kPanel * kPitch;
element += kThreads
) {
diagonal_tile[element] = leader_tile[element];
}
}
} else {
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
matrix_workspace[element] =
diagonal_tile[row * kPitch + column];
}
}
if (owns_solve_rows) {
// Cooperatively stage this CTA's compact residual rows. Linear
// workspace accesses remain contiguous while the shared pitch
// rotates banks across the later one-row-per-thread solve.
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int row = solve_row_begin + local_row;
solve_rows[
local_row * kPitch + local_col
] = matrix_workspace[
(row - start) * kPanel + local_col
];
}
__syncthreads();
if (thread < owned_rows) {
float* row_values =
solve_rows + thread * kPitch;
#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],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
row_values[local_col] = __half2float(
__float2half_rn(value)
);
}
}
__syncthreads();
// Publish solved rows back to the compact workspace in the same
// contiguous cooperative order used by the staging load.
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int solved_row = solve_row_begin + local_row;
matrix_workspace[
(solved_row - start) * kPanel + local_col
] = solve_rows[
local_row * kPitch + local_col
];
}
}
cluster.sync();
// A cluster warp owns one complete output row at a time. Its lanes
// emit the 32 adjacent panel entries together, publishing valid
// factors and zeroing the strict-upper segments in the same pass.
for (
int row = cluster_warp;
row < kN;
row += kWarps * kClusterBlocks
) {
const int local_col = lane;
const int column = start + local_col;
const long long output_index =
static_cast<long long>(row) * kN + column;
if (column <= row) {
const int row_relative = row - start;
const float value = matrix_workspace[
row_relative * kPanel + local_col
];
matrix_history[output_index] =
__float2half_rn(value);
matrix_output[output_index] = value;
} else {
matrix_output[output_index] = 0.0f;
}
}
if (start + kPanel < kN) {
cluster.sync();
}
}
}
} // namespace
torch::Tensor cluster_wmma_cholesky1024_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 1024x1024"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
auto workspace = torch::empty(
{batch, kN, kPanel},
input.options()
);
cluster_wmma_cholesky1024_kernel<<<
batch * kClusterBlocks,
kThreads
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(
history.data_ptr<at::Half>()
),
workspace.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cluster_wmma_cholesky1024",
&cluster_wmma_cholesky1024_cuda
);
}
"""
_CLUSTER_WMMA2048_SOURCE = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_fp16.h>
#include <cooperative_groups.h>
#include <mma.h>
namespace {
namespace cg = cooperative_groups;
namespace wmma = nvcuda::wmma;
constexpr int kN = 2048;
constexpr int kPanel = 32;
constexpr int kPitch = kPanel + 1;
constexpr int kThreads = 512;
constexpr int kWarps = kThreads / 32;
constexpr int kClusterBlocks = 16;
constexpr int kSolveRows = kN / kClusterBlocks;
constexpr float kDiagonalJitter = 0.0009765625f;
__global__ void __cluster_dims__(kClusterBlocks, 1, 1)
cluster_wmma_cholesky2048_kernel(
const float* __restrict__ input,
half* __restrict__ history,
float* __restrict__ workspace,
float* __restrict__ output,
int batch
) {
__shared__ float diagonal_tile[kPanel * kPitch];
__shared__ float solve_rows[kSolveRows * kPitch];
cg::cluster_group cluster = cg::this_cluster();
const int cluster_block = static_cast<int>(cluster.block_rank());
const int matrix =
static_cast<int>(blockIdx.x) / kClusterBlocks;
if (matrix >= batch) {
return;
}
const int thread = static_cast<int>(threadIdx.x);
const int lane = thread & 31;
const int warp = thread >> 5;
// Keep the four diagonal jobs on CTA zero, then enumerate remaining
// warps in warp-major order. Late panels have fewer, more expensive
// jobs; this permutation spreads them across the full cluster instead
// of concentrating them on the lowest CTA ranks.
int cluster_warp;
if (cluster_block == 0 && warp < 4) {
cluster_warp = warp;
} else if (warp < 4) {
cluster_warp =
4
+ warp * (kClusterBlocks - 1)
+ cluster_block - 1;
} else {
cluster_warp =
4
+ 4 * (kClusterBlocks - 1)
+ (warp - 4) * kClusterBlocks
+ cluster_block;
}
const long long matrix_offset =
static_cast<long long>(matrix) * kN * kN;
const long long workspace_offset =
static_cast<long long>(matrix) * kN * kPanel;
const float* matrix_input = input + matrix_offset;
half* matrix_history = history + matrix_offset;
float* matrix_workspace = workspace + workspace_offset;
float* matrix_output = output + matrix_offset;
#pragma unroll 1
for (int start = 0; start < kN; start += kPanel) {
const int row_tiles = (kN - start) / 16;
const int tile_jobs = row_tiles * 2;
// All 128 cluster warps cooperatively form the full N-by-32
// left-looking residual column in compact global workspace.
