reasoning
Let me analyze the problem:
1. We need to implement a depthwise 2D convolution with potentially asymmetric kernel sizes.
2. The reference is `nn.Conv2d` with `groups=in_channels` (depthwise conv).
3. Input dimensions: batch=32, in_channels=128, height=128, width=256
4. Kernel: height=3, width=7
5. stride=1, padding=0, dilation=1
Key parameters for the test case:
- Batch size: 32
- In channels = 128 (groups = 128, so depthwise)
- Input: 128x256
- Kernel: 3x7
- Output: 126x250 with padding=0, stride=1
Let me think about how to optimize this. A depthwise convolution is memory-bound, so we want to maximize memory bandwidth utilization.
For depthwise conv with kernel 3x7 on H100:
- Input: 32 * 128 * 128 * 256 * 4 bytes ≈ 512 MB (fp32)
- Output: 32 * 128 * 126 * 250 * 4 bytes ≈ 483 MB
- Weights: 128 * 3 * 7 * 4 bytes ≈ 10.5 KB
Since it's a 3x7 kernel, we have 21 multiply-adds per output element. Total FLOPs: 32 * 128 * 126 * 250 * 21 ≈ 26.8 GFLOPs.
At 3.35 TB/s memory bandwidth, if we need to read input+weights+write output, we're memory-bound.
A good approach is to use a tiling strategy where we load input tiles into shared memory and compute multiple output pixels per thread to maximize data reuse.
For depthwise conv specifically, each output channel only depends on one input channel, so we can parallelize by:
1. Batch dimension
2. Channel dimension
3. Spatial dimensions (height, width)
Since we have 32 * 128 = 4096 positions in the batch*channel space, and output spatial is 126*250 = 31500, total parallel work is 4096 * 31500 = 129M output pixels.
For H100 with 132 SMs, we want good occupancy and coalesced memory access.
Let me design a kernel:
- Each thread block handles one or more (batch, channel) slices
- Within each block, threads collaborate to compute a tile of output
- Use shared memory for input tiles
A practical approach:
- One block per (batch, channel) pair - gives 4096 blocks
- Each block computes the full 126x250 output for one channel of one batch item
- We can have each thread compute multiple output pixels
With 4096 blocks and 132 SMs, each SM gets ~31 blocks.
For the block configuration:
- Let's try a 2D block: e.g., 16x16 = 256 threads
- Each thread computes a strip of outputs
- We can tile in the width dimension
For a 3x7 kernel with padding=0:
- To compute an output tile of height TH by width TW, we need input of height (TH + 2) by width (TW + 6)
- With shared memory of 227KB, we can fit quite a large tile.
Let's think about shared memory capacity per block:
- Max 227KB
- For fp32, that's about 56K elements
If we process a tile of input size HxW:
- For output tile 16x64, input needed is 18x70 = 1260 elements * 4 bytes = ~5KB per phase
- Actually we need more because of depth - we can process multiple rows at a time.
Let me think about a classic approach:
- Have each thread compute one output pixel
- Block size: e.g., 16x16
- Load a tile of input into shared memory including halo
- Compute conv using shared memory
- The halo for 3x7 kernel means we need +2 in H and +6 in W
For output tile of 16x16:
- Input tile = 18x22 = 396 elements * 4 bytes = ~1.6KB
- Very small, can fit many tiles or larger tiles
For output tile of 32x32:
- Input tile = 34x38 = 1292 elements * 4 bytes = ~5KB
For output tile of 64x64:
- Input tile = 66x70 = 4620 elements * 4 bytes = ~18KB
Let's try larger tiles to amortize the halo cost.
Actually, since our output is 126x250:
- We could have each block compute a 16x16 or 32x32 tile
- Number of tiles: ceil(126/16) * ceil(250/16) * 4096 = 8 * 16 * 4096 = 524,288 blocks
- That's a lot of blocks but should be fine
Actually wait - I should reconsider. For depthwise conv where each channel is independent, another approach is to have each warp or thread handle one channel and process multiple spatial locations.
Let me think about an even simpler but effective approach: direct convolution with coalesced loads and unrolled loops.
Since the kernel is only 3x7 = 21 elements, unrolling should be fine.
Design option:
- Block: (BLOCK_H, BLOCK_W) threads
- Grid: (batch, channel, spatial_tiles)
- Each thread computes one output element
- Read input directly from global memory
- The weights can be cached in registers (only 21 floats per thread, but all threads in a block share the same weights for a channel)
Wait, for depthwise conv, all threads processing the same channel use the same weights. So we can load weights into shared memory once per block.
Let me refine:
- Assign each block to one (batch, channel)
- Block has 2D threads: e.g., 16x16 or 32x8
- Load kernel weights (3*7=21 floats) to shared memory
- Each thread computes multiple output pixels via a grid-stride loop or direct indexing
With output 126x250 = 31500 pixels per (batch, channel):
- If block has 256 threads, each thread computes ~123 pixels - that's a lot
- If block has 1024 threads (max), each thread computes ~31 pixels
A better approach: use 2D thread blocks where each thread computes one output pixel, and have enough blocks to cover the output.
Block size: (16, 16) = 256 threads
Grid for spatial: ceil(126/16) x ceil(250/16) = 8 x 16 = 128 blocks per (batch, channel)
Total blocks: 128 * 4096 = 524,288 blocks
This gives small blocks but many of them. Might have overhead.
Alternative: larger blocks
Block size: (32, 32) = 1024 threads
Grid: ceil(126/32) x ceil(250/32) = 4 x 8 = 32 blocks per (batch, channel)
Total blocks: 32 * 4096 = 131,072 blocks
Each block loads the input tile with halo into shared memory.
For a 32x32 output tile with 3x7 kernel:
- Input tile = 34x38 = 1292 floats = ~5KB shared memory
- Weights = 21 floats
- Total ~5.1KB - very reasonable
Actually, let me think about memory access patterns more carefully.
Input dimensions: [batch=32, channels=128, height=128, width=256]
The memory layout is NCHW (PyTorch default).
For a given (batch, channel), the spatial layout is row-major: x[b, c, h, w].
Memory access for kernel 3x7:
To compute output at (h, w), we read input at:
(h+0, w+0..6), (h+1, w+0..6), (h+2, w+0..6)
If threads in a block are computing a tile, we want coalesced access when loading input to shared memory.
Let me design a kernel with these specifics:
```cuda
template<int BLOCK_H, int BLOCK_W>
__global__ void depthwise_conv2d_kernel(
const float* input,
const float* weight,
const float* bias,
float* output,
int batch_size,
int in_channels,
int in_height,
int in_width,
int out_height,
int out_width,
int kernel_h,
int kernel_w,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
) {
// Each block handles one (batch, channel) and a spatial tile
int b = blockIdx.z / in_channels;
int c = blockIdx.z % in_channels;
int tile_h = blockIdx.y * BLOCK_H;
int tile_w = blockIdx.x * BLOCK_W;
int h = tile_h + threadIdx.y;
int w = tile_w + threadIdx.x;
// Load weights to shared memory
__shared__ float s_weight[3][7]; // for kernel 3x7
if (threadIdx.y < 3 && threadIdx.x < 7) {
s_weight[threadIdx.y][threadIdx.x] = weight[c * kernel_h * kernel_w + threadIdx.y * kernel_w + threadIdx.x];
}
// Load input tile to shared memory
// Input tile covers [tile_h, tile_h + BLOCK_H + kernel_h - 1] x [tile_w, tile_w + BLOCK_W + kernel_w - 1]
__shared__ float s_input[BLOCK_H + 2][BLOCK_W + 6];
// Need to load the entire tile plus halo
// ...
__syncthreads();
// Compute convolution
if (h < out_height && w < out_width) {
float sum = 0.0f;
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
sum += s_input[threadIdx.y + kh][threadIdx.x + kw] * s_weight[kh][kw];
}
}
if (bias != nullptr) sum += bias[c];
output[((b * in_channels + c) * out_height + h) * out_width + w] = sum;
}
}
```
However, there's a subtlety: the test case uses `bias=False`, so we can ignore bias. But we should still support it in the general case.
Let me rethink the shared memory loading. For a 32x32 output tile with 3x7 kernel:
- We need 34x38 input elements
- With 1024 threads, each thread loads ~1.3 elements on average
- We can have each thread load multiple elements in a grid-stride pattern
Let me write a more careful version:
```cuda
// Shared memory dimensions
#define BLOCK_H 16
#define BLOCK_W 16
#define KERNEL_H 3
#define KERNEL_W 7
__shared__ float s_input[BLOCK_H + KERNEL_H - 1][BLOCK_W + KERNEL_W - 1];
int in_tile_h = BLOCK_H + KERNEL_H - 1; // 18
int in_tile_w = BLOCK_W + KERNEL_W - 1; // 22
int in_tile_size = in_tile_h * in_tile_w; // 396
// Each thread loads multiple elements
for (int idx = threadIdx.y * BLOCK_W + threadIdx.x; idx < in_tile_size; idx += BLOCK_H * BLOCK_W) {
int local_h = idx / in_tile_w;
int local_w = idx % in_tile_w;
int global_h = tile_h + local_h;
int global_w = tile_w + local_w;
if (global_h < in_height && global_w < in_width) {
s_input[local_h][local_w] = input[((b * in_channels + c) * in_height + global_h) * in_width + global_w];
} else {
s_input[local_h][local_w] = 0.0f;
}
}
```
Since 396 / 256 = 1.55, each thread loads 1 or 2 elements. This is very efficient.
Then after syncthreads, each thread computes at most one output:
```cuda
if (h < out_height && w < out_width) {
float sum = 0.0f;
#pragma unroll
for (int kh = 0; kh < KERNEL_H; kh++) {
#pragma unroll
for (int kw = 0; kw < KERNEL_W; kw++) {
sum += s_input[threadIdx.y + kh][threadIdx.x + kw] * s_weight[kh][kw];
}
}
output[...] = sum;
}
```
Since our kernel sizes (3x7) are constants in the test, we can use template parameters or just hardcode them. Actually, to be general, we should probably use runtime parameters but with `#pragma unroll` when possible, or template specializations. But for this test case, the kernel is fixed at 3x7.
Wait, but the model should work for any valid parameters. The problem says "accept the same constructor arguments" but the test is with specific parameters. We should make it general enough.
Actually, I'll write a general kernel but the performance will be optimized for the test case. Using dynamic kernel sizes with loops is fine as long as we pragma unroll when the compiler can determine the bounds... but with runtime parameters it can't.
Actually, for the specific test, the kernel sizes are fixed but passed as parameters. I'll write a general kernel. The compiler might still optimize small constant loops if we pass them as template parameters.
Let me create a template version where kernel sizes are template parameters. But `load_inline` makes this a bit tricky because we need to instantiate templates or use runtime dispatch.
Actually, a simpler approach: I'll write a general kernel that handles arbitrary kernel sizes, and since the test has small kernel (3x7), the overhead is minimal. I'll also add `#pragma unroll` hints where I can use `if constexpr` or just trust the compiler. In CUDA C++, we can't use `if constexpr` in device code before certain standards, but `#pragma unroll` with a constant expression should work if we template.
Let me write a templated kernel specialized for common cases, and instantiate it for 3x7.
Actually, for simplicity and correctness, let's just write a good general kernel. Since 3 and 7 are small, loop overhead is minimal.
Let me think about the best tile size:
- Output: 126x250
- Try BLOCK_H=16, BLOCK_W=16:
- Tiles: 8x16 = 128 per (b,c)
- Shared: 18x22 = 396 floats = 1.6KB
- Very small shared mem, high block count
- Try BLOCK_H=8, BLOCK_W=32:
- Tiles: 16x8 = 128 per (b,c)
- Shared: 10x38 = 380 floats = 1.5KB
- Try BLOCK_H=32, BLOCK_W=32:
- Tiles: 4x8 = 32 per (b,c)
- Shared: 34x38 = 1292 floats = 5.2KB
- Each thread gets 1292/1024 ≈ 1.26 loads
- Seems reasonable
Actually, let me check: output height = 128 - 3 + 1 = 126, width = 256 - 7 + 1 = 250.
With BLOCK_H=32, tile_h covers: 0, 32, 64, 96. Last tile goes to 128 but output is only 126, so threads 126-127 are inactive in height.
With BLOCK_W=32, tile_w covers: 0, 32, 64, 96, 128, 160, 192, 224. Last tile goes to 256 but output is only 250.
Total blocks per (b,c): 4 * 8 = 32
Total blocks: 32 * 4096 = 131,072
Blocks per SM: 131072 / 132 ≈ 993
That's a lot but should be fine.
Actually, H100 has high block throughput. Let me also consider occupancy.
With 1024 threads per block and max 32 blocks per SM, max threads per SM = 32*1024 = 32768, but H100 has 2048 threads per SM limit, so only 2 blocks of 1024 can run concurrently per SM. Wait, that doesn't seem right.
Let me recheck H100 specs. H100 has 128 or 144 SMs (depending on SKU). Max threads per SM is 2048. So with 1024-thread blocks, max 2 blocks per SM concurrently. With 256-thread blocks, max 8 blocks per SM.
Occupancy matters! With only 2 blocks per SM for 1024-thread blocks, if those blocks have high latency (e.g., waiting on shared memory), we have limited ability to hide latency.
Actually, for memory-bound kernels, higher occupancy helps hide latency. Let me consider smaller blocks.
Block size 256 (16x16):
- Max 8 blocks per SM
- Shared memory 1.6KB, so SM can hold many
- Total blocks: 524,288
- Blocks per SM: 524,288 / 132 ≈ 3973
- Good occupancy
Block size 128 (16x8):
- Max 16 blocks per SM
- Total blocks: ~1M
For this problem, I'll go with 16x16 blocks. Let me try both and see which is faster.
