reasoning
reasoning (truncated 46865 chars): Let me analyze this task. I need to create a custom CUDA kernel that:
1. Takes quaternions and converts them to rotation matrices
2. Applies the rotation to points (matmul with R.T)
3. Adds translation
The reference implementation does:
1. Normalize quaternion
2. Convert quaternion to 3x3 rotation matrix
3. Transpose the rotation matrix
4. Matrix multiply points with R.T
5. Add translation
Let me write an optimized CUDA kernel for this. The key operations are:
- Quaternion normalization
- Rotation matrix computation from quaternion
- Batched matrix-vector multiplication (points @ R.T)
- Broadcasting addition of translation
Since B=8 and N=512, we have 8 * 512 = 4096 points total. This is a relatively small workload, so I need to be careful about kernel launch overhead.
Let me design the kernel:
Option 1: Single fused kernel that does everything
- Each thread handles one point (total 4096 threads)
- Each block handles one batch
- Load rotation matrix computed from quaternion into shared memory
Option 2: Two kernels
- Kernel 1: Compute rotation matrices from quaternions
- Kernel 2: Apply rotation and translation to points
For better memory access and reduced kernel launch overhead, let's go with a fused approach.
Let me write the kernel:
```cuda
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
__global__ void fused_quaternion_transform_kernel(
const float* __restrict__ points,
const float* __restrict__ quat,
const float* __restrict__ trans,
float* __restrict__ output,
const int batch_size,
const int num_points
) {
// Each thread handles one point
int tid = blockIdx.x * blockDim.x + threadIdx.x;
int batch_idx = tid / num_points;
int point_idx = tid % num_points;
if (batch_idx >= batch_size) return;
// Load quaternion for this batch
int quat_offset = batch_idx * 4;
float w = quat[quat_offset + 0];
float x = quat[quat_offset + 1];
float y = quat[quat_offset + 2];
float z = quat[quat_offset + 3];
// Normalize quaternion
float norm = sqrtf(w*w + x*x + y*y + z*z);
float inv_norm = 1.0f / (norm + 1e-8f);
w *= inv_norm;
x *= inv_norm;
y *= inv_norm;
z *= inv_norm;
// Compute rotation matrix elements
float xx = x*x, yy = y*y, zz = z*z;
float xy = x*y, xz = x*z, yz = y*z;
float wx = w*x, wy = w*y, wz = w*z;
// R is stored row-major: [R00, R01, R02, R10, R11, R12, R20, R21, R22]
// For p' = p @ R.T, we compute p' = p @ R^T
// If R^T has columns [R00, R10, R20], [R01, R11, R21], [R02, R12, R22]
// Then p'[0] = p[0]*R00 + p[1]*R10 + p[2]*R20
// p'[1] = p[0]*R01 + p[1]*R11 + p[2]*R21
// p'[2] = p[0]*R02 + p[1]*R12 + p[2]*R22
float R00 = 1.0f - 2.0f*(yy + zz);
float R01 = 2.0f*(xy - wz);
float R02 = 2.0f*(xz + wy);
float R10 = 2.0f*(xy + wz);
float R11 = 1.0f - 2.0f*(xx + zz);
float R12 = 2.0f*(yz - wx);
float R20 = 2.0f*(xz - wy);
float R21 = 2.0f*(yz + wx);
float R22 = 1.0f - 2.0f*(xx + yy);
// Load point
int point_offset = batch_idx * num_points * 3 + point_idx * 3;
float px = points[point_offset + 0];
float py = points[point_offset + 1];
float pz = points[point_offset + 2];
// Compute transformed point: p @ R.T
float out_x = px * R00 + py * R10 + pz * R20;
float out_y = px * R01 + py * R11 + pz * R21;
float out_z = px * R02 + py * R12 + pz * R22;
// Add translation
int trans_offset = batch_idx * 3;
out_x += trans[trans_offset + 0];
out_y += trans[trans_offset + 1];
out_z += trans[trans_offset + 2];
// Store result
output[point_offset + 0] = out_x;
output[point_offset + 1] = out_y;
output[point_offset + 2] = out_z;
}
torch::Tensor fused_quaternion_transform_cuda(
torch::Tensor points,
torch::Tensor quat,
torch::Tensor trans
) {
int batch_size = points.size(0);
int num_points = points.size(1);
auto output = torch::empty_like(points);
int total_threads = batch_size * num_points;
int block_size = 256;
int num_blocks = (total_threads + block_size - 1) / block_size;
fused_quaternion_transform_kernel<<<num_blocks, block_size>>>(
points.data_ptr<float>(),
quat.data_ptr<float>(),
trans.data_ptr<float>(),
output.data_ptr<float>(),
batch_size,
num_points
);
return output;
}
```
Wait, I should optimize this a bit more. Let me think about the memory access pattern and use shared memory for the rotation matrix.
