Implementation of blocked and parallel matrix multiplication for Assignment 4.

Implementation

• naive_matmul: Standard triple-nested loop baseline
• blocked_matmul: Cache-optimized; default block_size = 64, but block size 16 found to be optimal
• parallel_matmul: OpenMP-based with #pragma omp parallel for collapse(2)

Methodology

• All timings averaged over 5 independent runs for stable measurements
• Three additional modes added: default, blocks (block-size sweep), threads (thread-count sweep)

Key Results

• All 10 test cases pass correctness validation (output.raw, tolerance 1e-2)
• Block size experiment: tested 16/32/64/128 → block size 16 gives best speedup (2.33×) on Case 7; the conventional default of 64 was not optimal
• Thread count experiment: tested 1/2/4/8 → 2 threads optimal (1.52×) on the 2-core Codespaces environment; 8 threads slower than 1 due to scheduling overhead
• Combined optimal (block 16 + 2 threads) gives ~3× over naive

Full performance tables and analysis available in README.md.

Challenges

• Local Windows toolchain (no g++ installed); completed in GitHub Codespaces
• Codespaces 2-core CPU limit caps achievable parallel speedup
• Provided test cases are small (largest 256 × 300); larger matrices would showcase parallelism better
• Submitted late due to setup issues

Co-authored with Muhammad Zahid.