Actually, another consideration: the coarsening factor. If each thread computes multiple outputs, we can improve compute intensity.
For example, if each thread computes 2x2 outputs:
- Block size 16x16 threads computes 32x32 output tile
- Still use shared memory for input tile 34x38
- Each thread does 4 * 21 = 84 FMAs
- Better arithmetic intensity
Let me design a kernel where each thread computes a 2x2 block of outputs:
```cuda
// Each thread computes 2x2 outputs
const int OUT_PER_TH_H = 2;
const int OUT_PER_TH_W = 2;
// Block has 16x16 threads
// Computes 32x32 output tile
// Needs 34x38 input tile
int local_out_h = threadIdx.y * OUT_PER_TH_H; // 0, 2, 4, ..., 30
int local_out_w = threadIdx.x * OUT_PER_TH_W; // 0, 2, 4, ..., 30
float sum00 = 0, sum01 = 0, sum10 = 0, sum11 = 0;
for (int kh = 0; kh < KERNEL_H; kh++) {
for (int kw = 0; kw < KERNEL_W; kw++) {
float w = s_weight[kh][kw];
sum00 += s_input[local_out_h + kh][local_out_w + kw] * w;
sum01 += s_input[local_out_h + kh][local_out_w + kw + 1] * w;
sum10 += s_input[local_out_h + kh + 1][local_out_w + kw] * w;
sum11 += s_input[local_out_h + kh + 1][local_out_w + kw + 1] * w;
}
}
```
Wait, each thread needs to access different regions. With 16x16 threads and each computing 2x2, it should be fine.
Actually, the issue is register pressure. Each thread computing 4 outputs needs 4 accumulators = 16 bytes, plus some temporaries. With 256 threads, that's fine.
But there's another consideration: for output dimensions 126x250:
- With 32x32 tiles: 4 tiles in H, 8 tiles in W = 32 tiles
- With 16x16 threads computing 2x2: still 32 tiles for 126x250
- Actually 126/32 = 3.94 → 4 tiles; 250/32 = 7.81 → 8 tiles
Hmm, 32 tiles per (b,c) is still not many. With 4096 (b,c), total 131072 blocks.
Let me try a different structure. What if we process multiple channels per block?
For depthwise conv, channels are independent but share the same spatial dimensions. We could have a block process multiple channels to increase parallelism within the block.
If a block processes 4 channels and a 16x16 spatial tile:
- 16x16 threads, each computing one spatial position for one channel
- We can assign threadIdx.z for channels, but CUDA has 3D blocks
- Or assign groups of threads to different channels
Actually, a simpler way: have each warp (32 threads) handle one channel. Within a warp, threads handle different spatial positions. A block of 256 threads = 8 warps = 8 channels.
For output 126x250, with 8 channels per block:
- Number of channel batches: 128/8 = 16
- Spatial tiles per channel: ceil(126/16) * ceil(250/16) if block is 16x16... but now 8 channels share the block.
Wait, if we have 8 warps each processing 1 channel, and the block needs to load input for all 8 channels. Each channel's input is independent. So a block of 8 warps:
- Each warp has 32 threads
- For 1D warp: 32 threads can handle 32 spatial positions in a row
- We can have each warp load its channel's input and compute
This is getting complex. Let me start with the simpler approach: one block per (batch, channel, tile), 2D thread blocks.
Actually, I want to maximize throughput. Let me look at what CUTLASS or cuDNN does for depthwise conv. But I can't use those directly.
Let me think about another approach: use implicit GEMM or direct conv without shared memory. Since the kernel is small (3x7), the data reuse from shared memory helps but global memory caching on H100 might actually be quite good.
For direct global memory access:
- Each output pixel needs 21 input reads
- Each input pixel is reused by up to 21 output pixels (in the interior)
- But with direct global access, each thread reads its own 21 values
- 256 threads per block × 21 reads = 5376 reads per block
- With shared memory tile of 18×22 = 396 reads per block
- That's a 13.6× reduction in global memory reads!
So shared memory is definitely worth it.
Let me code up a kernel with:
- Block size: 16x16 threads
- Each block computes a 16x16 output tile
- One block per (batch, channel, tile)
Actually, I want to test if a larger tile is better. Let me try:
- Block: 32x8 threads (256 total)
- Output tile: 32x32 where each thread computes a 1x4 strip
- Or block: 16x16 threads, output tile: 16x16
I'll start with 16x16 threads computing 16x16 outputs with shared memory. Then if needed, optimize further.
Wait, I realize the test will compare against PyTorch's cuDNN depthwise conv, which is highly optimized. To beat it, I need a really good kernel.
Some sources suggest that for depthwise conv, a specialized kernel can sometimes beat cuDNN, especially for non-standard sizes. But it's challenging.
Let me think about what cuDNN might not do optimally:
1. cuDNN might use winograd or FFT for 3x3, but 3x7 is not a standard Winograd size
2. cuDNN's generic depthwise conv might not be as optimized as 3x3
For 3x7 with stride 1, it's essentially a small direct conv.
Another approach: vectorized loads and stores. H100 loves vectorized memory access (float4).
If input width is 256, which is divisible by 4, we can use float4 loads.
For a 3x7 kernel where each thread computes one output:
- We need to load 7 consecutive floats for each of 3 rows
- With float4, we can load 4 + 3 floats per row, but the overlap between adjacent output columns is 6 pixels
This is getting messy with vectorization. Let me think about a layout that enables vectorization.
If we process the width dimension in groups of 4, and each thread handles 4 consecutive outputs in width:
- For each of the 3 kernel rows, we need an input strip of width 10 (for 4 outputs with 7-wide kernel)
- We can load this with 2 float4s + 2 floats, or 3 float4s with some overlap
- Actually for output positions w, w+1, w+2, w+3, inputs are w..w+6, w+1..w+7, w+2..w+8, w+3..w+9 = total w..w+9, which is 10 floats.
Hmm, vectorization is tricky with overlapping windows.
Let me try another tactic: use shared memory and process each output tile. Within shared memory, we can load vectorized.
For an output tile of 16x16, input tile is 18x22. We need to load 18x22 = 396 floats.
396/4 = 99 float4 loads, but 22 is not divisible by 4. We could pad to 24: 18x24 would be 432 floats = 108 float4s.
Alternatively, we can load row by row with float4 plus remainder.
Actually, a cleaner approach: instead of trying to vectorize input loads to shared memory, focus on making the compute efficient and using enough threads to hide latency.
Here's a refined plan:
- Each block handles 1 batch, 1 channel, and a spatial tile
- Tile size: 32x32 outputs with 16x16 threads (each thread handles 2x2 outputs)
- This increases the compute per thread and amortizes sync overhead
- Input tile: 34x38
Let me calculate:
- 32x32 outputs per block
- 4x8 = 32 blocks per (batch, channel)
- 4096 (batch, channel) pairs
- Total: 131,072 blocks
- On 132 SMs: ~993 blocks per SM
With 16x16 = 256 threads per block:
- Max blocks per SM concurrently: min(2048/256=8, shared_memory/shared_per_block)
- Shared mem used: 34x38x4 = 5.2KB + 84 bytes for weights = ~5.3KB
- Max blocks per SM based on shared mem: 228KB/5.3KB ≈ 43
- But thread limit is 8
- So 8 blocks concurrently = 2048 threads per SM = 100% occupancy
This seems pretty good.
Each thread computes 4 outputs (2x2):
- Inner loops: 3x7 = 21 iterations
- Each iteration: 4 FMAs (one per output)
- Total: 84 FMAs per thread
- Per block: 256 * 84 = 21,504 FMAs
- Shared memory to feed this: input tile 34x38 = 1292 floats
- Compute per byte: ~21,504 / (1292 * 4) ≈ 4.16 FLOPs/byte
- For FP32, peak is 67 TFLOPS and memory is 3.35 TB/s, so arithmetic intensity needed for compute bound: 67/3.35 = 20 FLOPs/byte
- We're at 4.16, so definitely memory bound. Need to maximize memory bandwidth.
For memory bandwidth, we want:
1. Coalesced loads
2. Fewer global transactions (via shared memory and caching)
3. Sufficient occupancy to hide latency
With 8 blocks per SM and 100% occupancy, latency hiding should be decent.
Let me try an even more aggressive approach: larger tiles or more outputs per thread.
What about 64x64 output tiles with 16x16 threads where each thread computes 4x4 outputs?
- Block: 16x16 threads
- Output per block: 64x64 = 4096 outputs
- Input tile: 66x70 = 4620 floats = 18.5KB shared mem
- Blocks per (b,c): ceil(126/64) * ceil(250/64) = 2 * 4 = 8
- Total blocks: 8 * 4096 = 32,768
- Threads per block: 256
- Max concurrent blocks per SM: min(8, 228KB/18.5KB=12) = 8
- Still 100% occupancy
- Each thread: 16 * 21 = 336 FMAs
This gives fewer total blocks (32K vs 131K). H100 needs lots of blocks to keep all SMs busy. 32K blocks / 132 SMs = 245 blocks per SM. With 8-way concurrency, that's ~31 waves. Might be enough, but more is usually better.
Let me also consider: 32x64 output tiles with 16x16 threads computing 2x4 outputs.
- Output per block: 32x64
- Input: 34x70 = 2380 floats = 9.5KB
- Blocks per (b,c): 4 * 4 = 16
- Total: 16 * 4096 = 65,536
- This is in between.
I'll start with 16x16 threads computing 2x2 outputs (32x32 tile) and see how it performs.
Wait, one more consideration. Let me look at the exact output dimensions:
126 = 128 - 3 + 1 (no padding)
250 = 256 - 7 + 1
If I use 32x32 tiles:
- H tiles: 0-31, 32-63, 64-95, 96-127 → 4 tiles, but last tile only has valid outputs 96-125
- W tiles: 0-31, 32-63, 64-95, 96-127, 128-159, 160-191, 192-223, 224-255 → 8 tiles, last tile valid 224-249
So 32 blocks per (b,c). Good.
Now for each thread computing 2x2 outputs within its block:
- threadIdx.y = 0..15, threadIdx.x = 0..15
- Out positions: (block_y*32 + ty*2, block_x*32 + tx*2)
- and: (block_y*32 + ty*2 + 1, block_x*32 + tx*2)
- and: (block_y*32 + ty*2, block_x*32 + tx*2 + 1)
- and: (block_y*32 + ty*2 + 1, block_x*32 + tx*2 + 1)
Wait, if thread (0,0) computes outputs at (0,0), (0,1), (1,0), (1,1), then to compute these it needs inputs at:
- For (0,0): rows 0,1,2 and cols 0..6
- For (0,1): rows 0,1,2 and cols 1..7
- For (1,0): rows 1,2,3 and cols 0..6
- For (1,1): rows 1,2,3 and cols 1..7
So the union is rows 0..3 and cols 0..7. That's 4x8 = 32 inputs.
But if I use shared memory for the entire tile, all threads in the block need inputs from rows block_y*32 to block_y*32 + 33 (since max output is 31 and needs row 33 for kernel row 2), and cols block_x*32 to block_x*32 + 37.
Let me recalculate: output row index within block goes from 0 to 31. Max is 31. For kernel row 2 (0-indexed), we need input row 31 + 2 = 33. Since input height is 128, and tile starts at block_y*32, max input row needed = block_y*32 + 33. For block_y=0: 33. For block_y=3: 96+33=129. But input height is only 128. So for the last tile, we only have input rows 96..127, and need to pad for row 128, 129.
Similarly for width: block_x*32 + 37. For block_x=7: 224+37=261. Input width is 256. Need padding for 256..260.
So shared memory tile: 34x38.
Actually, the formula is: input_tile_h = output_tile_h + kernel_h - 1 = 32 + 3 - 1 = 34.
input_tile_w = output_tile_w + kernel_w - 1 = 32 + 7 - 1 = 38.
Yes, 34x38.
Now implementing the kernel:
```cpp
#include <torch/extension.h>
#include <cuda_runtime.h>
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH>
__global__ void depthwise_conv2d_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int batch_size,
int channels,
int in_h,
int in_w,
int out_h,
int out_w,
int kernel_h,
int kernel_w,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
) {
const int b = blockIdx.z / channels;
const int c = blockIdx.z % channels;
const int tile_y = blockIdx.y * BLOCK_H * OUT_H_PER_TH;
const int tile_x = blockIdx.x * BLOCK_W * OUT_W_PER_TH;
const int ty = threadIdx.y;
const int tx = threadIdx.x;
const int in_tile_h = BLOCK_H * OUT_H_PER_TH + kernel_h - 1;
const int in_tile_w = BLOCK_W * OUT_W_PER_TH + kernel_w - 1;
// Shared memory for input tile and weights
extern __shared__ float s_mem[];
float* s_input = s_mem;
float* s_weight = s_mem + in_tile_h * in_tile_w;
// Load weights (only first few threads)
const int weight_size = kernel_h * kernel_w;
for (int i = ty * BLOCK_W + tx; i < weight_size; i += BLOCK_H * BLOCK_W) {
s_weight[i] = weight[c * weight_size + i];
}
// Load input tile
const int in_tile_size = in_tile_h * in_tile_w;
const int global_y_base = tile_y - pad_h;
const int global_x_base = tile_x - pad_w;
for (int i = ty * BLOCK_W + tx; i < in_tile_size; i += BLOCK_H * BLOCK_W) {
const int local_y = i / in_tile_w;
const int local_x = i % in_tile_w;
const int global_y = global_y_base + local_y * stride_h; // wait, this assumes stride=1 for shared memory loading
const int global_x = global_x_base + local_x * stride_w;
if (global_y >= 0 && global_y < in_h && global_x >= 0 && global_x < in_w) {
s_input[local_y * in_tile_w + local_x] = input[((b * channels + c) * in_h + global_y) * in_w + global_x];
} else {
s_input[local_y * in_tile_w + local_x] = 0.0f;
}
}
__syncthreads();
// Compute output
const int out_y = tile_y + ty * OUT_H_PER_TH;
const int out_x = tile_x + tx * OUT_W_PER_TH;
// Each thread computes OUT_H_PER_TH x OUT_W_PER_TH outputs
float accum[OUT_H_PER_TH][OUT_W_PER_TH] = {0.0f};
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
float val = s_input[(ty * OUT_H_PER_TH + dy + kh) * in_tile_w + (tx * OUT_W_PER_TH + dx + kw)];
accum[dy][dx] += val * w;
}
}
}
}
// Write outputs
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
int oy = out_y + dy;
int ox = out_x + dx;
if (oy < out_h && ox < out_w) {
float val = accum[dy][dx];
if (bias != nullptr) val += bias[c];
output[((b * channels + c) * out_h + oy) * out_w + ox] = val;
}
}
}
}
```
Wait, I need to be more careful. With strides and dilations, the shared memory loading gets complicated. For the specific test case, stride=1, dilation=1, pad=0, but to be general I need to handle the general case.
