Let me understand the task. I need to implement a CUDA kernel for the Smith-Waterman-style local sequence alignment scoring algorithm. The reference implementation: 1. Takes a score_matrix of shape (B, M, N) 2. Creates H matrix of shape (B, M+1, N+1) initialized to 0 3. For each cell (i, j), computes: - match = H[:, i-1, j-1] + score_matrix[:, i-1, j-1] - delete = H[:, i-1, j] + gap_open - insert = H[:, i, j-1] + gap_open - zero = 0 - stack = [zero, match, delete, insert] - H[:, i, j] = temperature * logsumexp(stack / temperature) 4. Returns max over all H values for each batch This is essentially a dynamic programming algorithm with a soft-max relaxation. The challenge is that each cell depends on previous cells (i-1, j-1), (i-1, j), and (i, j-1), which creates a data dependency. For CUDA optimization: - The DP has dependencies that make it inherently sequential in the naive approach - However, we can use a diagonal wavefront approach to parallelize - Cells on the same anti-diagonal (i+j = constant) can be computed in parallel Let me think about the diagonal wavefront approach: - For k from 2 to M+N, compute all cells where i+j = k - This allows parallel computation within each diagonal Alternatively, for small sizes like M=N=32, we might want to have each thread block handle one batch, and have threads cooperate within the block. Given the small sizes (32x32), I think a good approach would be: - One thread block per batch element - Within each block, use multiple warps/threads to compute the DP in a diagonal wavefront pattern - Use shared memory to store H values for faster access I'll create a kernel where each thread block handles one batch. Since M and N are both 32, the H matrix is 33x33. I'll store H in shared memory and use a parallel scan pattern to compute diagonals efficiently. The kernel will load the score_matrix values, then iterate through diagonals, computing each cell's value based on its dependencies from the previous diagonal. For the diagonal computation, I need to handle the boundary cases carefully. Each diagonal k spans from row max(1, k-N) to row min(k-1, M), with the column determined by j = k - i. To avoid bank conflicts in shared memory, I'll need to carefully consider the access pattern. For a 33x33 matrix, the diagonals start at k=2 and extend through k=66, with lengths that grow then shrink symmetrically. At k=2, only one element exists; at k=3, two elements; this continues up to the maximum diagonal length at the center, then decreases back with a small number of elements on each diagonal (max 32), I should have one thread per element on the diagonal. I'll compute all elements on diagonal k in parallel, then synchronize before moving to k+1. Here's the optimized implementation: ```python import torch import torch.nn as nn from torch.utils.cpp_extension import load_inline cuda_source = """ #include <cuda.h> #include <cuda_runtime.h> #include <cmath> __device__ __forceinline__ float logsumexp4(float a, float b, float c, float d, float temp) { float inv_temp = 1.0f / temp; float x0 = 0.0f * inv_temp; float x1 = a * inv_temp; float x2 = b * inv_temp; float x3 = c * inv_temp; // Find max for numerical stability float max_val = fmaxf(fmaxf(x0, x1), fmaxf(x2, x3)); float sum = expf(x0 - max_val) + expf(x1 - max_val) + expf(x2 - max_val) + expf(x3 - max_val); return temp * (max_val + logf(sum)); } __global__ void smith_waterman_kernel( const float* __restrict__ score_matrix, float* __restrict__ output, int B, int M, int N, float gap_open, float temperature ) { extern __shared__ float H[]; int b = blockIdx.x; if (b >= B) return; // H is (M+1) x (N+1), stored in shared memory int H_size = (M + 1) * (N + 1); // Initialize H to 0 for (int idx = threadIdx.x; idx < H_size; idx += blockDim.x) { H[idx] = 0.0f; } __syncthreads(); // Load score matrix for this batch const float* S = score_matrix + b * M * N; // Process diagonals for (int k = 2; k <= M + N; k++) { int i_start = max(1, k - N); int i_end = min(k - 1, M); for (int i = i_start + threadIdx.x; i <= i_end; i += blockDim.x) { int j = k - i; int idx_prev = (i-1) * (N+1) + (j-1); int idx_del = (i-1) * (N+1) + j; int idx_ins = i * (N+1) + (j-1); int idx_curr = i * (N+1) + j; float match = H[idx_prev] + S[(i-1) * N + (j-1)]; float delete = H[idx_del] + gap_open; float insert = H[idx_ins] + gap_open; H[idx_curr] = logsumexp4(0.0f, match, delete, insert, temperature); } __syncthreads(); } // Find max in H float max_val = 0.0f; for (int idx = threadIdx.x; idx < H_size; idx += blockDim.x) { max_val = fmaxf(max_val, H[idx]); } // Reduce to find global max __shared__ float smax[256]; smax[threadIdx.x] = max_val; __syncthreads(); for (int s = blockDim.x / 2; s > 0; s >>= 1) { if (threadIdx.x < s) { smax[threadIdx.x] = fmaxf(smax[threadIdx.x], smax[threadIdx.x + s]); } __syncthreads(); } if (threadIdx.x == 0) { output[b] = smax[0]; } } torch::Tensor smith_waterman_cuda(torch::Tensor score_matrix, float gap_open, float temperature) { int B = score_matrix.size(0); int M = score_matrix.size(1); int N = score_matrix.size(2); auto output = torch::zeros({B}, score_matrix.options()); int threads = 256; int H_size = (M + 1) * (N + 1); size_t shared_mem = H_size * sizeof(float); smith_waterman_kernel<<<B, threads, shared_mem>>>( score_matrix.data_ptr<float>(), output.data_ptr<float>(), B, M, N, gap_open, temperature ); return output; } """ smith_waterman = load_inline( name='smith_waterman', cpp_sources='', cuda_sources=cuda_source, functions=['smith_waterman_cuda'], extra_cuda_cflags=['-O3'], verbose=True ) class ModelNew(nn.Module): def __init__(self, gap_open=-1.0, temperature=1.0): super().__init__() self.gap_open = gap_open self.temperature = temperature def forward(self, score_matrix: torch.Tensor) -> torch.Tensor: return smith_waterwaterman.smith_waterman_cuda(score_matrix, self.gap_open, self.temperature) ``` I need to verify the logsumexp computation matches the reference implementation exactly. The PyTorch version uses `torch.logsumexp(stack / temperature, dim=-1)` followed by multiplication by temperature, so my kernel's `logsumexp4` function should produce identical results. Looking at the stack ordering in the reference: `[zero, match, delete, insert]`, my implementation needs to follow the same sequence. Let me verify the indexing for accessing elements from the score matrix and H array—each element at position (i, j) depends on the previous row and column values. The score matrix indexing `S[(i-1)*N + (j-1)]` correctly retrieves `score_matrix[b, i-1, j-1]` when flattened, matching the expected computation. I also need to ensure zero is properly handled as a constant rather than a tensor. Looking at the reference implementation, the four terms being combined are zero, match, delete, and insert—in that exact order for the stack. My `logsumexp4` function should process these in the same sequence: 0.0f first, then match, then delete, then insert. Since the kernel launches with B blocks and shared memory requires at least 1089 floats (33×33), and CUDA provides 48KB per block, I have sufficient space for the diagonal wavefront computation even with a batch size of 16. For the reduction to find the maximum, I'm using a shared memory array of 256 floats. With 256 threads active in the block, each thread writes its local maximum to `smax[threadIdx.x]`, then a parallel reduction narrows this down to a single value. The reduction operates across all H elements, not just the initialized cells, but since H initializes to zero, this still correctly identifies the maximum score across the alignment matrix. There's a potential edge case though: if all computed H values remain negative due to the score matrix and gap penalties, the maximum could still be zero from the padding region. But that aligns with the reference implementation, which explicitly includes zero in the stack and calls `.max()` on the full flattened H tensor. So returning zero when all alignment scores are negative is the intended behavior. I should also make sure the kernel handles edge cases like batch size of 0 gracefully, and that the module name doesn't have typos like calling it "smith_waterwaterman" instead of "smith_waterman".