Matrix Multiplication Optimizations

Description

This project implements a minimalistic matrix multiplication focusing on various CPU optimization techniques such as:

• Tiling
• Loop flipping
• OpenMP for parallel processing
• BLAS (Basic Linear Algebra Subprograms)

Features

• Efficient matrix multiplication with different optimization strategies.
• Code implementations designed for performance on modern CPUs.
• OpenMP integration for multi-threading.
• BLAS for high-performance matrix operations.

Optimization Techniques and Performance Results

On a Apple M3 Max I get the following timings —

• Naive GEMM: ΔT=937,902µs (1.00x)
• Loop Flipping: ΔT=70,094µs (13.38x)
• Tiling: ΔT=71,804µs (13.06x)
• OpenMP (Parallelized): ΔT=10,752µs (87.23x)
• BLAS (Apple Accelerate Framework): ΔT=1,087µs (862.84x)

Note that the accelerate framework has access to special instructions, I take it as speed-of-light.