Actually, for simplicity, I can handle special cases. If stride=1 and dilation=1, use the shared memory approach. Otherwise fall back. But PyTorch will handle that anyway. Wait, this is a replacement for the PyTorch module, not just the test case.
Actually, I can check: if stride=1 and dilation=1, use the fast path. Otherwise, I can fall back to a simpler kernel or even to the reference PyTorch implementation. But I can't call PyTorch from the kernel - I'd have to do it in Python.
Wait, the forward function can check conditions and use the custom kernel when applicable. For depthwise conv with stride=1, dilation=1, our kernel should work well. For other parameters, I can still call the kernel since I wrote it generally. The performance might not be as good but it should be correct.
Actually, my kernel above handles arbitrary stride and dilation but the shared memory tile size is computed assuming we load a contiguous region. With stride or dilation, the relationship between output tile and input region changes. Let me think...
For stride=1, dilation=1, pad=p:
output[h][w] = sum_{kh,kw} input[h*stride - pad + kh*dilation][w*stride - pad + kw*dilation] * weight[kh][kw]
With stride=1, dilation=1:
output[h][w] = sum_{kh,kw} input[h - pad + kh][w - pad + kw] * weight[kh][kw]
So for output tile [tile_y, tile_y+TH) x [tile_x, tile_x+TW):
Input needed: [tile_y - pad, tile_y - pad + TH + KH - 1) x [tile_x - pad, tile_x - pad + TW + KW - 1)
This is what I wrote. For stride != 1 or dilation != 1, it's more complex. But the test case has stride=1, dilation=1.
Actually, to be general, let me support arbitrary parameters by computing the input bounds correctly.
For output at (oy, ox), the input access is at:
iy = oy * stride_h - pad_h + kh * dilation_h
ix = ox * stride_w - pad_w + kw * dilation_w
So for an output tile from oy_start to oy_end and ox_start to ox_end:
iy ranges from oy_start * stride_h - pad_h to (oy_end - 1) * stride_h - pad_h + (KH - 1) * dilation_h
ix ranges from ox_start * stride_w - pad_w to (ox_end - 1) * stride_w - pad_w + (KW - 1) * dilation_w
The tile size in input is:
in_tile_h = (oy_end - 1) * stride_h - oy_start * stride_h + (KH - 1) * dilation_h + 1
= (TH - 1) * stride_h + (KH - 1) * dilation_h + 1
Similarly for width.
So for general case:
in_tile_h = (BLOCK_H * OUT_H_PER_TH - 1) * stride_h + (kernel_h - 1) * dilation_h + 1
in_tile_w = (BLOCK_W * OUT_W_PER_TH - 1) * stride_w + (kernel_w - 1) * dilation_w + 1
And when loading input, local_y maps to global_y as:
global_y = oy_start * stride_h - pad_h + local_y * ?
Wait, the input indices don't map linearly to local indices when dilation is involved. The simplest general approach:
For local position (ly, lx) in the input tile, it corresponds to the input at:
iy = oy_start * stride_h - pad_h + ly * ?
Actually, the relationship depends on how we lay out the input tile. A simpler approach for general stride/dilation: use the formula directly.
For densely packed shared memory where s_input[ly][lx] stores the value at global position (oy_start*stride_h - pad_h + ly, ...), we need to account for the fact that not all intermediate global positions are accessed by the outputs due to stride.
Actually, even simpler: for stride=1, dilation=1 the shared memory layout is dense. For general stride/dilation, the shared memory layout can still be dense - we just load the bounding box of all input positions that any output in the tile might need.
Let me define:
iy_start = tile_y * stride_h - pad_h
iy_end = (tile_y + tile_h - 1) * stride_h - pad_h + (kernel_h - 1) * dilation_h + 1
in_tile_h = iy_end - iy_start
Then for an output at (oy, ox) within the tile, and kernel position (kh, kw):
iy = oy * stride_h - pad_h + kh * dilation_h
local_iy = iy - iy_start
Yes, this works! The shared memory is dense, but we access it with computed local indices.
So the general shared memory size:
in_tile_h = (tile_h - 1) * stride_h + (kernel_h - 1) * dilation_h + 1
in_tile_w = (tile_w - 1) * stride_w + (kernel_w - 1) * dilation_w + 1
And the access in the compute loop:
val = s_input[((ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h) * in_tile_w + ((tx * OUT_W_PER_TH + dx) * stride_w + kw * dilation_w)]
This is general and correct! Though the indexing gets more complex, it handles all cases.
Let me write a cleaner version:
```cpp
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH>
__global__ void depthwise_conv2d_kernel(...) {
...
const int in_tile_h = (BLOCK_H * OUT_H_PER_TH - 1) * stride_h + (kernel_h - 1) * dilation_h + 1;
const int in_tile_w = (BLOCK_W * OUT_W_PER_TH - 1) * stride_w + (kernel_w - 1) * dilation_w + 1;
...
for (int i = ty * BLOCK_W + tx; i < in_tile_h * in_tile_w; i += BLOCK_H * BLOCK_W) {
int local_y = i / in_tile_w;
int local_x = i % in_tile_w;
int global_y = tile_y * stride_h - pad_h + local_y;
int global_x = tile_x * stride_w - pad_w + local_x;
// load with bounds check
}
__syncthreads();
...
for (int kh = 0; kh < kernel_h; ++kh) {
for (int kw = 0; kw < kernel_w; ++kw) {
float w = s_weight[kh * kernel_w + kw];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; ++dy) {
int local_y = (ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h;
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; ++dx) {
int local_x = (tx * OUT_W_PER_TH + dx) * stride_w + kw * dilation_w;
accum[dy][dx] += s_input[local_y * in_tile_w + local_x] * w;
}
}
}
}
}
```
This is clean and general. Now let me think about block/tile sizes. Since in_tile_h and in_tile_w can be large for large strides/dilations, the shared memory might not fit. For the test case with stride=1, dilation=1:
- BLOCK_H=16, BLOCK_W=16, OUT_H_PER_TH=2, OUT_W_PER_TH=2
- in_tile_h = 31 + 2 + 1 = 34? Let me recalculate: (16*2 - 1)*1 + (3-1)*1 + 1 = 31 + 2 + 1 = 34. Yes.
- in_tile_w = (16*2 - 1)*1 + (7-1)*1 + 1 = 31 + 6 + 1 = 38. Yes.
For large kernel/stride/dilation, this might exceed shared memory. I should add a check in Python and use a fallback or smaller tiles. For now, let me just ensure it works for the test case.
Actually, I realize the most robust approach is to write the kernel and choose parameters dynamically based on the problem size. But `load_inline` with templates means I need to instantiate templates for specific sizes.
I can either:
1. Use runtime parameters (no templates for tile size) and let the compiler handle it
2. Instantiate multiple template specializations and dispatch
Option 1 is easier. I'll just define the block/tile sizes as constants in the kernel or pass them as template parameters with a few instantiations.
Actually, I'll use a single instantiation for the test case but keep the kernel general enough for other sizes by using runtime sizes for loops and dynamic shared memory. This is fine since the test has fixed sizes.
Let me write the full kernel code. I'll start with a simple but effective version.
One more thing: I should check if I can use `__restrict__` to help the compiler. Yes, good idea.
Also, I want to handle the bias correctly - add it if bias pointer is not null.
And importantly: depthwise conv means `groups = in_channels`, so `out_channels = in_channels` in the test. Wait, the constructor takes `out_channels` but then creates a depthwise conv with `groups=in_channels`. In standard depthwise conv, output channels = input channels (each channel produces one output channel). But there's also depthwise separable where you follow with 1x1 pointwise. Here, it seems like pure depthwise: `nn.Conv2d(in_channels, in_channels, ..., groups=in_channels)`.
Wait, looking at the constructor: `self.conv2d = nn.Conv2d(in_channels, in_channels, ..., groups=in_channels, bias=bias)`. So out_channels is actually ignored in favor of in_channels. But our replacement should match this behavior.
Actually, to be safe and match the reference exactly, I should use the same logic. But the problem says "accept the same constructor arguments" and "produce numerically equivalent outputs." So whether I use out_channels or in_channels internally, the output should match.
Since the reference uses `in_channels` for both in and out channels, I'll do the same in my kernel.
Now, let me write the Python code:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_src = r'''
#include <torch/extension.h>
#include <cuda_runtime.h>
// ... kernel ...
'''
cpp_src = r'''
// ... wrapper functions ...
'''
depthwise_conv2d = load_inline(
name='depthwise_conv2d',
cpp_sources=cpp_src,
cuda_sources=cuda_src,
functions=['forward'],
extra_cuda_cflags=['-O3', '--use_fast_math'],
verbose=True,
)
class ModelNew(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size_h, kernel_size_w,
stride_h=1, stride_w=1, padding_h=0, padding_w=0,
dilation_h=1, dilation_w=1, groups=1, bias=False):
super().__init__()
# Only support depthwise
self.in_channels = in_channels
self.out_channels = in_channels # depthwise
self.kernel_size_h = kernel_size_h
self.kernel_size_w = kernel_size_w
self.stride_h = stride_h
self.stride_w = stride_w
self.padding_h = padding_h
self.padding_w = padding_w
self.dilation_h = dilation_h
self.dilation_w = dilation_w
self.groups = in_channels
self.has_bias = bias
self.weight = nn.Parameter(torch.zeros(in_channels, 1, kernel_size_h, kernel_size_w))
if bias:
self.bias = nn.Parameter(torch.zeros(in_channels))
else:
self.register_parameter('bias', None)
def forward(self, x):
return depthwise_conv2d.forward(
x, self.weight, self.bias,
self.stride_h, self.stride_w,
self.padding_h, self.padding_w,
self.dilation_h, self.dilation_w
)
```
Wait, the shape of weight in PyTorch depthwise conv is [in_channels, 1, KH, KW] when groups=in_channels. Let me double check.
In `nn.Conv2d(in_channels, in_channels, kernel_size, groups=in_channels)`, the weight shape is `(in_channels, 1, KH, KW)` because each of the `in_channels` output channels is produced from `in_channels/groups = 1` input channel.
So my weight shape matches. Good.
But wait, I need to copy weights from a reference model if someone trains with Model and then uses ModelNew. Actually, looking at the test code structure, they probably instantiate ModelNew directly with `get_init_inputs()`. So I need to initialize weights properly.
Actually, in PyTorch, `nn.Conv2d` initializes weights with Kaiming uniform by default. My `ModelNew` uses `torch.zeros`. But the test only checks forward pass with random inputs - it doesn't compare against a trained model, it compares the output of ModelNew against the reference Model with the same input. So as long as both have the same weights, it's fine.
But how do tests work? They probably copy weights or just test with the default initialization. Looking at standard benchmark setup, they usually:
1. Create reference model
2. Create new model with same args
3. Copy weights from reference to new
4. Run both with same input
5. Compare outputs
If so, my `ModelNew` just needs to have weight parameters in compatible shapes and formats.
Actually, for `nn.Conv2d(in_channels, in_channels, (kh, kw), groups=in_channels)`, the weight is stored as `[out_channels, in_channels//groups, kh, kw] = [in_channels, 1, kh, kw]`.
Let me make sure my parameter shape matches exactly.
Now, for the kernel, I need to think about how to handle the weight layout. In PyTorch, `conv2d.weight` is `[C, 1, KH, KW]` for depthwise. I'll reshape it to `[C, KH*KW]` or `[C, KH, KW]` in the kernel.
Actually, for CUDA kernel access, it's easiest to have it as a flat array `[C * KH * KW]`. I'll pass `weight.data_ptr()` and access it appropriately.
Let me write the complete kernel code now.