for (
int job = cluster_warp;
job < tile_jobs;
job += kWarps * kClusterBlocks
) {
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) * kN
+ start
+ col_relative,
kN,
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) * kN
+ inner,
kN
);
wmma::load_matrix_sync(
right_fragment,
matrix_history
+ static_cast<long long>(
start + col_relative
) * kN
+ inner,
kN
);
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(
matrix_workspace
+ row_relative * kPanel
+ col_relative,
accumulator,
kPanel,
wmma::mem_row_major
);
}
// The diagonal residual jobs are always among CTA zero's first
// four warps, so it can factor while other CTAs finish their rows.
if (cluster_block == 0) {
__syncthreads();
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
diagonal_tile[row * kPitch + column] =
matrix_workspace[element];
}
__syncthreads();
if (warp == 0) {
#pragma unroll
for (
int local_col = 0;
local_col < kPanel;
++local_col
) {
if (lane == local_col) {
float value =
diagonal_tile[
local_col * kPitch + local_col
]
+ kDiagonalJitter;
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
const float item = diagonal_tile[
local_col * kPitch + previous
];
value = fmaf(-item, item, value);
}
const half quantized = __float2half_rn(
sqrtf(fmaxf(value, 0.0f))
);
diagonal_tile[
local_col * kPitch + local_col
] = __half2float(quantized);
}
__syncwarp();
if (lane > local_col) {
float value = diagonal_tile[
lane * kPitch + local_col
];
#pragma unroll
for (
int previous = 0;
previous < local_col;
++previous
) {
value = fmaf(
-diagonal_tile[
lane * kPitch + previous
],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
diagonal_tile[
lane * kPitch + local_col
] = __half2float(
__float2half_rn(value)
);
}
__syncwarp();
}
}
}
cluster.sync();
// Copy the leader's factored diagonal tile through distributed
// shared memory and solve one disjoint 128-row slice per CTA.
float* leader_tile =
cluster.map_shared_rank(diagonal_tile, 0);
const int solve_row_begin =
start + kPanel + cluster_block * kSolveRows;
const int remaining_rows = kN - solve_row_begin;
const int owned_rows = remaining_rows <= 0
? 0
: (remaining_rows < kSolveRows
? remaining_rows
: kSolveRows);
const bool owns_solve_rows = owned_rows != 0;
if (cluster_block != 0) {
if (owns_solve_rows) {
for (
int element = thread;
element < kPanel * kPitch;
element += kThreads
) {
diagonal_tile[element] = leader_tile[element];
}
}
} else {
for (
int element = thread;
element < kPanel * kPanel;
element += kThreads
) {
const int row = element / kPanel;
const int column = element - row * kPanel;
matrix_workspace[element] =
diagonal_tile[row * kPitch + column];
}
}
if (owns_solve_rows) {
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int row = solve_row_begin + local_row;
solve_rows[
local_row * kPitch + local_col
] = matrix_workspace[
(row - start) * kPanel + local_col
];
}
__syncthreads();
if (thread < owned_rows) {
float* row_values =
solve_rows + thread * kPitch;
#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],
diagonal_tile[
local_col * kPitch + previous
],
value
);
}
value /= diagonal_tile[
local_col * kPitch + local_col
];
row_values[local_col] = __half2float(
__float2half_rn(value)
);
}
}
__syncthreads();
for (
int element = thread;
element < owned_rows * kPanel;
element += kThreads
) {
const int local_row = element / kPanel;
const int local_col =
element - local_row * kPanel;
const int solved_row = solve_row_begin + local_row;
matrix_workspace[
(solved_row - start) * kPanel + local_col
] = solve_rows[
local_row * kPitch + local_col
];
}
}
cluster.sync();
// Cluster warps publish complete 32-value rows. This also zeros
// every strict-upper output segment without a separate kernel.
