Tutorials

Work through the optimization ladder step by step. Each tutorial is self-contained: it explains a concept, shows the relevant code, and points to the research notes for the full mathematics.

The path through the ladder

Naive
  └─ dot-product extraction (AddDot)
       └─ unrolling
            └─ fused micro-kernel  (matmul: 4×4  /  matvec: 4×1)
                 └─ register accumulators
                      └─ pointer arithmetic
                           └─ vectorization
                                └─ cache blocking  (mc × kc)
                                     └─ matrix packing
                                          └─ fully-packed micro-kernel

Table of contents

#	Tutorial	What you'll learn
00	Overview	How the ladder is organized and how to use it
01	Build & run the ladder	Compile everything, run levels, measure
02	Reading GFLOPS & roofline	Interpreting numbers; memory- vs compute-bound
03	matmul: naive → micro-kernel	optim0 → optim8
04	matmul: blocking & packing	optim9 → optim14
05	matvec: the 4-output kernel	the 4×1 kernel and why it differs
06	Writing a new level	How to add optim15 yourself

Research notes

For the complete mathematics of each level, see the matmul research notes and matvec research notes sections (one page per optimN).