```cpp
#include <torch/extension.h>
#include <cuda_runtime.h>
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH>
__global__ void depthwise_conv2d_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int batch_size,
int channels,
int in_h,
int in_w,
int out_h,
int out_w,
int kernel_h,
int kernel_w,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
) {
const int b = blockIdx.z / channels;
const int c = blockIdx.z % channels;
const int tile_h = BLOCK_H * OUT_H_PER_TH;
const int tile_w = BLOCK_W * OUT_W_PER_TH;
const int tile_y = blockIdx.y * tile_h;
const int tile_x = blockIdx.x * tile_w;
const int ty = threadIdx.y;
const int tx = threadIdx.x;
const int in_tile_h = (tile_h - 1) * stride_h + (kernel_h - 1) * dilation_h + 1;
const int in_tile_w = (tile_w - 1) * stride_w + (kernel_w - 1) * dilation_w + 1;
extern __shared__ float s_mem[];
float* s_input = s_mem;
float* s_weight = s_mem + in_tile_h * in_tile_w;
// Load weights
const int weight_size = kernel_h * kernel_w;
for (int i = ty * BLOCK_W + tx; i < weight_size; i += BLOCK_H * BLOCK_W) {
s_weight[i] = weight[c * weight_size + i];
}
// Load input tile
const int in_tile_size = in_tile_h * in_tile_w;
const int in_offset = (b * channels + c) * in_h * in_w;
const int iy_start = tile_y * stride_h - pad_h;
const int ix_start = tile_x * stride_w - pad_w;
#pragma unroll
for (int i = ty * BLOCK_W + tx; i < in_tile_size; i += BLOCK_H * BLOCK_W) {
int local_y = i / in_tile_w;
int local_x = i % in_tile_w;
int global_y = iy_start + local_y;
int global_x = ix_start + local_x;
s_input[i] = (global_y >= 0 && global_y < in_h && global_x >= 0 && global_x < in_w)
? input[in_offset + global_y * in_w + global_x]
: 0.0f;
}
__syncthreads();
// Compute
const int out_y = tile_y + ty * OUT_H_PER_TH;
const int out_x = tile_x + tx * OUT_W_PER_TH;
float accum[OUT_H_PER_TH][OUT_W_PER_TH];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
accum[dy][dx] = 0.0f;
}
}
#pragma unroll
for (int kh = 0; kh < kernel_h; kh++) {
#pragma unroll
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int local_y = (ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h;
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
int local_x = (tx * OUT_W_PER_TH + dx) * stride_w + kw * dilation_w;
float val = s_input[local_y * in_tile_w + local_x];
accum[dy][dx] += val * w;
}
}
}
}
// Write output
const int out_offset = (b * channels + c) * out_h * out_w;
const float bval = (bias != nullptr) ? bias[c] : 0.0f;
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int oy = out_y + dy;
if (oy < out_h) {
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
int ox = out_x + dx;
if (ox < out_w) {
output[out_offset + oy * out_w + ox] = accum[dy][dx] + bval;
}
}
}
}
}
torch::Tensor forward(
torch::Tensor input,
torch::Tensor weight,
c10::optional<torch::Tensor> bias,
int stride_h, int stride_w,
int pad_h, int pad_w,
int dilation_h, int dilation_w
) {
int batch_size = input.size(0);
int channels = input.size(1);
int in_h = input.size(2);
int in_w = input.size(3);
int kernel_h = weight.size(2);
int kernel_w = weight.size(3);
int out_h = (in_h + 2 * pad_h - dilation_h * (kernel_h - 1) - 1) / stride_h + 1;
int out_w = (in_w + 2 * pad_w - dilation_w * (kernel_w - 1) - 1) / stride_w + 1;
auto output = torch::empty({batch_size, channels, out_h, out_w}, input.options());
const int BLOCK_H = 16;
const int BLOCK_W = 16;
const int OUT_H_PER_TH = 2;
const int OUT_W_PER_TH = 2;
const int tile_h = BLOCK_H * OUT_H_PER_TH;
const int tile_w = BLOCK_W * OUT_W_PER_TH;
dim3 block(BLOCK_W, BLOCK_H);
dim3 grid(
(out_w + tile_w - 1) / tile_w,
(out_h + tile_h - 1) / tile_h,
batch_size * channels
);
int in_tile_h = (tile_h - 1) * stride_h + (kernel_h - 1) * dilation_h + 1;
int in_tile_w = (tile_w - 1) * stride_w + (kernel_w - 1) * dilation_w + 1;
size_t shared_mem_size = (in_tile_h * in_tile_w + kernel_h * kernel_w) * sizeof(float);
depthwise_conv2d_kernel<BLOCK_H, BLOCK_W, OUT_H_PER_TH, OUT_W_PER_TH><<<grid, block, shared_mem_size>>>(
input.data_ptr<float>(),
weight.data_ptr<float>(),
bias.has_value() ? bias.value().data_ptr<float>() : nullptr,
output.data_ptr<float>(),
batch_size, channels, in_h, in_w, out_h, out_w,
kernel_h, kernel_w, stride_h, stride_w,
pad_h, pad_w, dilation_h, dilation_w
);
return output;
}
```
Wait, `load_inline` auto-generates the pybind11 module. I shouldn't include a `PYBIND11_MODULE` block. And the functions list should just contain the host-side wrapper names.
One concern: `c10::optional<torch::Tensor>` in the wrapper signature. Does pybind11 handle this well with the auto-generated module? `load_inline` generates bindings from the function signatures. It should handle optional tensors.
Actually, looking at the `load_inline` documentation, it parses `cpp_sources` to find function declarations. `c10::optional` should be fine, but I can also use `torch::optional`.
Another approach is to just have two versions or pass a pointer. Let me use a simpler approach: pass the bias tensor and a boolean flag, or just pass it even if it's empty.
Actually, `torch::Tensor bias` with a check for `bias.defined()` is simpler. But the user has requested `bias=False` by default, and when bias=False, there is no bias parameter. So I need to handle this in Python.
Wait, in my `ModelNew`, I can just pass `self.bias` and in the kernel check if it's defined. But PyTorch tensors from `nn.Parameter` are always defined (they exist as tensors, though they might not be used).
If bias=False in `__init__`, I set `self.bias = None`. Then in `forward`, I can pass `self.bias if self.bias is not None else torch.empty(0)` and a boolean. Or simpler: just handle it in Python.
Let me think of a cleaner approach. Since `load_inline` auto-generates bindings, simple function signatures work best.
```cpp
torch::Tensor forward(
torch::Tensor input,
torch::Tensor weight,
torch::Tensor bias,
int stride_h, int stride_w,
int pad_h, int pad_w,
int dilation_h, int dilation_w
) {
...
float* bias_ptr = bias.defined() && bias.numel() > 0 ? bias.data_ptr<float>() : nullptr;
...
}
```
Then in Python:
```python
bias_tensor = self.bias if self.bias is not None else torch.empty(0, device=x.device, dtype=x.dtype)
return depthwise_conv2d.forward(x, self.weight, bias_tensor, ...)
```
This is clean and robust.
Another concern: I need to make sure the kernel handles all edge cases, particularly when tile sizes don't divide evenly. My kernel already has bounds checks on output writes and input loads (with zero padding).
One bug I notice: when I iterate over shared memory with `i < in_tile_size`, I'm using `i += BLOCK_H * BLOCK_W`, but in some cases with large shared memory and small blocks, this might not cover everything if there aren't enough threads. Wait, `BLOCK_H * BLOCK_W = 256`, and `in_tile_size` for the test case is 34*38=1292, so all elements are loaded with 5 rounds (256*5=1280, plus 12 more in round 6). That's correct.
Another issue: float array `float accum[OUT_H_PER_TH][OUT_W_PER_TH]` with OUT_H_PER_TH=2, OUT_W_PER_TH=2. This should be fine for registers.
Let me also consider using `__launch_bounds__` to hint register usage. But 256 threads per block with moderate register usage should be fine.
Actually, for the compute loop, `#pragma unroll` on `kernel_h` and `kernel_w` when they're runtime values won't actually unroll. To get unrolling, I need them to be compile-time constants. I could create a dispatch mechanism:
```cpp
if (kernel_h == 3 && kernel_w == 7) {
// call templated version with <3, 7>
} else {
// call general version
}
```
But in device code, I can't easily do runtime dispatch like this without separate kernel instantiations. Let me think...
Actually, I can write a host-side dispatch:
```cpp
if (kernel_h == 3 && kernel_w == 7) {
kernel<16, 16, 2, 2><<<...>>>(..., 3, 7, ...);
} else {
// generic or fallback
}
```
But the template parameters in my kernel only control block/tile sizes, not kernel sizes. The kernel sizes are passed as function arguments. So I can't easily unroll over them without more templates.
Since the test case uses 3x7, let me make a special case for small kernels. Actually, for 3x7 with loops of 3 and 7, the overhead is minimal. Modern GPUs handle small loops well, especially with `#pragma unroll` which the compiler might partially apply if it knows the bounds come from shared memory or registers (which it does by the time the loop executes).
Actually, with `s_weight` in shared memory, the compiler can see the loop bounds are constants within the kernel context? No, `kernel_h` and `kernel_w` are runtime parameters to the kernel, so the compiler can't unroll them without knowing them at compile time.
But since they're only 3 and 7, the loop overhead is tiny relative to the memory accesses.
Let me also think about whether I should use `float4` for some loads. For test case input width 256, loading 4 floats at a time from global memory could help. But the shared memory stores would then need to be scalar or we need special handling. Given the complexity, let me start without vectorization and see if performance is sufficient.
Actually, another optimization: the compiler might vectorize automatically when it sees coalesced patterns. And with `-O3 --use_fast_math`, it should optimize well.
One more thing: should I transpose the weight layout? Currently weight is `[C, 1, KH, KW]`. In the kernel, I access `weight[c * weight_size + kh * KW + kw]`. Since different threads in the same warp access the same `c` (same block), they all read the same weight values. This is a broadcast access from global memory, which is efficient (threads read the same cache line, and it gets broadcast).
Wait, actually in my kernel I load weights into shared memory first. So the global memory access pattern for weights is: threads 0..20 load weight[0..20] for channel c. This is sequential and coalesced. Other threads don't participate. Then all threads read from shared memory. This is efficient.
For input loading: threads in a block load consecutive elements of the input tile. If I iterate with `i = ty * BLOCK_W + tx` and stride by `BLOCK_H * BLOCK_W`, the first 256 threads load elements 0..255 of the input tile consecutively. This is coalesced.
However, the input tile is 2D, so consecutive `i` values correspond to consecutive memory locations in my linearized layout. Yes, they do: `local_y = i / in_tile_w`, `local_x = i % in_tile_w`. Consecutive `i` values mostly map to consecutive `x` with occasional jumps at row boundaries. This is still fairly coalesced as long as `in_tile_w` is nice.
For `in_tile_w = 38`, consecutive `i` values map to positions (0,0), (0,1), ..., (0,37), (1,0), (1,1), etc. This is completely coalesced because consecutive threads access consecutive elements.
Great, so the memory access is well-coalesced.
Now let me consider if there are any issues with the shared memory bank conflicts. The input tile is accessed as `s_input[local_y * in_tile_w + local_x]` where `in_tile_w = 38`. Threads in a warp that compute adjacent output pixels will access adjacent `local_x` values, which means adjacent shared memory locations. With 32 banks and 38-width rows, consecutive columns are in different banks (38 mod 32 != 0, so the next row shifts by 6 banks). No conflicts for consecutive column access.
For the compute loop: `s_input[local_y * in_tile_w + local_x]` where `local_x` can vary by thread. If adjacent threads access the same `local_y` but different `local_x`, and `local_x` differs by 1, then they access adjacent shared memory locations, which map to different banks. No conflicts.
Actually, with `OUT_W_PER_TH=2`, threads in a warp are computing output columns 0,2,4,...,30,32,...? Wait, let me recalculate.
Block size is 16x16 threads. Thread tx=0 computes output columns tile_x + 0, 1. Thread tx=1 computes tile_x + 2, 3. So thread tx accesses `local_x = 0*2 * stride + kw, 0*2 * stride + kw + 1` for its first output, then `1*2 * stride + kw, 1*2 * stride + kw + 1` for second. The other threads in the warp do similar.
So threads 0..15 in a warp access local_x values that are 0,1,2,3,...,31 (for a given kh and dy). These are all distinct and contiguous, so no bank conflicts.
Good.
Now, what about writes? Each thread writes 4 output values. The output layout is [batch, channel, height, width] with width being the fastest changing dimension. Thread tx=0 writes to columns 0,1; tx=1 writes to columns 2,3. So for a given row, threads write to adjacent columns. This is coalesced (especially if we write row by row).
Actually, the writes are inside nested loops over dy and dx. For dy=0 and dx varying, we write to adjacent memory locations. With 16 threads in x-dimension, and each writing 2 values, the writes for a single dy span 32 consecutive floats. That's a full warp's worth of coalesced writes (actually, a warp is 32 threads, we have 16 threads writing 2 values each for 32 writes total). But these 16 threads execute sequentially in the inner loop, not simultaneously. So each store instruction only writes a single float. That's not great for coalescing!
To fix this, I should restructure: have all threads in the warp write their same-dx values together, or better yet, have each thread write its outputs in a way that naturally coalesces.
Actually, a simpler approach: if I make `OUT_W_PER_TH=1`, then all 16 threads in x write to adjacent columns simultaneously in a single instruction. But then each thread only computes 2 outputs (2x1), which might reduce arithmetic intensity.
Or I can keep OUT_W_PER_TH=2 but write carefully. The issue is that within a thread, the two writes happen sequentially. But across the warp, thread tx writes columns 2*tx and 2*tx+1. If all threads write their first output simultaneously, we'd have writes to columns 0,2,4,...,30 - which are strided and not fully coalesced. But on H100, sub-warp coalescing can still handle this reasonably. Actually, modern GPUs can coalesce scattered accesses within a warp fairly well if they fall within the same cache line.
For 32 columns (16 threads × 2), each being 4 bytes, that's 128 bytes. An L1 cache line is 128 bytes. So all writes for a single dy and dx across the block's x-dimension fit in one or two cache lines. This should be fine.
Let me not worry too much about the write pattern. I'll run the kernel and see.
Now let me think about if there are optimizations I can apply specifically for small kernels and the H100 architecture.
For H100, some considerations:
- Tensor Memory Accelerator (TMA) for asynchronous data movement
- Warp group cluster for multi-block cooperation
- But these require newer CUDA versions and might be complex
I'll stick to classic shared memory approach.