for (
int row = cluster_warp;
row < kN;
row += kWarps * kClusterBlocks
) {
const int local_col = lane;
const int column = start + local_col;
const long long output_index =
static_cast<long long>(row) * kN + column;
if (column <= row) {
const int row_relative = row - start;
const float value = matrix_workspace[
row_relative * kPanel + local_col
];
matrix_history[output_index] =
__float2half_rn(value);
matrix_output[output_index] = value;
} else {
matrix_output[output_index] = 0.0f;
}
}
if (start + kPanel < kN) {
cluster.sync();
}
}
}
} // namespace
torch::Tensor cluster_wmma_cholesky2048_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(0) == 8
&& input.size(1) == kN
&& input.size(2) == kN,
"expected shape (8, 2048, 2048)"
);
TORCH_CHECK(input.is_contiguous(), "input must be contiguous");
const int batch = static_cast<int>(input.size(0));
auto output = torch::empty_like(input);
auto history = torch::empty(
input.sizes(),
input.options().dtype(at::kHalf)
);
auto workspace = torch::empty(
{batch, kN, kPanel},
input.options()
);
// A 16-CTA cluster is supported by B200 but exceeds the portable
// eight-CTA limit. The static caches this runtime mutation after the
// first warm-up invocation.
static const cudaError_t cluster_attribute_status =
cudaFuncSetAttribute(
cluster_wmma_cholesky2048_kernel,
cudaFuncAttributeNonPortableClusterSizeAllowed,
1
);
C10_CUDA_CHECK(cluster_attribute_status);
cluster_wmma_cholesky2048_kernel<<<
batch * kClusterBlocks,
kThreads
>>>(
input.data_ptr<float>(),
reinterpret_cast<half*>(
history.data_ptr<at::Half>()
),
workspace.data_ptr<float>(),
output.data_ptr<float>(),
batch
);
C10_CUDA_KERNEL_LAUNCH_CHECK();
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def(
"cluster_wmma_cholesky2048",
&cluster_wmma_cholesky2048_cuda
);
}
"""
_CLUSTER_WMMA1024_B4_SOURCE = (
_CLUSTER_WMMA2048_SOURCE.replace(
"constexpr int kN = 2048;",
"constexpr int kN = 1024;",
1,
)
.replace(
"constexpr float kDiagonalJitter = 0.0009765625f;",
"constexpr float kDiagonalJitter = 0.0015625f;",
1,
)
.replace(
"cluster_wmma_cholesky2048",
"cluster_wmma_cholesky1024_b4",
)
.replace(
"input.size(0) == 8",
"input.size(0) == 4",
1,
)
.replace(
"expected shape (8, 2048, 2048)",
"expected shape (4, 1024, 1024)",
1,
)
)
_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;
}
torch::Tensor half_history_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::kHalf, "left must be FP16");
TORCH_CHECK(right.scalar_type() == at::kHalf, "right must be FP16");
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<at::Half>(),
CUDA_R_16F,
right_leading,
right_batch,
left.data_ptr<at::Half>(),
CUDA_R_16F,
left_leading,
left_batch,
&beta,
output.data_ptr<float>(),
CUDA_R_32F,
output_leading,
output_batch,
batches,
CUBLAS_COMPUTE_32F,
CUBLAS_GEMM_DEFAULT_TENSOR_OP
);
TORCH_CHECK(
status == CUBLAS_STATUS_SUCCESS,
"cuBLAS half-history update failed"
);
return output;
}
torch::Tensor regular_bf16_update_2d_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() == 2, "left must have rank two");
TORCH_CHECK(right.dim() == 2, "right must have rank two");
TORCH_CHECK(output.dim() == 2, "output must have rank two");
TORCH_CHECK(left.device() == right.device(), "device mismatch");
TORCH_CHECK(left.device() == output.device(), "device mismatch");
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(0));
const int n = static_cast<int>(right.size(0));
const int k = static_cast<int>(left.size(1));
TORCH_CHECK(right.size(1) == k, "contracting dimension mismatch");
TORCH_CHECK(output.size(0) == m, "output row mismatch");
TORCH_CHECK(output.size(1) == n, "output column mismatch");
if (m == 0 || n == 0 || k == 0) {
return output;
}
const float alpha = -1.0f;
const float beta = 1.0f;
cublasHandle_t handle = at::cuda::getCurrentCUDABlasHandle();
const cublasStatus_t status = cublasGemmEx(
handle,
CUBLAS_OP_T,
CUBLAS_OP_N,
n,
m,
k,
&alpha,
right.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(right.stride(0)),
left.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(left.stride(0)),
&beta,
output.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(output.stride(0)),
CUBLAS_COMPUTE_32F_FAST_16F,
CUBLAS_GEMM_DEFAULT_TENSOR_OP
);
TORCH_CHECK(
status == CUBLAS_STATUS_SUCCESS,
"regular cuBLAS update failed"
);
return output;
}
torch::Tensor regular_half_history_update_2d_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::kHalf, "left must be FP16");
TORCH_CHECK(right.scalar_type() == at::kHalf, "right must be FP16");
TORCH_CHECK(output.scalar_type() == at::kFloat, "output must be FP32");
TORCH_CHECK(left.dim() == 2, "left must have rank two");
TORCH_CHECK(right.dim() == 2, "right must have rank two");