Actually, with only 8 batches and 512 points per batch, the total threads is only 4096. Each thread does a fair amount of computation (normalizing quaternion, computing rotation matrix, matrix-vector multiplication). This might be compute-bound rather than memory-bound.
Let me think about optimizations:
1. Use shared memory to store the rotation matrix per block (but with 256 threads per block, threads from different batches might be in the same block)
2. Vectorize loads/stores using float4
3. Use register rotation matrix (current approach)
Actually, let me reconsider the threading. If I have 8 batches with 512 points each, and I launch with 256 threads per block:
- Total threads needed: 4096
- Number of blocks: 16
Each block processes 256 points. If 256 threads from the same block cover points from different batches, they'd need different rotation matrices. Let me check:
- Block 0: threads 0-255, covering batch 0 points 0-255
- Block 1: threads 256-511, covering batch 0 points 256-511
- Block 2: threads 512-767, covering batch 1 points 0-255
- ...
So each block processes points from one batch (or at most two batches at the boundary). This is good! We can use shared memory for the rotation matrix.
Actually, let me recalculate:
- Block 0: threads 0-255 → batch 0, points 0-255 (256 points)
- Block 1: threads 256-511 → batch 0, points 256-511 (256 points)
- Block 2: threads 512-767 → batch 1, points 0-255 (256 points)
- ...
- Block 15: threads 3840-4095 → batch 7, points 256-511 (256 points)
Each block handles exactly one batch (since 512 / 256 = 2 blocks per batch).
Actually wait, the division might not work out perfectly. Let me be more careful:
- Total points: 8 * 512 = 4096
- With 256 threads per block: ceil(4096/256) = 16 blocks
- Block 0 handles threads 0-255 (batch 0, points 0-255)
- Block 1 handles threads 256-511 (batch 0, points 256-511)
- ...
- Block 15 handles threads 3840-4095 (batch 7, points 256-511)
Hmm, but what if num_points isn't a multiple of block_size? Let me handle that case.
Actually, let me design a better approach:
- Use 1D grid with each thread handling one point
- Compute rotation matrix per thread (fast, just arithmetic)
- No shared memory needed for such small rotation matrices
Let me also consider using vectorized loads (float3 or float4) for better memory throughput.
Actually, let me try a simpler but correct implementation first, then optimize if needed:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
__global__ void fused_quaternion_transform_kernel(
const float* __restrict__ points,
const float* __restrict__ quat,
const float* __restrict__ trans,
float* __restrict__ output,
const int batch_size,
const int num_points
) {
const int tid = blockIdx.x * blockDim.x + threadIdx.x;
const int total_points = batch_size * num_points;
if (tid >= total_points) return;
const int batch_idx = tid / num_points;
const int point_idx = tid % num_points;
// Load quaternion for this batch
const float w = quat[batch_idx * 4 + 0];
const float x = quat[batch_idx * 4 + 1];
const float y = quat[batch_idx * 4 + 2];
const float z = quat[batch_idx * 4 + 3];
// Normalize quaternion
const
...[ omitted 46865 characters ]...
