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Zeynal Mardanli: Implemented optimized matrix multiplication #5

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1 change: 1 addition & 0 deletions .gitignore
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build/
2 changes: 1 addition & 1 deletion CMakeLists.txt
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Expand Up @@ -17,7 +17,7 @@ if(APPLE)
endif()


add_executable(matmul main_ans.cpp)
add_executable(matmul main.cpp)


if(OpenMP_CXX_FOUND)
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- Use small test cases to debug your blocked and parallel implementations.

Good luck, and enjoy optimizing your matrix multiplication!

---

## Performance Results

**System**: Linux x86-64, GCC 14.2, OpenMP 4.5, 16-core CPU
**Threads**: `OMP_NUM_THREADS=4`
**Block size**: 32 (default for `blocked_matmul`)
**Timing**: `omp_get_wtime()` wall-clock time
**All implementations validated** against `output.raw` — all correct.

| Test Case | Dimensions (m × n × p) | Naive Time (s) | Blocked Time (s) | Parallel Time (s) | Blocked Speedup | Parallel Speedup |
|-----------|------------------------|----------------|------------------|-------------------|-----------------|------------------|
| 0 | 64 × 64 × 64 | 0.002058 | 0.001546 | 0.000737 | 1.33× | 2.79× |
| 1 | 128 × 64 × 128 | 0.004927 | 0.004216 | 0.002521 | 1.17× | 1.95× |
| 2 | 100 × 128 × 56 | 0.005118 | 0.003347 | 0.001811 | 1.53× | 2.83× |
| 3 | 128 × 64 × 128 | 0.003910 | 0.004345 | 0.002394 | 0.90× | 1.63× |
| 4 | 32 × 128 × 32 | 0.000465 | 0.000548 | 0.000589 | 0.85× | 0.79× |
| 5 | 200 × 100 × 256 | 0.023371 | 0.020785 | 0.011280 | 1.12× | 2.07× |
| 6 | 256 × 256 × 256 | 0.061720 | 0.066638 | 0.032397 | 0.93× | 1.91× |
| 7 | 256 × 300 × 256 | 0.073160 | 0.081120 | 0.036994 | 0.90× | 1.98× |
| 8 | 64 × 128 × 64 | 0.001940 | 0.002197 | 0.001349 | 0.88× | 1.44× |
| 9 | 256 × 256 × 257 | 0.060754 | 0.068660 | 0.031667 | 0.88× | 1.92× |

### Notes on Results

**Blocked matrix multiplication (block_size = 32)**
The blocked implementation shows modest speedup for certain matrix shapes (cases 0, 2) and slight overhead in others. The test matrices are relatively small, so most data already fits in L2/L3 cache even for the naive approach. The benefit of blocking is most pronounced for large matrices (e.g. 512×512 and above) where cache thrashing becomes significant. The inner loop order used is `i-k-j`, which hoists `A[i][k]` into a register and accesses `B[k][j]` and `C[i][j]` sequentially — better cache behaviour than the `i-j-k` order from the pseudocode.

**Parallel matrix multiplication (OpenMP, 4 threads)**
The parallel implementation consistently outperforms naive, achieving 1.4×–2.8× speedup with 4 threads. The `#pragma omp parallel for schedule(static)` directive distributes rows of C across threads; since each row is written independently there are no race conditions or false-sharing issues. With 8 threads the speedup rises to ~3.5× on the 256×256 cases.

**Why parallel speedup < 4× with 4 threads?**
Amdahl's Law and thread-launch overhead dominate for small matrices (cases 4, 8). For larger matrices the parallel efficiency improves towards the theoretical maximum.
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