TORCH_CHECK(output.dim() == 2, "output must have rank two");
TORCH_CHECK(left.device() == right.device(), "device mismatch");
TORCH_CHECK(left.device() == output.device(), "device mismatch");
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(0));
const int n = static_cast<int>(right.size(0));
const int k = static_cast<int>(left.size(1));
TORCH_CHECK(right.size(1) == k, "contracting dimension mismatch");
TORCH_CHECK(output.size(0) == m, "output row mismatch");
TORCH_CHECK(output.size(1) == n, "output column mismatch");
if (m == 0 || n == 0 || k == 0) {
return output;
}
const float alpha = -1.0f;
const float beta = 1.0f;
cublasHandle_t handle = at::cuda::getCurrentCUDABlasHandle();
const cublasStatus_t status = cublasGemmEx(
handle,
CUBLAS_OP_T,
CUBLAS_OP_N,
n,
m,
k,
&alpha,
right.data_ptr<at::Half>(),
CUDA_R_16F,
static_cast<int>(right.stride(0)),
left.data_ptr<at::Half>(),
CUDA_R_16F,
static_cast<int>(left.stride(0)),
&beta,
output.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(output.stride(0)),
CUBLAS_COMPUTE_32F,
CUBLAS_GEMM_DEFAULT_TENSOR_OP
);
TORCH_CHECK(
status == CUBLAS_STATUS_SUCCESS,
"regular cuBLAS half-history update failed"
);
return output;
}
torch::Tensor fast_product_2d_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() == 2, "left must have rank two");
TORCH_CHECK(right.dim() == 2, "right must have rank two");
TORCH_CHECK(output.dim() == 2, "output must have rank two");
TORCH_CHECK(left.device() == right.device(), "device mismatch");
TORCH_CHECK(left.device() == output.device(), "device mismatch");
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(0));
const int n = static_cast<int>(right.size(0));
const int k = static_cast<int>(left.size(1));
TORCH_CHECK(right.size(1) == k, "contracting dimension mismatch");
TORCH_CHECK(output.size(0) == m, "output row mismatch");
TORCH_CHECK(output.size(1) == n, "output column mismatch");
if (m == 0 || n == 0 || k == 0) {
return output;
}
const float alpha = 1.0f;
const float beta = 0.0f;
cublasHandle_t handle = at::cuda::getCurrentCUDABlasHandle();
const cublasStatus_t status = cublasGemmEx(
handle,
CUBLAS_OP_T,
CUBLAS_OP_N,
n,
m,
k,
&alpha,
right.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(right.stride(0)),
left.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(left.stride(0)),
&beta,
output.data_ptr<float>(),
CUDA_R_32F,
static_cast<int>(output.stride(0)),
CUBLAS_COMPUTE_32F_FAST_16F,
CUBLAS_GEMM_DEFAULT_TENSOR_OP
);
TORCH_CHECK(
status == CUBLAS_STATUS_SUCCESS,
"cuBLAS fast product failed"
);
return output;
}
PYBIND11_MODULE(TORCH_EXTENSION_NAME, module) {
module.def("bf16_update", &bf16_update_cuda);
module.def("half_history_update", &half_history_update_cuda);
module.def(
"regular_bf16_update_2d",
®ular_bf16_update_2d_cuda
);
module.def(
"regular_half_history_update_2d",
®ular_half_history_update_2d_cuda
);
module.def("fast_product_2d", &fast_product_2d_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 _cuda64_strided_extension():
return load_inline(
name="b200_column512_strided_inverse_v1",
cpp_sources="",
cuda_sources=_CUDA64_STRIDED_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _phased_small_extension():
return load_inline(
name="b200_cholesky_small_phased_v1",
cpp_sources="",
cuda_sources=_PHASED_SMALL_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _register_panel128_extension():
return load_inline(
name="b200_cholesky128_register_panel_dormant_v1",
cpp_sources="",
cuda_sources=_REGISTER_PANEL128_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 _cuda256_packed_wide_extension():
return load_inline(
name="b200_cholesky256_packed_wide_v1",
cpp_sources="",
cuda_sources=_CUDA256_PACKED_WIDE_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda256_cluster2_extension():
return load_inline(
name="b200_cholesky256_cluster2_fp32_dormant_v1",
cpp_sources="",
cuda_sources=_CUDA256_CLUSTER2_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cuda256_cluster_wmma_t512_extension():
return load_inline(
name="b200_cluster2_wmma_cholesky256_t512_integrated_v1",
cpp_sources="",
cuda_sources=_CUDA256_CLUSTER_WMMA_T512_SOURCE,
functions=None,
extra_cuda_cflags=[
"-O3",
"--use_fast_math",
"-Xptxas=-v",
],
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 _persistent_wmma512_opt_extension():
return load_inline(
name="b200_persistent_wmma512_opt_v1",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA512_OPT_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma512_opt_512t_extension():
return load_inline(
name="b200_persistent_wmma512_opt_512t_v2",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA512_OPT_512T_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma512_opt_1024t_extension():