dx = blockIdx.y * blockDim.x + threadIdx.x;
if (point_idx >= num_points) return;
const int point_offset = (batch_idx * num_points + point_idx) * 3;
const float px = points[point_offset + 0];
const float py = points[point_offset + 1];
const float pz = points[point_offset + 2];
float out_x = px * R[0] + py * R[3] + pz * R[6];
float out_y = px * R[1] + py * R[4] + pz * R[7];
float out_z = px * R[2] + py * R[5] + pz * R[8];
out_x += t[0];
out_y += t[1];
out_z += t[2];
output[point_offset + 0] = out_x;
output[point_offset + 1] = out_y;
output[point_offset + 2] = out_z;
}
torch::Tensor fused_quaternion_transform_cuda(
torch::Tensor points,
torch::Tensor quat,
torch::Tensor trans
) {
const int batch_size = points.size(0);
const int num_points = points.size(1);
auto output = torch::empty_like(points);
const int block_size = 256;
const int blocks_per_batch = (num_points + block_size - 1) / block_size;
dim3 grid(batch_size, blocks_per_batch);
fused_quaternion_transform_kernel<<<grid, block_size>>>(
points.data_ptr<float>(),
quat.data_ptr<float>(),
trans.data_ptr<float>(),
output.data_ptr<float>(),
num_points
);
return output;
}
"""
cpp_source = """
torch::Tensor fused_quaternion_transform_cuda(
torch::Tensor points,
torch::Tensor quat,
torch::Tensor trans
);
"""
fused_transform = load_inline(
name='fused_quaternion_transform',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['fused_quaternion_transform_cuda'],
extra_cuda_cflags=['-O3'],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self):
super().__init__()
def forward(self, points, quat, trans):
return fused_transform.fused_quaternion_transform_cuda(points, quat, trans)
```
This should be a correct and efficient implementation. Let me submit it.
Wait, I should also handle the case where the input tensors might not be contiguous. Let me add `.contiguous()` calls or check for contiguity.
Actually, `torch::empty_like(points)` creates a tensor with the same shape and dtype as `points`, but it might have different memory layout. To ensure correct output, I should make sure the inputs are contiguous or handle strided access.
For simplicity, let me add `.contiguous()` to the inputs in the Python wrapper:
```python
def forward(self, points, quat, trans):
points = points.contiguous()
quat = quat.contiguous()
trans = trans.contiguous()
return fused_transform.fused_quaternion_transform_cuda(points, quat, trans)
```
But this might add overhead. Let me instead assume the inputs are contiguous (which is the default for PyTorch tensors created with `torch.randn`).
Actually, looking at the `get_inputs()` function:
```python
def get_inputs():
points = torch.randn(batch_size, num_points, 3)
quat = torch.randn(batch_size, 4)
trans = torch.randn(batch_size, 3)
return [points, quat, trans]
```
These tensors are created with `torch.randn`, which produces contiguous tensors by default. So I should be fine.
Let me also add a CUDA error check:
```cuda
C10_CUDA_CHECK(cudaGetLastError());
```
But this is typically done by PyTorch's CUDA utilities. Let me just submit the current implementation.
Actually, one more thing: I should use `torch::Tensor` instead of `torch::Tensor` in the function signature for const references to avoid unnecessary copies. Let me update the function signature:
```cpp
torch::Tensor fused_quaternion_transform_cuda(
const torch::Tensor& points,
const torch::Tensor& quat,
const torch::Tensor& trans
) {
...
}
```
Actually, looking at PyTorch's conventions, passing by value is fine since `torch::Tensor` is a smart pointer that doesn't copy the underlying data.
