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High-Performance Matrix Multiplication

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).

Intro

Matrix multiplication is a mathematical operation that defines the product of

	import boto3
	import apsw

	BLOCK_SIZE = 64 * 1024
	EMPTY_BLOCK = b"".join([b"\x00"] * BLOCK_SIZE)

	# Inheriting from a base of "" means the default vfs
	class S3VFS(apsw.VFS):
	def __init__(self, s3, bucket, vfsname=f"s3vfs", basevfs=""):
	self.vfsname = vfsname

	<!DOCTYPE html>
	<html lang="en">
	<head>
	<meta charset="utf-8" />
	<meta name="viewport" content="width=device-width, initial-scale=1" />
	<title>scratch</title>
	<style>
	body {
	font-family: Hack, Menlo, Monaco, 'Droid Sans Mono', 'Courier New', monospace;
	white-space: pre;

	import React, { useReducer, useEffect, useRef } from 'react';
	import firebase from 'firebase/app';
	import equal from 'deep-equal';

	function filterKeys(raw, allowed) {
	if (!raw) {
	return raw;
	}
	let s = new Set(allowed);
	return Object.keys(raw)

	/** @license React v16.2.0
	* react-dom.development.js
	*
	* Copyright (c) 2013-present, Facebook, Inc.
	*
	* This source code is licensed under the MIT license found in the
	* LICENSE file in the root directory of this source tree.
	*/

	'use strict';