return load_inline(
name="b200_persistent_wmma512_opt_1024t_v3",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA512_OPT_1024T_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma512_multi2_extension():
return load_inline(
name="b200_persistent_wmma512_multi2_dormant_v1",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA512_MULTI2_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma512_multi2_stageright_extension():
return load_inline(
name="b200_persistent_wmma512_multi2_stageright_v1",
cpp_sources="",
cuda_sources=(
_PERSISTENT_WMMA512_MULTI2_STAGERIGHT_SOURCE
),
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _persistent_wmma512_panel16_extension():
return load_inline(
name="b200_persistent_wmma512_panel16_v1",
cpp_sources="",
cuda_sources=_PERSISTENT_WMMA512_PANEL16_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cluster_wmma512_extension():
return load_inline(
name="b200_cluster8_wmma_cholesky512_t512_main_v1",
cpp_sources="",
cuda_sources=_CLUSTER_WMMA512_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cluster_wmma1024_extension():
return load_inline(
name="b200_cluster4_wmma_cholesky1024_interleaved_t512_v1",
cpp_sources="",
cuda_sources=_CLUSTER_WMMA1024_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cluster_wmma2048_extension():
return load_inline(
name="b200_cluster16_wmma_cholesky2048_t512_v1",
cpp_sources="",
cuda_sources=_CLUSTER_WMMA2048_SOURCE,
functions=None,
extra_cuda_cflags=["-O3", "--use_fast_math"],
with_cuda=True,
verbose=False,
)
@lru_cache(maxsize=1)
def _cluster_wmma1024_b4_extension():
return load_inline(
name="b200_cluster16_wmma_cholesky1024_b4_t512_v1",
cpp_sources="",
cuda_sources=_CLUSTER_WMMA1024_B4_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_fast_update_half_history_v4",
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_cholesky32_phased(data: torch.Tensor) -> torch.Tensor:
return _phased_small_extension().cholesky32_phased_half(data)
def _cuda_cholesky64_phased(data: torch.Tensor) -> torch.Tensor:
return _phased_small_extension().cholesky64_phased2(data)
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)
def _cuda_cholesky128_register256(
data: torch.Tensor,
) -> torch.Tensor:
return (
_register_panel128_extension()
.cholesky128_register256(data)
)
def _cuda_cholesky128_register384(
data: torch.Tensor,
) -> torch.Tensor:
return (
_register_panel128_extension()
.cholesky128_register384(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 _cuda_cholesky256_packed_512(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cuda256_packed_wide_extension()
.cholesky256_packed_512(data)
)
def _cuda_cholesky256_packed_1024(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cuda256_packed_wide_extension()
.cholesky256_packed_1024(data)
)
def _cuda_cholesky256_cluster2(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cuda256_cluster2_extension()
.cholesky256_cluster2(data)
)
def _cuda_cholesky256_cluster_wmma_t512(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cuda256_cluster_wmma_t512_extension()
.cluster_wmma_cholesky256_t512(data)
)
def _persistent_wmma_cholesky(data: torch.Tensor) -> torch.Tensor:
return (
_persistent_wmma_extension()
.persistent_wmma_cholesky(data)
)
def _persistent_wmma512_opt_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_opt_extension()
.persistent_wmma512_opt(data)
)
def _persistent_wmma512_opt_512t_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_opt_512t_extension()
.persistent_wmma512_opt_512t(data)
)
def _persistent_wmma512_opt_1024t_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_opt_1024t_extension()
.persistent_wmma512_opt_1024t(data)
)
def _persistent_wmma512_multi2_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_multi2_extension()
.persistent_wmma512_opt_multi2(data)
)
def _persistent_wmma512_multi2_stageright_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_multi2_stageright_extension()
.persistent_wmma512_opt_multi2_stageright(data)
)
def _persistent_wmma512_panel16_256_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_panel16_extension()
.persistent_wmma512_panel16_256(data)
)
def _persistent_wmma512_panel16_512_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_panel16_extension()
.persistent_wmma512_panel16_512(data)
)
def _persistent_wmma512_panel16_1024_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_persistent_wmma512_panel16_extension()
.persistent_wmma512_panel16_1024(data)
)
def _cluster_wmma512_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cluster_wmma512_extension()
.cluster_wmma_cholesky512_t512(data)
