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learning about high performance matmul on cpu. the fastest kernels i've implemented are blis and blis_12x8 in blis.h

best blis configs:

blis<N, 128, 64, 1024>    // for N = 1024
blis_12x8<N, 96, 48, 960> // for N = 1920

to benchmark all (half-decent) kernels, make bench && ./bench. only the blis kernels are multi threaded. remove -fopenmp from clags to limit to single thread. compare against numpy with python test-numpy.py. change value of N as required.

initializing b (in c = ab) makes the baseline matmul go from 40 gflops to 15 gflops on my computer. this does not happen on other people's computers. see the output of baseline.cpp

cpu details:

Model name:             AMD Ryzen 5 PRO 4650U with Radeon Graphics
  Thread(s) per core:   2
  Core(s) per socket:   6
Caches (sum of all):      
  L1d:                    192 KiB (6 instances)
  L1i:                    192 KiB (6 instances)
  L2:                     3 MiB (6 instances)
  L3:                     8 MiB (2 instances)

i have randomly initialized b in the benchmarks otherwise the blis kernels are too fast to accurately judge their performance.

N = 1024
baseline: 17.8267 GFLOPS/s
layered: 40.7594 GFLOPS/s
layered2: 40.2947 GFLOPS/s
blis: 148.928 GFLOPS/s

N = 1920
baseline: 7.56156 GFLOPS/s
blis_12x8: 254.638 GFLOPS/s

gpu bench: (N = 2048)

baseline_cuda: 170.983 GFLOPS/s
gmem_coalesced: 1315.48 GFLOPS/s
smem_blocked: 1607.82 GFLOPS/s
smem_blocked2: 1649.84 GFLOPS/s
thread_blocked: 5399.37 GFLOPS/s
thread_blocked2: 3765.12 GFLOPS/s

goal: 200 gflops destroyed

150 gflops on N = 1024. numpy gets 210. \ 250 gflops on N = 1920. numpy gets 280.

currently the blis 12x8 kernel requires N to be divisible by 12, so i can't use it with N = 1024. if i figure out how to handle N not divisible by 12, i should be able to get a big boost on N = 1024. todo for now.

• siboehm's article
• marek's article
• case study in algorithms for modern hardware
• blis paper
• gotoblas paper
• avx blis implementation walkthrough and visualization by @riemannianmani