Let me finalize and submit:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
__global__ void fused_quaternion_transform_kernel(
const float* __restrict__ points,
const float* __restrict__ quat,
const float* __restrict__ trans,
float* __restrict__ output,
const int num_points
) {
__shared__ float R[9];
__shared__ float t[3];
const int batch_idx = blockIdx.x;
const int tid = threadIdx.x;
// First thread in block loads quaternion and computes rotation matrix
if (tid == 0) {
const float w = quat[batch_idx * 4 + 0];
const float x = quat[batch_idx * 4 + 1];
const float y = quat[batch_idx * 4 + 2];
const float z = quat[batch_idx * 4 + 3];
// Normalize quaternion
const float norm_sq = w*w + x*x + y*y + z*z;
const float norm = sqrtf(norm_sq);
const float inv_norm = 1.0f / fmaxf(norm, 1e-8f);
const float nw = w * inv_norm;
const float nx = x * inv_norm;
const float ny = y * inv_norm;
const float nz = z * inv_norm;
// Compute rotation matrix elements
const float xx = nx*nx, yy = ny*ny, zz = nz*nz;
const float xy = nx*ny, xz = nx*nz, yz = ny*nz;
const float wx = nw*nx, wy = nw*ny, wz = nw*nz;
R[0] = 1.0f - 2.0f*(yy + zz);
R[1] = 2.0f*(xy - wz);
R[2] = 2.0f*(xz + wy);
R[3] = 2.0f*(xy + wz);
R[4] = 1.0f - 2.0f*(xx + zz);
R[5] = 2.0f*(yz - wx);
R[6] = 2.0f*(xz - wy);
R[7] = 2.0f*(yz + wx);
R[8] = 1.0f - 2.0f*(xx + yy);
// Load translation
t[0] = trans[batch_idx * 3 + 0];
t[1] = trans[batch_idx * 3 + 1];
t[2] = trans[batch_idx * 3 + 2];
}
__syncthreads();
// Each thread handles one point
const int point_idx = blockIdx.y * blockDim.x + threadIdx.x;
if (point_idx >= num_points) return;
// Load point
const int point_offset = (batch_idx * num_points + point_idx) * 3;
const float px = points[point_offset + 0];
const float py = points[point_offset + 1];
const float pz = points[point_offset + 2];
// Compute transformed point: p @ R.T + t
float out_x = px * R[0] + py * R[3] + pz * R[6];
float out_y = px * R[1] + py * R[4] + pz * R[7];
float out_z = px * R[2] + py * R[5] + pz * R[8];
// Add translation
out_x += t[0];
out_y += t[1];
out_z += t[2];
// Store result
output[point_offset + 0] = out_x;
output[point_offset + 1] = out_y;
output[point_offset + 2] = out_z;
}
torch::Tensor fused_quaternion_transform_cuda(
torch::Tensor points,
torch::Tensor quat,
torch::Tensor trans
) {
const int batch_size = points.size(0);
const int num_points = points.size(1);
auto output = torch::empty_like(points);
const int block_size = 256;
const int blocks_per_batch = (num_points + block_size - 1) / block_size;
dim3 grid(batch_size, blocks_per_batch);
fused_quaternion_transform_kernel<<<grid, block_size>>>(
points.data_ptr<float>(),
quat.data_ptr<float>(),
trans.data_ptr<float>(),
output.data_ptr<float>(),
num_points
);
return output;
}
"""
cpp_source = """
torch::Tensor fused_quaternion_transform_cuda(
torch::Tensor points,
torch::Tensor quat,
torch::Tensor trans
);
"""
fused_transform = load_inline(
name='fused_quaternion_transform_v2',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['fused_quaternion_transform_cuda'],
extra_cuda_cflags=['-O3'],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self):
super().__init__()
def forward(self, points, quat, trans):
return fused_transform.fused_quaternion_transform_cuda(points, quat, trans)
```
This looks good. Let me submit this implementation.