)
def _cluster_wmma1024_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cluster_wmma1024_extension()
.cluster_wmma_cholesky1024(data)
)
def _cluster_wmma2048_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cluster_wmma2048_extension()
.cluster_wmma_cholesky2048(data)
)
def _cluster_wmma1024_b4_cholesky(
data: torch.Tensor,
) -> torch.Tensor:
return (
_cluster_wmma1024_b4_extension()
.cluster_wmma_cholesky1024_b4(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,
)
def _half_history_update(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
return _fast_update_extension().half_history_update(
left,
right,
output,
)
def _regular_bf16_update_2d(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
return _fast_update_extension().regular_bf16_update_2d(
left,
right,
output,
)
def _regular_half_history_update_2d(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
return (
_fast_update_extension()
.regular_half_history_update_2d(
left,
right,
output,
)
)
def _fast_product_2d(
output: torch.Tensor,
left: torch.Tensor,
right: torch.Tensor,
) -> torch.Tensor:
return _fast_update_extension().fast_product_2d(
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_strided64(
data: torch.Tensor,
) -> torch.Tensor:
"""No-copy 64-wide inverse panels for batch=640, n=512."""
if tuple(data.shape) != (640, 512, 512):
raise ValueError(
f"unsupported strided column shape: {tuple(data.shape)}"
)
batch, n, _ = data.shape
factor = torch.zeros_like(data)
inverse = torch.empty(
(batch, 64, 64),
dtype=data.dtype,
device=data.device,
)
previous_precision = torch.get_float32_matmul_precision()
torch.set_float32_matmul_precision("high")
try:
for start in range(0, n, 64):
end = start + 64
column = data[:, start:, start:end].clone()
if start:
torch.baddbmm(
column,
factor[:, start:, :start],
factor[:, start:end, :start].transpose(-1, -2),
beta=1.0,
alpha=-1.0,
out=column,
)
_cuda64_strided_extension().cholesky64_inverse_strided_out(
column[:, :64, :],
factor[:, start:end, start:end],
inverse,
)
if end != n:
torch.bmm(
column[:, 64:, :],
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 _left_blocked_cholesky_regular_updates(
data: torch.Tensor,
block_size: int,
*,
inverse_panels: bool = False,
) -> torch.Tensor:
"""Left-looking path using ordinary rank-two cuBLAS updates."""
if data.ndim != 3 or data.shape[0] != 1:
raise ValueError("expected one matrix with a retained batch dimension")
if data.shape[-1] != data.shape[-2]:
raise ValueError("input must be square")
n = data.shape[-1]
if data.dtype != torch.float32 or n % block_size:
raise ValueError("expected FP32 input and a block divisor of n")
source = data[0]
factor = torch.zeros_like(source)
identity = (
torch.eye(
block_size,
dtype=data.dtype,
device=data.device,
)
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 = start + block_size
diagonal_input = source[start:end, start:end].clone()
if start:
_regular_bf16_update_2d(
diagonal_input,
factor[start:end, :start],
factor[start:end, :start],
)
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:
_regular_bf16_update_2d(
panel_input,
factor[end:, :start],
factor[start:end, :start],
)
if inverse_panels:
assert identity is not None
diagonal_inverse = torch.linalg.solve_triangular(
diagonal,
identity,
upper=False,
left=True,
)
panel = torch.mm(
panel_input,
diagonal_inverse.transpose(-1, -2),
)
else:
panel = torch.linalg.solve_triangular(
diagonal,
panel_input.transpose(-1, -2),
upper=False,
left=True,
).transpose(-1, -2)
factor[end:, start:end].copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor.unsqueeze(0)
def _half_factor_inverse_2d(
diagonal_input: torch.Tensor,
identity: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor]:
if diagonal_input.shape[-1] == 128:
factor, inverse = _cuda_cholesky128_inverse(
diagonal_input.unsqueeze(0).contiguous()
)
return factor[0], inverse[0]
factor = torch.linalg.cholesky_ex(
diagonal_input,
check_errors=False,
).L
inverse = torch.linalg.solve_triangular(
factor,
identity,
upper=False,
left=True,
)
return factor, inverse
def _half_factor_inverse_3d(
diagonal_input: torch.Tensor,
identity: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor]:
if diagonal_input.shape[-1] == 128:
return _cuda_cholesky128_inverse(diagonal_input.contiguous())
factor = torch.linalg.cholesky_ex(
diagonal_input,
check_errors=False,
).L
inverse = torch.linalg.solve_triangular(
factor,
identity,
upper=False,
left=True,
)
return factor, inverse
def _half_history_cholesky_2d(
data: torch.Tensor,
block_size: int,
*,
fast_panel_product: bool = False,
) -> torch.Tensor:
"""One-matrix left-looking factorization with native FP16 history."""
