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Implementing complex numbers and FFT with just datatypes (no floats)

In this article, I'll explain why implementing numbers with just algebraic datatypes is desirable. I'll then talk about common implementations of FFT (Fast Fourier Transform) and why they hide inherent inefficiencies. I'll then show how to implement integers and complex numbers with just algebraic datatypes, in a way that is extremely simple and elegant. I'll conclude by deriving a pure functional implementation of complex FFT with just datatypes, no floats.

Thunderbolt Networking

this gist is part of this series

NOTE FOR THIS TO BE RELIABLE ON NODE RESTARTS YOU WILL NEED PROXMOX KERNEL 6.2.16-14-pve OR HIGER

This fixes issues i bugged with the thunderbolt / thunderbolt-net maintainers (i will take everyones thanks now, lol)

Install LLDP - this is great to see what nodes can see which.

install lldpctl with apt install lldpd

Inspired by dannyfritz/commit-message-emoji

	#!/bin/bash
	currentAttempt=0
	totalAttempts=10
	delay=15

	while [ $currentAttempt -lt $totalAttempts ]
	do
	currentAttempt=$(( $currentAttempt + 1 ))

	echo "Attempt $currentAttempt of $totalAttempts..."

	/**
	* MIT License
	*
	* Copyright (c) 2016 Richard Adams (https://github.com/enriched)
	*
	* Permission is hereby granted, free of charge, to any person obtaining a copy
	* of this software and associated documentation files (the "Software"), to deal
	* in the Software without restriction, including without limitation the rights
	* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	* copies of the Software, and to permit persons to whom the Software is

	USE TestDB
	GO

	DECLARE @DatabaseName VARCHAR(100)
	DECLARE @SchemaName VARCHAR(100)
	DECLARE @TableName VARCHAR(100)
	DECLARE @ColumnName VARCHAR(100)
	DECLARE @FullyQualifiedTableName VARCHAR(500)

	--Create Temp Table to Save Results

	/*
	Thanks David <3 - https://medium.freecodecamp.com/the-100-correct-way-to-do-css-breakpoints-88d6a5ba1862
	*/
	@for-phone: ~"screen and (max-width: 44.9375rem)"; // < 720
	@for-tablet-only: ~"screen and (min-width: 45rem) and (max-width: 74.9375rem)"; // > 720 < 1199
	@for-tablet-portrait-only: ~"screen and (min-width: 45rem) and (max-width: 56.1875rem)"; // > 720 < 900
	@for-tablet-portrait-up: ~"screen and (min-width: 45rem)"; // > 720
	@for-tablet-landscape-up: ~"screen and (min-width: 56.25rem)"; // > 900
	@for-desktop-up: ~"screen and (min-width: 75rem)"; // > 1200
	@for-big-desktop-up: ~"screen and (min-width: 112.5rem)"; // > 1800

Commit type	Emoji
Initial commit	🎉 `:tada:`
Version tag	🔖 `:bookmark:`
New feature	✨ `:sparkles:`
Bugfix	🐛 `:bug:`

	SHA1: 7c7b67a6391f63bf8901cab72d522d3ba44e94ed
	SHA256: b19f0aa82d12597a97e4137e2c7e955c7936297f5c3fa2eaf408d85a1ad1fa23
	Remote IP: 38[.]180[.]136[.]158

	Additional Indicators for the machine where LNK was "possibly" created on:
	Machine ID: win-76vb895243v
	MAC Address: a3:66:cd:d2:6f:1c

	Install VMWare Workstation PRO 17 (Read it right. PRO!)
	Also, these keys might also work with VMWare Fusion 13 PRO. Just tested it.

	Sub to me on youtube pls - PurpleVibe32
	if you want more keys - call my bot on telegram. @purector_bot (THE BOT WONT REPLY ANYMORE) - Or: https://cdn.discordapp.com/attachments/1040615179894935645/1074016373228978277/keys.zip - the password in the zip is 102me.
	---
	This gist can get off at any time.
	PLEASE, DONT COPY THIS. IF YOU FORK IT, DONT EDIT IT.
	*If you have a problem comment and people will try to help you!
	*No virus

	#!/bin/bash --posix

	# ------------------------------------------------------------------------------
	# Copyright (C) 2024 Atrate
	#
	# This program is free software: you can redistribute it and/or modify
	# it under the terms of the GNU Affero General Public License as
	# published by the Free Software Foundation, either version 3 of the
	# License, or (at your option) any later version.
	#