Actually, I just realized: for the test case with no bias, I should still handle it correctly. And I should make sure my `ModelNew` constructor exactly matches `Model`'s constructor in terms of what it stores and its behavior.
One more thing: I need to initialize weights the same way as PyTorch if we're training or if weights aren't copied. The test probably copies weights, but to be safe, let me use the same initialization as PyTorch's Conv2d.
PyTorch Conv2d uses `kaiming_uniform_` with `a=sqrt(5)` for weights, and uniform for bias. But again, tests typically copy weights. I'll skip custom init and just use `nn.Parameter(torch.empty(...))` or the default.
Wait, PyTorch's `nn.Conv2d` calls `reset_parameters()` in `__init__`. But if the benchmark copies weights from reference to new model, this doesn't matter. If it doesn't, we need matching initialization. I'll just use the standard approach: create Conv2d in `__init__` and extract its weight/bias, or copy the initialization.
Actually, a simpler and safer approach: in my `ModelNew.__init__`, I can create a temporary `nn.Conv2d` with the same parameters and copy its shape and initialization logic.
```python
def __init__(self, ...):
super().__init__()
ref_conv = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w),
stride=(stride_h, stride_w), padding=(padding_h, padding_w),
dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)
self.weight = nn.Parameter(ref_conv.weight.detach().clone())
if bias:
self.bias = nn.Parameter(ref_conv.bias.detach().clone())
# store other params
```
Wait, but creating an `nn.Conv2d` just to copy weights is wasteful. But it's only done once at construction, and `nn.Conv2d.__init__` is cheap. Even better, I can just initialize manually:
```python
self.weight = nn.Parameter(torch.empty(in_channels, 1, kernel_size_h, kernel_size_w))
nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))
if bias:
self.bias = nn.Parameter(torch.empty(in_channels))
fan_in, _ = nn.init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in)
nn.init.uniform_(self.bias, -bound, bound)
```
But actually, the easiest thing is just to match the parameter shapes exactly. The benchmark framework will handle weight initialization/copying.
Let me look at how typical benchmark harnesses work. They usually do something like:
```python
model = Model(*get_init_inputs())
model_new = ModelNew(*get_init_inputs())
# Copy weights
model_new.load_state_dict(model.state_dict(), strict=False)
# Or manually copy parameters
```
If this is the case, my `ModelNew` just needs to have compatible `state_dict` entries. `self.weight` and optionally `self.bias` should match.
Actually, looking at the reference model: it has `self.conv2d` which is a `nn.Conv2d`, so its state dict would have `conv2d.weight` and `conv2d.bias`. My `ModelNew` has just `weight` and `bias`.
Wait, this is important! If the benchmark copies weights using `state_dict`, the keys won't match. But looking at the test code provided, there's no explicit weight copying shown. The benchmark likely handles initialization internally.
Let me reconsider: the task says "Replace the forward computation." The benchmark might:
1. Create both models
2. Initialize them (possibly with fixed seed or matching init)
3. Run forward
4. Compare outputs
If they use standard PyTorch init, both will have random weights, and outputs won't match! So they must be copying weights or using deterministic init.
In most kernel optimization benchmarks, the harness copies parameters from the reference to the new model. The exact mechanism might be by matching parameter names or shapes, or by some custom code.
To be safe, I should make sure my `ModelNew` has a compatible parameter structure. Since the reference stores weight in `conv2d.weight`, and I store in `weight`, there might be an issue if the harness naively copies by name.
But I can't control the benchmark harness. Let me just write the most natural implementation and trust that the harness handles weight copying properly.
Actually, I just realized: I can make my `ModelNew` have a `conv2d` attribute too, and just not use it in forward! That way state dict keys match.
```python
class ModelNew(nn.Module):
def __init__(self, ...):
super().__init__()
self.conv2d = nn.Conv2d(in_channels, in_channels, ...)
# store params for fast access
self.has_bias = bias
def forward(self, x):
return depthwise_conv2d.forward(x, self.conv2d.weight, self.conv2d.bias if self.has_bias else None, ...)
```
This is clever! The `conv2d` parameter ensures compatibility, and we use its weights in our custom forward. But creating an `nn.Conv2d` just for parameters is a bit wasteful but totally fine.
Wait, there's an issue: `self.conv2d = nn.Conv2d(...)` means the module also has all the `nn.Conv2d` buffers and parameters. When we call our custom kernel, we're essentially bypassing the conv2d computation but using its weights. The state dict would have `conv2d.weight` which matches the reference.
This seems like the safest approach. And `nn.Conv2d` init is standard.
But hmm, in forward, `self.conv2d.bias` is a parameter if `bias=True`, and `None` if `bias=False`. If `bias=False`, passing `None` to our C++ function might not work well with the pybind11 auto-generated bindings. Let me pass an empty tensor in that case.
Let me write the complete code now.
Actually, I want to also handle half-precision (fp16/bf16) in case tests run with those. But the problem says "fp32 precision" for numerical equivalence, and the test uses `torch.rand` which produces fp32 by default. Let me stick to fp32.
I'll write the code, compile, and test.
Wait, one optimization I want to try: instead of loading all input tile elements to shared memory in a single loop, I should make sure the bounds checking doesn't introduce too much divergence. With `pad=0` in the test, most tiles are in-bounds except edges. For edge tiles, many threads in the block will simultaneously hit the boundary check simultaneously (all threads with the same `local_y` will have the same `global_y`). Branch divergence within a warp happens when some threads in the warp take one branch and others take another. If all threads in a warp have the same condition outcome, there's no divergence.
For a 16x16 thread block, 16 threads in the same warp row might have different `local_x` but the same `local_y` (depending on how threads map to warps). In CUDA, threads within a warp are typically `threadIdx.x` varying fastest. So for a 16x16 block, a warp contains threads where `threadIdx.y` is the same or adjacent, and `threadIdx.x` varies across the warp.
Actually, for a 2D block of 16x16, the linear thread ID is `threadIdx.y * 16 + threadIdx.x`. A warp of 32 threads contains:
- For thread IDs 0..15: `ty=0, tx=0..15`
- For thread IDs 16..31: `ty=1, tx=0..15`
So a warp contains two rows. For input loading, `i = ty * 16 + tx`. Warp 0 loads `i=0..31`. These map to:
- `i=0..15`: (0,0) to (0,15)
- `i=16..31`: (1,0) to (1,15)
Wait, no. My loading loop uses `i = ty * BLOCK_W + tx` where BLOCK_W=16. So for block size 16x16:
- Thread (0,0): i=0
- Thread (0,1): i=1
- ...
- Thread (0,15): i=15
- Thread (1,0): i=16
- ...
- Thread (15,15): i=255
For the loading loop, we iterate with stride 256. So warp 0 (threads 0-31) loads elements i=0..31 in the first iteration. Thread 0 loads element 0, thread 1 loads element 1, etc.
For element i, `local_y = i / in_tile_w`, `local_x = i % in_tile_w`.
With `in_tile_w=38`:
- i=0: (0,0), i=1: (0,1), ..., i=15: (0,15)
- i=16: (0,16), i=17: (0,17), ..., i=31: (0,31)
So a warp loads 32 consecutive elements in the first row of the shared memory tile. For elements in the same row, `global_y` is the same, so the boundary condition `global_y >= 0 && global_y < in_h` is the same for all threads in that portion of the warp. For `global_x`, it varies, but boundary conditions might differ.
For top and bottom edge tiles, `global_y` might be out of bounds for some rows. If a warp loads row 0 and row 1 simultaneously, and row 0 is out of bounds but row 1 is in bounds, we get divergence.
For the test case with pad=0:
- Top edge tile (tile_y=0): iy_start=0. Rows 0..33 are all in bounds (in_h=128). No divergence.
- Bottom edge tile (tile_y=96): iy_start=96. Rows 0..33 in the tile map to global_y=96..129. Rows 34..? Wait, in_tile_h=34 for our test. So rows 0..33 map to 96..129. Global_y >=128 for rows 32,33. That's 2 rows out of bounds.
- In a warp, threads loading i=0..31 are all in row 0 (global_y=96), which is in bounds.
- Threads loading i=32..63 are in row 1 or 0? Let's see: 32/38=0, 33/38=0, ..., 37/38=0. i=32..37 are in row 0. i=38 is in row 1.
Actually for in_tile_w=38:
- i=0..37: row 0
- i=38..75: row 1
- i=76..113: row 2
- i=114..151: row 3
- etc.
Warp 0 loads i=0..31, all in row 0. No y-divergence.
Warp 1 loads i=32..63: i=32..37 in row 0, i=38..63 in row 1.
For bottom tile, rows 0 and 1 correspond to global_y=96,97 - both in bounds. No divergence.
Warp 2 loads i=64..95: i=64..75 in row 1, i=76..95 in row 2. Both in bounds.
In fact, for this test case no warp will have y-divergence because even the bottom rows are in bounds until row 32 (global_y=128). Wait, in_tile_h=34, so rows 32 and 33 map to global_y=128,129 which are out of bounds.
i for row 32: 32*38 = 1216 to 32*38+37 = 1253
i for row 33: 33*38 = 1254 to 33*38+37 = 1291
These are loaded by warps with base i:
- Warp for i=1216: threads 1216..1247. This warp has i=1216..1253 which spans row 32 and row 33. Both rows are out of bounds! So all threads in this warp take the "out of bounds" branch. No divergence.
- Warp for i=1248: i=1248..1279. But in_tile_size=1292, so this warp loads i=1248..1291 (last 44 elements). All in rows 32,33. All out of bounds.
So for this test case, there's no branch divergence! Great.
For edge cases in width:同理, rightmost tile has some columns out of bounds. But within a warp loading contiguous elements, whether they cross the boundary depends.
Actually, for the test case it's fine. For general cases there might be some divergence but it's acceptable.
Let me write the complete code now.
Actually, I realize I should also think about whether I need to handle the case where shared memory exceeds the limit. For general parameters, I'll add a check and fall back to PyTorch if needed. But for the kernel to compile and work, I need to handle it.
Let me add a fallback in Python:
```python
def forward(self, x):
out_h = (x.size(2) + 2 * self.padding_h - self.dilation_h * (self.kernel_size_h - 1) - 1) // self.stride_h + 1
out_w = (x.size(3) + 2 * self.padding_w - self.dilation_w * (self.kernel_size_w - 1) - 1) // self.stride_w + 1
# Check if our optimized kernel parameters fit
tile_h = 32
tile_w = 32
in_tile_h = (tile_h - 1) * self.stride_h + (self.kernel_size_h - 1) * self.dilation_h + 1
in_tile_w = (tile_w - 1) * self.stride_w + (self.kernel_size_w - 1) * self.dilation_w + 1
shared_mem = (in_tile_h * in_tile_w + self.kernel_size_h * self.kernel_size_w) * 4
if shared_mem > 48 * 1024: # Conservative limit
# Fall back to PyTorch's conv2d
return torch.nn.functional.conv2d(x, self.conv2d.weight, self.conv2d.bias,
stride=(self.stride_h, self.stride_w),
padding=(self.padding_h, self.padding_w),
dilation=(self.dilation_h, self.dilation_w),
groups=self.in_channels)
# Use custom kernel
...
```
Wait, but I can't use PyTorch's conv2d because the reference IS PyTorch's conv2d and we need to be faster. A fallback to reference is fine for correctness on edge cases, but for the main test case we should use the custom kernel.
But actually, I should just make sure my kernel handles the test case. Fordeep optimization, I might not need a fallback. But it's good practice.
Hmm, another thought: can I use `libtorch` APIs directly in the C++ wrapper instead of raw CUDA? That would be using `at::conv2d` which might just call cuDNN anyway. But the point is to write a custom CUDA kernel.
Alright, let me write the code and compile it. I'll start with the kernel as I designed it.
One more optimization idea: split the kernel into multiple smaller kernels specialized for common configurations, and instantiate them at compile time. But `load_inline` makes runtime dispatch tricky because we'd need multiple kernel instantiations and a host-side switch.
I'll just write one general kernel. If speedup is insufficient, I'll add template instantiations.
Let me also consider if I should use `half` or `__half` for fp16 support. The test is fp32, so no need.
Now let me write the Python module:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
import math
cuda_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH>
__global__ void depthwise_conv2d_kernel(...) {
// ... as designed ...
}
"""
cpp_source = """
torch::Tensor forward(torch::Tensor input, torch::Tensor weight, torch::Tensor bias,
int stride_h, int stride_w, int pad_h, int pad_w, int dilation_h, int dilation_w) {
// ... dispatch kernel ...
}
"""
# Use load_inline
depthwise_conv2d = load_inline(
name='depthwise_conv2d',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['forward'],
extra_cuda_cflags=['-O3', '--use_fast_math'],
verbose=False,
)
```
Wait, I need to be careful with `load_inline`. The CUDA code goes in `cuda_sources` and C++ host code in `cpp_sources`. The `functions` parameter tells pybind11 which functions to expose.
One common issue: if there's a compilation error in the CUDA code, it can be hard to debug. Let me make sure the code compiles.
Also, I should check if `c10::optional` works well. Instead, I'll just pass a `torch::Tensor bias` and check `bias.defined()`.
Let me write a clean version and compile. If it fails, I'll iterate.
Actually, I want to think about grid dimensions. Currently `blockIdx.z = batch * channels`. With batch=32 and channels=128, that's 4096. The maximum grid size in z-dimension is 65535 on most architectures, but newer ones support larger. 4096 is well within limits. Good.
One more optimization: for the specific test case, the weights are 3x7=21 floats. I could unroll the kernel loops manually or use template parameters for the kernel dimensions to enable unrolling.
Let me create a specialized path for small kernels:
```cpp
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH, int KH, int KW>
__global__ void depthwise_conv2d_kernel_specialized(...) {
// Same kernel but with KH, KW as template params for unrolling
...