n = data.shape[-1]
if data.ndim != 2 or data.shape[-2] != n:
raise ValueError("expected one square matrix")
if data.dtype != torch.float32 or n % block_size:
raise ValueError("expected FP32 input and a block divisor of n")
factor = torch.zeros_like(data)
history = torch.empty_like(data, dtype=torch.float16)
identity = torch.eye(
block_size,
dtype=data.dtype,
device=data.device,
)
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:
_half_history_update(
column,
history[start:, :start],
history[start:end, :start],
)
diagonal, diagonal_inverse = _half_factor_inverse_2d(
column[:block_size, :].contiguous(),
identity,
)
diagonal_history = history[start:end, start:end]
diagonal_history.copy_(diagonal)
factor[start:end, start:end].copy_(diagonal)
if end == n:
continue
panel = factor[end:, start:end]
if fast_panel_product:
_fast_product_2d(
panel,
column[block_size:, :],
diagonal_inverse,
)
else:
torch.mm(
column[block_size:, :],
diagonal_inverse.transpose(-1, -2),
out=panel,
)
panel_history = history[end:, start:end]
panel_history.copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _half_history_cholesky_2d_regular_updates(
data: torch.Tensor,
block_size: int,
) -> torch.Tensor:
"""FP16-history path using ordinary rank-two cuBLAS updates."""
n = data.shape[-1]
if data.ndim != 2 or data.shape[-2] != n:
raise ValueError("expected one square matrix")
if data.dtype != torch.float32 or n % block_size:
raise ValueError("expected FP32 input and a block divisor of n")
factor = torch.zeros_like(data)
history = torch.empty_like(data, dtype=torch.float16)
identity = torch.eye(
block_size,
dtype=data.dtype,
device=data.device,
)
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:
_regular_half_history_update_2d(
column,
history[start:, :start],
history[start:end, :start],
)
diagonal, diagonal_inverse = _half_factor_inverse_2d(
column[:block_size, :].contiguous(),
identity,
)
history[start:end, start:end].copy_(diagonal)
factor[start:end, start:end].copy_(diagonal)
if end == n:
continue
panel = factor[end:, start:end]
torch.mm(
column[block_size:, :],
diagonal_inverse.transpose(-1, -2),
out=panel,
)
history[end:, start:end].copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _tensor_fp8_history_scales_2d(
data: torch.Tensor,
diagonal_shift_fraction: float,
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""Return scalar E4M3 scales and an optional scale-invariant shift."""
max_diagonal = torch.diagonal(data).clamp_min(
torch.finfo(torch.float32).tiny
).amax()
diagonal_shift = max_diagonal * diagonal_shift_fraction
factor_bound = (max_diagonal + diagonal_shift).sqrt()
dequant_scale = (factor_bound / 384.0).clamp_min(
torch.finfo(torch.float32).tiny
)
return dequant_scale, dequant_scale.reciprocal(), diagonal_shift
def _tensor_fp8_history_cholesky_2d(
data: torch.Tensor,
block_size: int,
*,
diagonal_shift_fraction: float = 0.0,
) -> torch.Tensor:
"""FP32 factorization with a tensor-scaled E4M3 history shadow."""
