This is a short post that explains how to write a high-performance matrix multiplication program on modern processors. In this tutorial I will use a single core of the Skylake-client CPU with AVX2, but the principles in this post also apply to other processors with different instruction sets (such as AVX512).
Matrix multiplication is a mathematical operation that defines the product of
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sh -c "$(curl -fsSL https://raw.github.com/ohmyzsh/ohmyzsh/master/tools/install.sh)"
| Latency Comparison Numbers (~2012) | |
| ---------------------------------- | |
| L1 cache reference 0.5 ns | |
| Branch mispredict 5 ns | |
| L2 cache reference 7 ns 14x L1 cache | |
| Mutex lock/unlock 25 ns | |
| Main memory reference 100 ns 20x L2 cache, 200x L1 cache | |
| Compress 1K bytes with Zippy 3,000 ns 3 us | |
| Send 1K bytes over 1 Gbps network 10,000 ns 10 us | |
| Read 4K randomly from SSD* 150,000 ns 150 us ~1GB/sec SSD |
Using Python's built-in defaultdict we can easily define a tree data structure:
def tree(): return defaultdict(tree)That's it!