#pragma unroll
for (int kh = 0; kh < KH; kh++) {
#pragma unroll
for (int kw = 0; kw < KW; kw++) {
...
}
}
}
```
Then dispatch:
```cpp
if (kernel_h == 3 && kernel_w == 7) {
kernel<16, 16, 2, 2, 3, 7><<<...>>>(...);
} else {
// general case
}
```
This should give better performance for the test case. Let me include this.
But wait, there's a complication: when KH and KW are template parameters, the shared memory for weights can also be sized as `s_weight[KH][KW]` which might be slightly more efficient. And the compiler can fully unroll the loops.
Given that the test uses 3x7, I'll add a specialized 3x7 path. For generality, I'll also include a general path.
Actually, let me just make the kernel dimensions template parameters for all cases, and create overloads for common sizes. But I don't know all test cases. For the given test, 3x7 is what matters.
Let me write a dispatch table:
```cpp
#define DISPATCH_SPECIALIZED(kernel_h, kernel_w, ...) \
if (kernel_h == 3 && kernel_w == 7) { \
depthwise_conv2d_kernel<16, 16, 2, 2, 3, 7><<<grid, block, shared_mem_size>>>(__VA_ARGS__); \
} else { \
depthwise_conv2d_kernel_general<16, 16, 2, 2><<<grid, block, shared_mem_size>>>(__VA_ARGS__, kernel_h, kernel_w); \
}
```
But this requires two kernel implementations which is more code. Let me just write one general kernel and trust the compiler. For a 3-element and 7-element loop, even without unrolling, the overhead is tiny.
Actually, on H100, small loops are handled well. The main bottleneck is memory bandwidth, not loop overhead. I'll stick with the general kernel.
Wait, I just realized I should also consider another optimization: channel-wise parallelism within a block. Currently each block handles one (batch, channel). With 4096 blocks and 132 SMs, that's ~31 blocks per SM. With concurrency of 8 blocks per SM, we have about 4 waves of blocks. That's sufficient to keep the GPU busy.
Actually, 4096 blocks / (132 SMs * 8 blocks/SM) = 3.88 waves. With 100% occupancy, that should be fine.
But wait - can we actually fit 8 blocks of 256 threads each concurrently? H100 has 2048 threads per SM max, so 2048/256 = 8 blocks. Yes.
Shared memory per block: 34*38*4 + 21*4 = 5.2KB. 8 blocks * 5.2KB = 41.6KB. H100 SM has 228KB shared mem, so we can fit up to 43 blocks but thread limit caps at 8.
Occupancy = 8/32 (max blocks per SM) = 25%? No, max blocks per SM is 32 on H100, but the thread limit of 2048 restricts us to 8 blocks of 256. Occupancy is typically measured as ratio of actual warps to max warps. Max warps per SM = 64 (2048 threads / 32). Actual warps = 8 blocks * 8 warps/block = 64 warps. So occupancy is 100%!
Great.
But what if I increase to 512 threads per block? Then max blocks = 4, warps = 4*16 = 64. Still 100%. But total blocks would be halved.
What about 1024 threads? Max blocks = 2, warps = 2*32 = 64. Still 100% occupancy. Total blocks = 131072/4 = 32768. Blocks per SM = 32768/132 = 248. With concurrency of 2, that's 124 waves. This seems worse than 8 blocks with 4 waves, because block launch overhead isn't perfectly amortized.
Actually, the number of waves matters less when there's enough total work. What matters more is:
1. Occupancy (100% in all cases above)
2. Register usage and latency hiding
3. Memory coalescing
With smaller blocks (256 threads), we have more blocks which gives the hardware more flexibility in scheduling. I'll stick with 256 threads.
Let me now write the actual code.
One more thought: should I use `constexpr` for tile sizes within the kernel instead of template parameters? Since `load_inline` generates C++, I can use templates. Let me use template parameters as I planned.
Actually, I realize I might run into issues with `extern __shared__ float s_mem[]` when I also want `s_weight` to have a specific 2D layout. I'll use 1D indexing for shared memory to avoid layout issues. Or I can use separate shared memory arrays if I know sizes at compile time, but they're runtime-sized.
With `extern __shared__ float s_mem[];`, I use it as:
```cpp
float* s_input = s_mem;
float* s_weight = s_mem + in_tile_h * in_tile_w;
```
And access with `s_input[local_y * in_tile_w + local_x]`. This is clean.
Actually, one more optimization: I can use `half2` or other vector types, but for fp32 float2 is available. The issue is that input width 256 is divisible by 2 but not by 4 if we consider the tile width with padding. For the test case, let me just use float.
For output writes, I could use float2 if each thread writes 2 consecutive values in x. With OUT_W_PER_TH=2, thread tx writes columns 2*tx and 2*tx+1, which are consecutive. I could store them as a float2. But writing a float2 requires casting the pointer, and we need to ensure 8-byte alignment. The output array is aligned, and for columns that are multiples of 2, float2 should be fine.
Actually, let's try: for a given `dy`, output columns for threads are:
tx=0: col 0,1
tx=1: col 2,3
...
tx=15: col 30,31
These are perfectly aligned float2 writes if tile_x is a multiple of 2. In our grid, tile_x = blockIdx.x * 32. So for blockIdx.x=0, cols 0,1 are at offset 0, which is 8-byte aligned. For blockIdx.x=1, cols 32,33 are at offset 32*4=128, which is also 8-byte aligned. Great!
So I can use float2 stores:
```cpp
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int oy = out_y + dy;
if (oy < out_h) {
float2 val2;
val2.x = accum[dy][0];
val2.y = accum[dy][1];
float* out_ptr = output + out_offset + oy * out_w + out_x;
if (out_x + 1 < out_w) {
*((float2*)out_ptr) = val2;
} else if (out_x < out_w) {
out_ptr[0] = val2.x;
}
}
}
```
This halves the number of store instructions. For memory-bound kernels on H100, this can help.
Similarly for the bias, I need to add it before storing:
```cpp
val2.x = accum[dy][0] + bval;
val2.y = accum[dy][1] + bval;
```
But `bval` might be 0 if no bias. Fine.
Actually, let me think if I can use vector loads for shared memory too. When loading from global to shared memory, consecutive threads load consecutive floats. I could use float2 loads for pairs of threads. But the complexity might not be worth it.
Let me include the float2 output stores.
Similarly, could I use float2 for input loads? Consecutive threads load consecutive floats. If two threads (2*i and 2*i+1) each load one float, they naturally form a float2 load if we use `__ldg` or pointer casting.
Actually, for the input loading loop, if I pair up threads:
```cpp
for (int i = (ty * BLOCK_W + tx) * 2; i < in_tile_size; i += BLOCK_H * BLOCK_W * 2) {
int i0 = i;
int i1 = i + 1;
// load two floats
}
```
But I need to be careful with bounds checking. And if `in_tile_size` is odd, the last element needs special handling. It's getting complex.
For the first version, I'll use scalar loads for input and vector stores for output.
Wait, another idea: if I make `OUT_W_PER_TH = 1` and `BLOCK_W = 32`, then each thread computes one output, and I can use 1D coalescing naturally. Let me reconsider.
With `BLOCK_H=16, BLOCK_W=32, OUT_H_PER_TH=1, OUT_W_PER_TH=1`:
- Block: 512 threads
- Output tile: 16x32
- Input tile: 18x38 = 684 floats = 2.7KB
- Shared mem: ~2.8KB
- Max concurrent blocks: min(2048/512=4, 228KB/2.8KB=81) = 4
- Occupancy: 4 * 16 warps = 64 warps / 64 max = 100%
- Total blocks: ceil(126/16) * ceil(250/32) * 4096 = 8 * 8 * 4096 = 262,144
- Blocks per SM: 262144/132 ≈ 1986, with concurrency 4, that's ~496 waves
Compared to 16x16 block with 2x2 outputs per thread:
- Block: 256 threads
- Output tile: 32x32
- Total blocks: 4 * 8 * 4096 = 131,072
- Blocks per SM: ~993, concurrency 8, ~124 waves
The 16x16 with 2x2 might have better data reuse because larger tiles mean less halo overhead. Let me calculate halo ratio:
- For 16x16 tile with 3x7 kernel: input=18x22=396, output=256. Ratio: 396/256 = 1.55 inputs per output.
- For 32x32 tile with 3x7 kernel: input=34x38=1292, output=1024. Ratio: 1292/1024 = 1.26 inputs per output.
- For 16x32 tile with 3x7 kernel: input=18x38=684, output=512. Ratio: 684/512 = 1.34.
So 32x32 tile has better data reuse. But with 2x2 per thread, we also have better compute intensity.
I think 16x16 threads with 2x2 outputs is a good balance. Let me stick with it.
Now, one concern about the compute loop: with `OUT_H_PER_TH=2` and `OUT_W_PER_TH=2`, the compiler generates nested loops. Will it allocate too many registers?
Each thread needs:
- 4 accumulators: 4 * 4 = 16 bytes
- Some index variables: maybe 8-12 registers
- Loop variables: a few more
Total should be well under 255 registers per thread. With 256 threads, total registers = 256 * ~32 = 8192. Per SM max is 65536 (64K 32-bit registers). So even with 8 blocks, we'd use 8 * 8192 = 65536 = exactly the limit. If register usage is higher, we might drop occupancy.
Let me try to minimize register pressure. Actually, H100 has 64K registers per SM. With 8 blocks of 256 threads, each thread can use up to 64K/8/256 = 32 registers. That's quite tight!
Wait, 64K registers per SM. 8 blocks * 256 threads = 2048 threads. 64K / 2048 = 32 registers per thread. But the compiler might spill if we need more, or it might reduce occupancy.
Actually, let me recheck. H100 has 64K 32-bit registers per SM. If each thread uses 64 registers, then max threads = 64K/64 = 1024. For 2048 threads, each can use at most 32 registers. But wait, 64K registers per SM and 2048 max threads per SM means 32 registers per thread if all threads are active.
However, if the compiler uses 64 registers per thread, we can only have 1024 threads per SM, which is 4 blocks of 256. Occupancy drops to 50%. This is bad!
To avoid this, I should check and try to keep register usage low.
Techniques to reduce registers:
1. Use fewer automatic variables
2. Mark arrays as `__shared__` instead of local when possible
3. Reduce loop nesting or unrolling control
For my kernel, `float accum[2][2]` is 4 floats on the stack (registers). That's fine. The compiler might optimize this. But with all the indexing arithmetic, it might use more registers.
Let me try a simpler variant to reduce register pressure:
```cpp
float sum00 = 0.0f, sum01 = 0.0f, sum10 = 0.0f, sum11 = 0.0f;
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
int base_y = (ty * 2) * stride_h + kh * dilation_h;
int base_x = (tx * 2) * stride_w + kw * dilation_w;
sum00 += s_input[base_y * in_tile_w + base_x] * w;
sum01 += s_input[base_y * in_tile_w + base_x + stride_w] * w;
sum10 += s_input[(base_y + stride_h) * in_tile_w + base_x] * w;
sum11 += s_input[(base_y + stride_h) * in_tile_w + base_x + stride_w] * w;
}
}
```
Wait, this assumes stride=1 for the output spacing, but with general stride, the relationship between adjacent outputs is:
output (y, x) and (y, x+1) differ by stride_w in input x.
output (y, x) and (y+1, x) differ by stride_h in input y.
For test case stride=1, yes. For general, I should use:
```cpp
sum00 += s_input[(base_y) * in_tile_w + (base_x)] * w;
sum01 += s_input[(base_y) * in_tile_w + (base_x + stride_w)] * w;
sum10 += s_input[(base_y + stride_h) * in_tile_w + (base_x)] * w;
sum11 += s_input[(base_y + stride_h) * in_tile_w + (base_x + stride_w)] * w;
```
This uses fewer registers because I compute `base_y` and `base_x` once per kernel element. The four accesses use these base values with small offsets.
And I use scalar variables instead of an array, which the compiler can optimize better.
Great, I'll use this approach.
For the general case (not just 2x2), I can't hardcode. But since I'm using template parameters, I could unroll if OUT_H_PER_TH and OUT_W_PER_TH are known. But for now, I'll keep the array-based version for generality.
Actually, for the specific test case, I'll just write a direct 2x2 version manually. But for generality, I need to support arbitrary sizes.
Let me write a version that works for arbitrary OUT_H_PER_TH and OUT_W_PER_TH (up to some max) using loops, but with the array.
Actually, another thought: since the test case is fixed, I could just hardcode everything for the test case and not worry about generality. But the problem says "accept the same constructor arguments" which implies it should work for any valid input. At minimum, it should work for the constructor signature.
I'll write a general kernel but with the instantiation parameters fixed at 16,16,2,2.
Alright, I think I've overthought this. Let me write the code and compile.
Actually, one more strategy: I can check what cuDNN/conv2d would do for this specific case and see if there's an even smarter approach.
For depthwise 3x7 conv on 128x256 input:
- FLOPs: ~26.8 GFLOPs
- Memory: ~1GB total traffic if naive
- Time at 3.35 TB/s: ~0.3 ms
- Time at 67 TFLOPS: ~0.4 ms
So we'd expect ~0.3-0.4 ms for the kernel.
PyTorch cuDNN reference might be around 0.2-0.5 ms. To beat it, I need to be close to memory bandwidth limit.
Let me also consider: could I use half-precision internally even for fp32 input? Like load as fp32, convert to fp16, compute in fp16 Tensor Cores, convert back? No, that would lose precision and the tolerance is tight (1e-4 for fp32). Plus the overhead of conversion probably isn't worth it for such a small kernel.
What about using implicit GEMM formulation? For depthwise conv, each channel has its own 3x7 kernel applied to its own input. Not much GEMM structure.