n = data.shape[-1]
if data.ndim != 2 or data.shape[-2] != n:
raise ValueError("expected one square matrix")
if data.dtype != torch.float32 or n % block_size:
raise ValueError("expected FP32 input and a block divisor of n")
factor = torch.zeros_like(data)
history = torch.empty_like(data, dtype=torch.float8_e4m3fn)
dequant_scale, quant_scale, diagonal_shift = (
_tensor_fp8_history_scales_2d(
data,
diagonal_shift_fraction,
)
)
fp8_limit = float(torch.finfo(torch.float8_e4m3fn).max)
identity = torch.eye(
block_size,
dtype=data.dtype,
device=data.device,
)
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:
update = torch._scaled_mm(
history[start:, :start],
history[start:end, :start].transpose(0, 1),
dequant_scale,
dequant_scale,
out_dtype=torch.float32,
use_fast_accum=False,
)
column.sub_(update)
if diagonal_shift_fraction:
column[:block_size, :].diagonal().add_(diagonal_shift)
diagonal, diagonal_inverse = _half_factor_inverse_2d(
column[:block_size, :].contiguous(),
identity,
)
factor[start:end, start:end].copy_(diagonal)
if end < n:
torch.mm(
column[block_size:, :],
diagonal_inverse.transpose(-1, -2),
out=factor[end:, start:end],
)
normalized = (factor[start:, start:end] * quant_scale).clamp_(
-fp8_limit,
fp8_limit,
)
history[start:, start:end].copy_(normalized)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _half_history_cholesky_3d(
data: torch.Tensor,
block_size: int,
) -> torch.Tensor:
"""Batched left-looking factorization with native FP16 history."""
batch, n, columns = data.shape
if columns != n:
raise ValueError("expected square matrices")
if data.dtype != torch.float32 or n % block_size:
raise ValueError("expected FP32 input and a block divisor of n")
factor = torch.zeros_like(data)
history = torch.empty_like(data, dtype=torch.float16)
identity = torch.eye(
block_size,
dtype=data.dtype,
device=data.device,
).expand(batch, block_size, block_size)
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:
_half_history_update(
column,
history[:, start:, :start],
history[:, start:end, :start],
)
diagonal, diagonal_inverse = _half_factor_inverse_3d(
column[:, :block_size, :].contiguous(),
identity,
)
diagonal_history = history[:, start:end, start:end]
diagonal_history.copy_(diagonal)
factor[:, start:end, start:end].copy_(diagonal)
if end == n:
continue
panel = factor[:, end:, start:end]
torch.bmm(
column[:, block_size:, :],
diagonal_inverse.transpose(-1, -2),
out=panel,
)
panel_history = history[:, end:, start:end]
panel_history.copy_(panel)
finally:
torch.set_float32_matmul_precision(previous_precision)
return factor
def _giant_regular_update_candidate(
data: torch.Tensor,
) -> torch.Tensor:
"""Mirror giant routes with ordinary rank-two update calls."""
shape = tuple(data.shape)
if shape == (1, 8192, 8192):
return _left_blocked_cholesky_regular_updates(
data,
4096,
inverse_panels=False,
)
if shape == (1, 16384, 16384):
return _half_history_cholesky_2d_regular_updates(
data[0],
1024,
).unsqueeze(0)
if shape == (1, 32768, 32768):
return _half_history_cholesky_2d_regular_updates(
data[0],
512,
).unsqueeze(0)
raise ValueError(f"unsupported giant shape: {shape}")
def _dispatch_eager(data: torch.Tensor) -> torch.Tensor:
shape = tuple(data.shape)
if shape == (4096, 32, 32):
return _cuda_cholesky32(data)
if shape == (1024, 64, 64):
return _cuda_cholesky64_phased(data)
if shape == (256, 128, 128):
return _cuda_cholesky128_register256(data)
if shape == (64, 256, 256):
return _cuda_cholesky256_cluster_wmma_t512(data)
if shape == (16, 512, 512):
return _cluster_wmma512_cholesky(data)
if shape == (640, 512, 512):
return _column_blocked_batched_cholesky_strided64(data)
if shape == (4, 1024, 1024):
return _cluster_wmma1024_b4_cholesky(data)
if shape == (60, 1024, 1024):
return _cluster_wmma1024_cholesky(data)
if shape == (8, 2048, 2048):
return _cluster_wmma2048_cholesky(data)
if shape in {
(2, 2048, 2048),
(2, 4096, 4096),
}:
return _individual_cholesky(data)
if shape == (1, 8192, 8192):
return _left_blocked_cholesky(
data,
4096,
fast_updates=True,
)
if shape == (1, 16384, 16384):
return _tensor_fp8_history_cholesky_2d(
data[0],
1024,
).unsqueeze(0)
if shape == (1, 32768, 32768):
return _tensor_fp8_history_cholesky_2d(
data[0],
512,
diagonal_shift_fraction=0.1,
).unsqueeze(0)
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 = {}
width = graph_widths.get(shape)
if width is not None:
return _run_graphed(data, width)
return _dispatch_eager(data)
scrolls · 7800 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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