Peter Naur's classic 1985 essay "Programming as Theory Building" argues that a program is not its source code. A program is a shared mental construct (he uses the word theory) that lives in the minds of the people who work on it. If you lose the people, you lose the program. The code is merely a written representation of the program, and it's lossy, so you can't reconstruct
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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Latency Comparison Numbers (~2012) | |
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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 |