call → submit_kernel
callsubmit_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__global__ void fused_quaternion_transform_kernel(\n const float* __restrict__ points,\n const float* __restrict__ quat,\n const float* __restrict__ trans,\n float* __restrict__ output,\n const int num_points\n) {\n __shared__ float R[9];\n __shared__ float t[3];\n \n const int batch_idx = blockIdx.x;\n const int tid = threadIdx.x;\n \n // First thread in block loads quaternion and computes rotation matrix\n if (tid == 0) {\n const float w = quat[batch_idx * 4 + 0];\n const float x = quat[batch_idx * 4 + 1];\n const float y = quat[batch_idx * 4 + 2];\n const float z = quat[batch_idx * 4 + 3];\n \n // Normalize quaternion\n const float norm_sq = w*w + x*x + y*y + z*z;\n const float norm = sqrtf(norm_sq);\n const float inv_norm = 1.0f / fmaxf(norm, 1e-8f);\n const float nw = w * inv_norm;\n const float nx = x * inv_norm;\n const float ny = y * inv_norm;\n const float nz = z * inv_norm;\n \n // Compute rotation matrix elements\n const float xx = nx*nx, yy = ny*ny, zz = nz*nz;\n const float xy = nx*ny, xz = nx*nz, yz = ny*nz;\n const float wx = nw*nx, wy = nw*ny, wz = nw*nz;\n \n R[0] = 1.0f - 2.0f*(yy + zz);\n R[1] = 2.0f*(xy - wz);\n R[2] = 2.0f*(xz + wy);\n R[3] = 2.0f*(xy + wz);\n R[4] = 1.0f - 2.0f*(xx + zz);\n R[5] = 2.0f*(yz - wx);\n R[6] = 2.0f*(xz - wy);\n R[7] = 2.0f*(yz + wx);\n R[8] = 1.0f - 2.0f*(xx + yy);\n \n // Load translation\n t[0] = trans[batch_idx * 3 + 0];\n t[1] = trans[batch_idx * 3 + 1];\n t[2] = trans[batch_idx * 3 + 2];\n }\n \n __syncthreads();\n \n // Each thread handles one point\n const int point_idx = blockIdx.y * blockDim.x + threadIdx.x;\n \n if (point_idx >= num_points) return;\n \n // Load point\n const int point_offset = (batch_idx * num_points + point_idx) * 3;\n const float px = points[point_offset + 0];\n const float py = points[point_offset + 1];\n const float pz = points[point_offset + 2];\n \n // Compute transformed point: p @ R.T + t\n float out_x = px * R[0] + py * R[3] + pz * R[6];\n float out_y = px * R[1] + py * R[4] + pz * R[7];\n float out_z = px * R[2] + py * R[5] + pz * R[8];\n \n // Add translation\n out_x += t[0];\n out_y += t[1];\n out_z += t[2];\n \n // Store result\n output[point_offset + 0] = out_x;\n output[point_offset + 1] = out_y;\n output[point_offset + 2] = out_z;\n}\n\ntorch::Tensor fused_quaternion_transform_cuda(\n torch::Tensor points,\n torch::Tensor quat,\n torch::Tensor trans\n) {\n const int batch_size = points.size(0);\n const int num_points = points.size(1);\n \n auto output = torch::empty_like(points);\n \n const int block_size = 256;\n const int blocks_per_batch = (num_points + block_size - 1) / block_size;\n \n dim3 grid(batch_size, blocks_per_batch);\n \n fused_quaternion_transform_kernel<<<grid, block_size>>>(\n points.data_ptr<float>(),\n quat.data_ptr<float>(),\n trans.data_ptr<float>(),\n output.data_ptr<float>(),\n num_points\n );\n \n return output;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_quaternion_transform_cuda(\n torch::Tensor points,\n torch::Tensor quat,\n torch::Tensor trans\n);\n\"\"\"\n\nfused_transform = load_inline(\n name='fused_quaternion_transform_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_quaternion_transform_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self):\n super().__init__()\n \n def forward(self, points, quat, trans):\n return fused_transform.fused_quaternion_transform_cuda(points, quat, trans)"
}