Alright, let me code it up. I'll use the shared memory tile approach with 16x16 threads and 2x2 outputs per thread.
One modification: instead of `__shared__ float s_weight[...]`, since weight is only 21 floats, I could store it in registers by having each thread load a subset and then broadcast. But shared memory is fast and simpler. Actually, 21 floats per block is trivial in shared memory (84 bytes).
Wait, let me optimize the weight access further. Currently:
```cpp
float w = s_weight[kh * kernel_w + kw];
```
With kernel_h=3, kernel_w=7. The compiler might unroll this if it's a small constant, but since it's a runtime parameter, it won't. However, the shared memory access itself is fast. Let me keep it.
Actually, since all threads in the block read the same weight at the same time (broadcast), shared memory can handle this in a single cycle (or 3 cycles on older GPUs, but H100 is fast). No bank conflicts.
For the input access pattern in the compute loop:
```cpp
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int local_y = (ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h;
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
int local_x = (tx * OUT_W_PER_TH + dx) * stride_w + kw * dilation_w;
accum[dy][dx] += s_input[local_y * in_tile_w + local_x] * w;
}
}
}
}
```
If `stride=1, dilation=1`, and `OUT_H_PER_TH=OUT_W_PER_TH=2`:
- For a fixed (kh, kw), threads in a warp access:
- ty=0, tx=0: local_y=0 or 1, local_x=0 or 1 (with kh,kw offsets)
- ty=0, tx=1: local_y=0 or 1, local_x=2 or 3
- ...
- ty=15, tx=15: local_y=30 or 31, local_x=30 or 31
So within a warp, for a given (kh, kw, dy), threads access local_x values that are 0,2,4,...,30 (for dy, dx loops). Wait, no. Let me trace more carefully.
For warp 0 (threads 0..31):
- Thread i corresponds to ty = i/16, tx = i%16
- For dy=0, dx=0: local_y = ty*2 + kh, local_x = tx*2 + kw
- For dy=0, dx=1: local_y = ty*2 + kh, local_x = tx*2 + 1 + kw
- etc.
So at a specific time in the loop, say dy=0, dx=0, all threads access:
local_y = (i/16)*2 + kh, local_x = (i%16)*2 + kw
For warp 0 (i=0..31):
i=0..15: ty=0, local_y=0+kh or 1+kh (depending on dx), local_x=0+kw,2+kw,4+kw,...,30+kw
i=16..31: ty=1, local_y=2+kh or 3+kh, local_x=0+kw,2+kw,...,30+kw
With in_tile_w=38:
Consecutive threads (0,1,2,... in warp) have local_x = kw, kw+2, kw+4, ..., kw+30, kw, kw+2, ..., kw+30
Wait, that's strided by 2! Threads 0 and 1 access local_x=kw and kw+2. With 32 banks, these might not conflict (kw mod 32 and (kw+2) mod 32 differ by 2), but the accesses are not contiguous, which means the load can't be fully coalesced.
Actually, for shared memory, coalescing doesn't apply in the same way as global memory. Each thread independently accesses shared memory. Shared memory bandwidth is much higher, and bank conflicts depend on whether different threads in the same warp hit the same bank.
With strided access by 2:
- Thread 0: bank (kw) % 32
- Thread 1: bank (kw+2) % 32
- Thread 2: bank (kw+4) % 32
- ...
- Thread 15: bank (kw+30) % 32
- Thread 16: bank (in_tile_w*(2+kh) + kw) % 32 = (76 + kw) % 32 = (12 + kw) % 32
For kw=0: banks 0,2,4,...,30,12,14,...,10
These are all distinct! Because threads 0..15 use even banks 0..30, and threads 16..31 use even banks 12..10 (wrapping). Wait, thread 16: 12, thread 17: 14, ..., thread 25: 30, thread 26: 0, thread 27: 2, ..., thread 31: 10.
So the 32 threads have banks: 0,2,4,...,30,12,14,16,...,10. Are there duplicates?
- 0: thread 0, thread 26
- 2: thread 1, thread 27
- 4: thread 2, thread 28
- 6: thread 3, thread 29
- 8: thread 4, thread 30
- 10: thread 5, thread 31
- 12: thread 6, thread 16
- 14: thread 7, thread 17
- 16: thread 8, thread 18
- 18: thread 9, thread 19
- 20: thread 10, thread 20
- 22: thread 11, thread 21
- 24: thread 12, thread 22
- 26: thread 13, thread 23
- 28: thread 14, thread 24
- 30: thread 15, thread 25
We have exactly 2-way bank conflicts! Each bank is accessed by exactly 2 threads. This doubles the shared memory access time.
Hmm, 2-way conflicts aren't terrible but they do hurt. For 4-way conflicts it would be worse.
Can I eliminate this? If I access with stride 1 instead of 2, there are no conflicts. But then I'd need to restructure the computation.
Actually, the bank conflict analysis above is for the compute loop. In the loading loop, we also have potential conflicts, but since we use contiguous accesses, there are none.
To fix compute bank conflicts, I could:
1. Change the thread-to-output mapping so adjacent threads compute adjacent outputs
2. Or restructure so each thread computes a row-major sequence
If each thread computes a contiguous strip in width, e.g., thread (ty, tx) computes outputs at:
(ty*2, tx*2), (ty*2, tx*2+1), (ty*2+1, tx*2), (ty*2+1, tx*2+1)
Then in the compute loop for a fixed (kh, kw, dy=0, dx=0):
Thread (0,0) accesses local_x=kw
Thread (0,1) accesses local_x=kw+2
Still strided by 2. Same problem.
What if I make `OUT_W_PER_TH=1` and `BLOCK_W=32`? Then:
Thread (ty, tx) computes output at (ty*str_h, tx*str_w).
For fixed (kh,kw): local_x = tx * stride_w + kw.
With stride_w=1: local_x = tx + kw. Adjacent threads have adjacent local_x. No bank conflicts!
Let me reconsider the block configuration:
- BLOCK_H=16, BLOCK_W=32 (512 threads)
- OUT_H_PER_TH=2, OUT_W_PER_TH=1
- Output tile: 32x32
Wait, if each thread computes 2 outputs in height and 1 in width:
- 16x32 threads compute 32x32 outputs
- Input tile: 34x38
- Input tile size: 1292 floats = 5.2KB (same as before)
- Threads per block: 512
- Max concurrent blocks: min(2048/512=4, ...) = 4
- Total blocks: ceil(126/32)*ceil(250/32)*4096 = 4*8*4096 = 131,072
- Warps per block: 16
- Occupancy: 4*16/64 = 100%
For the compute loop with OUT_W_PER_TH=1:
Thread tx accesses local_x = tx + kw for dy=0. Adjacent threads have adjacent local_x. No bank conflicts!
For dy=1: local_x = tx + kw still (same x). Great.
For height: dy=0 has local_y = ty*2 + kh, dy=1 has local_y = ty*2 + 1 + kh.
In a warp (32 threads), threads have varying tx and fixed or varying ty.
For BLOCK_H=16, BLOCK_W=32:
Thread i: ty = i/32 (0 or 1 for first 64 threads), tx = i%32.
Actually for 512 threads: 16 rows * 32 columns.
Warp 0: threads 0..31 which are ty=0, tx=0..31.
Warp 1: threads 32..63 which are ty=1, tx=0..31.
Etc.
For warp 0 (ty=0, tx=0..31):
- dy=0: local_y = 0 + kh, local_x = tx + kw
- All threads have same local_y, adjacent local_x. No conflicts!
For warp 1 (ty=1, tx=0..31):
- dy=0: local_y = 2 + kh, local_x = tx + kw
- Same pattern, no conflicts.
This is much better for shared memory bank conflicts!
But now each thread computes only 2 outputs instead of 4. So fewer FMAs per thread: 2 * 21 = 42 instead of 84. Still reasonable.
Actually, let me think about another option: BLOCK_H=8, BLOCK_W=32 with OUT_H_PER_TH=4, OUT_W_PER_TH=1.
- Threads: 256
- Output tile: 32x32
- Warp 0: ty=0, tx=0..31
- Warp 1: ty=1, tx=0..31
- ...
- Warp 7: ty=7, tx=0..31
For warp 0, dy=0..3:
- dy=0: local_y=0+kh
- dy=1: local_y=1+kh
- dy=2: local_y=2+kh
- dy=3: local_y=3+kh
All threads in warp have adjacent local_x. For a fixed dy, same local_y across warp. No conflicts!
But within the loop over dy, different dy values have different local_y. That's fine.
I think OUT_W_PER_TH=1 is better for bank conflicts. Let me go with that.
For the block size, I'll use:
- BLOCK_H=16, BLOCK_W=32
- OUT_H_PER_TH=2, OUT_W_PER_TH=1
Wait, with 16x32=512 threads, output tile is 32x32. Let me check total blocks:
- 4 tiles in H, 8 in W = 32 per (b,c)
- Total: 32*4096 = 131,072
- Blocks per SM: 131072/132 = 993
- Concurrent blocks per SM: 2048/512 = 4
- Waves: 993/4 = 248
With 256 threads (BLOCK_H=8, BLOCK_W=32, OUT_H_PER_TH=4, OUT_W_PER_TH=1):
- Output tile: 32x32
- Total blocks: same 131,072
- Concurrent blocks: 2048/256 = 8
- Waves: 993/8 = 124
More waves with smaller blocks might give better latency hiding. Let me go with 256 threads.
BLOCK_H=8, BLOCK_W=32, OUT_H_PER_TH=4, OUT_W_PER_TH=1.
For the compute loop:
```cpp
float sum0 = 0.0f, sum1 = 0.0f, sum2 = 0.0f, sum3 = 0.0f;
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
int base_y = ty * 4 + kh;
int base_x = tx + kw;
sum0 += s_input[base_y * in_tile_w + base_x] * w;
sum1 += s_input[(base_y + 1) * in_tile_w + base_x] * w;
sum2 += s_input[(base_y + 2) * in_tile_w + base_x] * w;
sum3 += s_input[(base_y + 3) * in_tile_w + base_x] * w;
}
}
```
This assumes stride=1. For general stride:
```cpp
int base_y = (ty * 4) * stride_h + kh * dilation_h;
int base_x = tx * stride_w + kw * dilation_w;
sum0 += s_input[base_y * in_tile_w + base_x] * w;
sum1 += s_input[(base_y + stride_h) * in_tile_w + base_x] * w;
sum2 += s_input[(base_y + 2*stride_h) * in_tile_w + base_x] * w;
sum3 += s_input[(base_y + 3*stride_h) * in_tile_w + base_x] * w;
```
For the general case with loops over dy, dx:
```cpp
for (int kh = 0; kh < kernel_h; kh++) {
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int local_y = (ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h;
int local_x = tx * stride_w + kw * dilation_w;
accum[dy] += s_input[local_y * in_tile_w + local_x] * w;
}
}
}
```
Where `accum` is an array of size OUT_H_PER_TH. This is clean.
And with OUT_W_PER_TH=1, adjacent threads access adjacent local_x. No bank conflicts.
Wait, I should also consider output writes. With OUT_W_PER_TH=1 and BLOCK_W=32, adjacent threads write to adjacent output columns. For float writes, this is fully coalesced! We can even use float2 or float4 if we pair threads, but plain float is already coalesced.
For OUT_H_PER_TH=4, each thread writes 4 outputs in different rows (not adjacent in memory, since rows are separated by out_w). These are strided writes, each coalesced within the warp for that row, but 4 separate write instructions. Fine.
Actually, I can write a float4 if the output pointer is aligned! For a given row, columns 0..31 written by 32 threads. If I reinterpret-cast to float4, each pair of threads could write together. But it's complex.
Let me just use scalar writes.
Another option: what if I make each thread compute multiple columns too? Like OUT_W_PER_TH=2 but restructure to avoid bank conflicts?
With OUT_W_PER_TH=2 and BLOCK_W=16:
Local_x = tx*2 + kw. Adjacent threads (tx=0,1) access local_x=kw, kw+2. That's strided by 2.
To avoid this, I could transpose the layout in shared memory. Instead of row-major, store as column-major or with padding. But the access pattern isn't regular enough.
Actually, another idea: `__shared__ float s_input[in_tile_h][in_tile_w + 1];` The +1 padding shifts the bank alignment for different rows. But for the specific strided access pattern, it might help with some conflicts but not all.
Or I could transpose the thread mapping: have threads 0..15 handle all columns in groups, and threads 16..31 handle others. No, that's messy.
I think OUT_W_PER_TH=1 is the cleanest solution.
Now, with BLOCK_H=8, BLOCK_W=32, OUT_H_PER_TH=4:
- 256 threads per block
- 32x32 output tile
- 128 total blocks per (b,c)?? Wait.
- Output H=126, tile_h=32, tiles = ceil(126/32)=4
- Output W=250, tile_w=32, tiles = ceil(250/32)=8
- Total per (b,c): 4*8=32
- Total blocks: 32*4096=131072
Hmm, same total blocks as before. But now with 256 threads instead of 512, concurrency is 8 vs 4. So we get more concurrent blocks (8 vs 4), and the same number of total blocks. This should be better.
What if I make the tile even larger to reduce halo overhead?
BLOCK_H=8, BLOCK_W=64, OUT_H_PER_TH=4, OUT_W_PER_TH=1:
- Tile: 32x64
- Tiles per (b,c): 4*4=16
- Total blocks: 16*4096=65536
- Threads: 512
- Concurrent: 4
- Halo: input=34x70=2380 floats=9.5KB
- Shared mem total: ~9.5KB + 84B = ~9.6KB
- 4 blocks * 9.6KB = 38.4KB < 228KB. Fine.
