CUDA GEMM Kernels

This project contains CUDA implementations of matrix multiplication (GEMM).

• naive_gemm.cu: a straightforward GEMM kernel
• opt_gemm.cu: an optimized version using tiling and shared memory
• and so on..

1. Problem Definition

• Input:
  • Matrix (A): size (m \times k)
  • Matrix (B): size (k \times n)
• Output:
  • Matrix (C): size (m \times n), where (C = A \times B)

All matrices are assumed to be row‑major float arrays.

2. Kernel Description

• naive_gemm

  • Each thread computes a single element C[row, col].
  • The kernel directly reads A[row, :] and B[:, col] from global memory and performs the multiply–accumulate loop.
  • The implementation is simple but does not optimize memory reuse or access patterns.

• opt_gemm

  • Uses TILE_SIZE × TILE_SIZE tiles for computation.
  • Uses __shared__ memory to cache tiles of A and B and reuse them within a block.
  • Organizes global memory accesses to be coalesced, improving bandwidth utilization.