But 65536 blocks might be fewer than ideal. With 4 concurrent per SM, that's 65536/132/4 = 124 waves. Still decent.
What about BLOCK_H=8, BLOCK_W=64, OUT_H_PER_TH=8, OUT_W_PER_TH=1?
- Tile: 64x64
- Threads: 512
- Tiles per (b,c): 2*4=8
- Total: 8*4096=32768
- Concurrent: 4
- Waves: 32768/132/4 = 62
62 waves might be enough. But with fewer blocks, the GPU has less flexibility.
Let me stick with 32x32 tiles (BLOCK_H=8, BLOCK_W=32, OUT_H_PER_TH=4, OUT_W_PER_TH=1). If performance isn't sufficient, I'll try larger tiles.
Actually, I want to try one more thing. What about OUT_H_PER_TH=1, OUT_W_PER_TH=1 with larger blocks?
BLOCK_H=16, BLOCK_W=16:
- 256 threads, 16x16 tile
- Total blocks: 8*16*4096 = 524288
- Concurrent: 8
- Waves: 524288/132/8 = 496
- Small shared mem: 18x22=396, total ~1.6KB
With so many waves and small shared mem, this might have less reuse but more parallelism. Let me try both and compare.
I'll code up the 8x32 with 4x1 first. If it's too slow, I'll try 16x16 with 1x1.
Actually, you know what, I'll write a flexible kernel and try one configuration. Let me just write it and compile.
Here's my final kernel design:
- BLOCK_H=8, BLOCK_W=32
- OUT_H_PER_TH=4, OUT_W_PER_TH=1
- Tile: 32x32 output
- Input tile: 34x38 (for stride=1, pad=0, kernel=3x7)
- Shared memory: ~5.2KB
- Threads per block: 256
- 100% occupancy (8 blocks per SM)
- 131,072 total blocks
Let me write the code.
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
import math
CUDA_SOURCE = r'''
#include <torch/extension.h>
#include <cuda_runtime.h>
template <int BLOCK_H, int BLOCK_W, int OUT_H_PER_TH, int OUT_W_PER_TH>
__global__ void depthwise_conv2d_kernel(
const float* __restrict__ input,
const float* __restrict__ weight,
const float* __restrict__ bias,
float* __restrict__ output,
int batch_size,
int channels,
int in_h,
int in_w,
int out_h,
int out_w,
int kernel_h,
int kernel_w,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
) {
const int b = blockIdx.z / channels;
const int c = blockIdx.z % channels;
const int tile_h = BLOCK_H * OUT_H_PER_TH;
const int tile_w = BLOCK_W * OUT_W_PER_TH;
const int tile_y = blockIdx.y * tile_h;
const int tile_x = blockIdx.x * tile_w;
const int ty = threadIdx.y;
const int tx = threadIdx.x;
const int in_tile_h = (tile_h - 1) * stride_h + (kernel_h - 1) * dilation_h + 1;
const int in_tile_w = (tile_w - 1) * stride_w + (kernel_w - 1) * dilation_w + 1;
extern __shared__ float s_mem[];
float* s_input = s_mem;
float* s_weight = s_mem + in_tile_h * in_tile_w;
// Load weights
const int weight_size = kernel_h * kernel_w;
const int tid = ty * BLOCK_W + tx;
const int nthreads = BLOCK_H * BLOCK_W;
#pragma unroll
for (int i = tid; i < weight_size; i += nthreads) {
s_weight[i] = weight[c * weight_size + i];
}
// Load input tile with zero padding
const int in_offset = (b * channels + c) * in_h * in_w;
const int iy_start = tile_y * stride_h - pad_h;
const int ix_start = tile_x * stride_w - pad_w;
const int in_tile_size = in_tile_h * in_tile_w;
#pragma unroll
for (int i = tid; i < in_tile_size; i += nthreads) {
int local_y = i / in_tile_w;
int local_x = i % in_tile_w;
int global_y = iy_start + local_y;
int global_x = ix_start + local_x;
s_input[i] = (global_y >= 0 && global_y < in_h && global_x >= 0 && global_x < in_w)
? input[in_offset + global_y * in_w + global_x]
: 0.0f;
}
__syncthreads();
// Compute outputs
const int out_y = tile_y + ty * OUT_H_PER_TH;
const int out_x = tile_x + tx * OUT_W_PER_TH;
float accum[OUT_H_PER_TH];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
accum[dy] = 0.0f;
}
#pragma unroll
for (int kh = 0; kh < kernel_h; kh++) {
#pragma unroll
for (int kw = 0; kw < kernel_w; kw++) {
float w = s_weight[kh * kernel_w + kw];
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int local_y = (ty * OUT_H_PER_TH + dy) * stride_h + kh * dilation_h;
int local_x = tx * stride_w + kw * dilation_w;
accum[dy] += s_input[local_y * in_tile_w + local_x] * w;
}
}
}
// Write outputs
const int out_offset = (b * channels + c) * out_h * out_w;
const float bval = (bias != nullptr) ? bias[c] : 0.0f;
#pragma unroll
for (int dy = 0; dy < OUT_H_PER_TH; dy++) {
int oy = out_y + dy;
if (oy < out_h) {
#pragma unroll
for (int dx = 0; dx < OUT_W_PER_TH; dx++) {
int ox = out_x + dx;
if (ox < out_w) {
output[out_offset + oy * out_w + ox] = accum[dy] + bval;
}
}
}
}
}
torch::Tensor forward_cuda(
torch::Tensor input,
torch::Tensor weight,
torch::Tensor bias,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
) {
int batch_size = input.size(0);
int channels = input.size(1);
int in_h = input.size(2);
int in_w = input.size(3);
int kernel_h = weight.size(2);
int kernel_w = weight.size(3);
int out_h = (in_h + 2 * pad_h - dilation_h * (kernel_h - 1) - 1) / stride_h + 1;
int out_w = (in_w + 2 * pad_w - dilation_w * (kernel_w - 1) - 1) / stride_w + 1;
auto output = torch::empty({batch_size, channels, out_h, out_w}, input.options());
const int BLOCK_H = 8;
const int BLOCK_W = 32;
const int OUT_H_PER_TH = 4;
const int OUT_W_PER_TH = 1;
const int tile_h = BLOCK_H * OUT_H_PER_TH;
const int tile_w = BLOCK_W * OUT_W_PER_TH;
dim3 block(BLOCK_W, BLOCK_H);
dim3 grid(
(out_w + tile_w - 1) / tile_w,
(out_h + tile_h - 1) / tile_h,
batch_size * channels
);
int in_tile_h = (tile_h - 1) * stride_h + (kernel_h - 1) * dilation_h + 1;
int in_tile_w = (tile_w - 1) * stride_w + (kernel_w - 1) * dilation_w + 1;
size_t shared_mem_size = (in_tile_h * in_tile_w + kernel_h * kernel_w) * sizeof(float);
depthwise_conv2d_kernel<BLOCK_H, BLOCK_W, OUT_H_PER_TH, OUT_W_PER_TH><<<grid, block, shared_mem_size>>>(
input.data_ptr<float>(),
weight.data_ptr<float>(),
bias.defined() && bias.numel() > 0 ? bias.data_ptr<float>() : nullptr,
output.data_ptr<float>(),
batch_size,
channels,
in_h,
in_w,
out_h,
out_w,
kernel_h,
kernel_w,
stride_h,
stride_w,
pad_h,
pad_w,
dilation_h,
dilation_w
);
return output;
}
'''
CPP_SOURCE = r'''
torch::Tensor forward_cuda(
torch::Tensor input,
torch::Tensor weight,
torch::Tensor bias,
int stride_h,
int stride_w,
int pad_h,
int pad_w,
int dilation_h,
int dilation_w
);
'''
depthwise_conv2d = load_inline(
name='depthwise_conv2d',
cpp_sources=CPP_SOURCE,
cuda_sources=CUDA_SOURCE,
functions=['forward_cuda'],
extra_cuda_cflags=['-O3', '--use_fast_math'],
verbose=False,
)
class ModelNew(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size_h, kernel_size_w,
stride_h=1, stride_w=1, padding_h=0, padding_w=0,
dilation_h=1, dilation_w=1, groups=1, bias=False):
super().__init__()
self.in_channels = in_channels
self.kernel_size_h = kernel_size_h
self.kernel_size_w = kernel_size_w
self.stride_h = stride_h
self.stride_w = stride_w
self.padding_h = padding_h
self.padding_w = padding_w
self.dilation_h = dilation_h
self.dilation_w = dilation_w
self.groups = in_channels
self.has_bias = bias
self.weight = nn.Parameter(torch.empty(in_channels, 1, kernel_size_h, kernel_size_w))
nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))
if bias:
self.bias = nn.Parameter(torch.empty(in_channels))
fan_in, _ = nn.init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in) if fan_in > 0 else 0
nn.init.uniform_(self.bias, -bound, bound)
else:
self.register_parameter('bias', None)
def forward(self, x):
if self.bias is not None:
bias_tensor = self.bias
else:
bias_tensor = torch.empty(0, device=x.device, dtype=x.dtype)
return depthwise_conv2d.forward_cuda(
x,
self.weight,
bias_tensor,
self.stride_h,
self.stride_w,
self.padding_h,
self.padding_w,
self.dilation_h,
self.dilation_w
)
```
Wait, a couple of issues:
1. In `CPP_SOURCE`, I declared the function but it's already defined in `CUDA_SOURCE`. `load_inline` compiles both sources together. So the declaration in `CPP_SOURCE` and definition in `CUDA_SOURCE` should work. But actually, `load_inline` puts both in the same translation unit. Having just the declaration in `cpp_sources` and the definition in `cuda_sources` should be fine.
2. The `forward_cuda` function name: I should make sure it matches what's in `functions=['forward_cuda']`.
3. I should check if there are issues with `torch::Tensor bias` being undefined. In my Python code, I pass an empty tensor when bias is None. The C++ code checks `bias.defined() && bias.numel() > 0`.
4. One issue: when `groups` is passed but not equal to `in_channels`, the reference creates a grouped conv but not necessarily depthwise. But the docstring says "depthwise 2D convolution" and the reference uses `groups=in_channels`. I'll just follow the reference and use `groups=in_channels`.
Wait, I should match the reference exactly. The reference `Model.__init__` uses `groups=in_channels` regardless of the `groups` parameter passed in. Let me double check:
```python
self.conv2d = nn.Conv2d(in_channels, in_channels, (kernel_size_h, kernel_size_w), stride=(stride_h, stride_w), padding=(padding_h, padding_w), dilation=(dilation_h, dilation_w), groups=in_channels, bias=bias)
```
Yes, it ignores the `groups` argument and always uses `in_channels` for groups. So my model should do the same.
Alright, let me compile and test this.
But wait, I realize there might be an issue with the `extern __shared__ float s_mem[]` and the template. The size of `s_weight` depends on `kernel_h` and `kernel_w`, which are runtime parameters. Since `s_mem` is just a pointer to dynamically allocated shared memory, that's fine. But I need to make sure the `extern __shared__` array works inside a templated kernel. It should.
Another issue: in CUDA, `extern __shared__` can only appear once per kernel. I'm using it once. Good.
Let me also think about whether the kernel is general enough for all valid inputs, or if I need to handle edge cases. For example, if `stride_h=2` and `dilation_h=2` with a large kernel, `in_tile_h` could be very large. Let me check the maximum:
With BLOCK_H=8, OUT_H_PER_TH=4, tile_h=32.
in_tile_h = 31*stride_h + (kernel_h-1)*dilation_h + 1
If stride_h=10, kernel_h=10, dilation_h=10: in_tile_h = 310 + 90 + 1 = 401.
in_tile_w similarly could be large.
Shared mem = (401 * ... + ...) * 4.
For typical convs, this should be under 48KB, but for extreme cases it might exceed. I'll add a fallback in Python.
Actually, looking at the constructor args and typical usage, shared memory should be fine for reasonable configurations. I'll skip the fallback for now and add it if needed.
Let me compile. I'll use the compile_kernel function to check for errors without running correctness tests.
Wait, I need to make sure my Python code is a complete module that defines `ModelNew`. Let me write it as a single string.
One more thing: in `CPP_SOURCE`, I don't need to declare the function if it's defined in CUDA_SOURCE. But `load_inline` needs to know what's being exposed. The `functions` parameter tells pybind11 which functions to look for. Both `cpp_sources` and `cuda_sources` are compiled together, so as long as the function signature is visible, it should work.
Actually, `load_inline` often expects `cpp_sources` to contain the declarations that pybind11 will use. The auto-generated pybind11 module will try to bind `forward_cuda` by looking for it in the compiled sources. Since it's defined in `cuda_sources`, it should be found.
Let me test if empty `cpp_sources` works...
Looking at `torch.utils.cpp_extension.load_inline` docs: `cpp_sources` is a string or list of strings containing C++ source code. `cuda_sources` is similar for CUDA. Both are compiled into the same shared library.
I think I can put everything in `cuda_sources` and leave `cpp_sources` empty, or vice versa. But some setups require at least one of each. I'll put the declaration in `cpp_sources` and definition in `cuda_sources`.
Actually, looking at examples, it's common to put host wrappers in `cpp_sources` and kernels in `cuda_sources`. But for simplicity, I can put everything in `cpp_sources` and include the `.cu` code there with `__global__` inline. Wait no, `cpp_sources` is compiled with the C++ compiler, which might not handle CUDA syntax.
So I definitely need `cuda_sources` for the `__global__` kernel. And the host function `forward_cuda` can go in either. But actually, `forward_cuda` calls `<<< >>>` which is CUDA syntax, so it must be in `cuda_sources` or compiled with nvcc.
I'll put everything in `cuda_sources` and use an empty or minimal `cpp_sources`.
Let me write the code as a single Python string and compile.