Linear Feedback Shift Registers for the Uninitiated, Part VII: LFSR Implementations, Idiomatic C, and Compiler Explorer
The last four articles were on algorithms used to compute with finite fields and shift registers:
- multiplicative inverse
- discrete logarithm
- determining characteristic polynomial from the LFSR output
Today we’re going to come back down to earth and show how to implement LFSR updates on a microcontroller. We’ll also talk a little bit about something called “idiomatic C” and a neat online tool for experimenting with the C compiler.
Lazy Properties in Python Using Descriptors
This is a bit of a side tangent from my normal at-least-vaguely-embedded-related articles, but I wanted to share a moment of enlightenment I had recently about descriptors in Python. The easiest way to explain a descriptor is a way to outsource attribute lookup and modification.
Python has a bunch of “magic” methods that are hooks into various object-oriented mechanisms that let you do all sorts of ridiculously clever things. Whether or not they’re a good idea is another...
Android for Embedded Devices - 5 Reasons why Android is used in Embedded Devices
The embedded purists are going to hate me for this. How can you even think of using Android on an embedded system ? It’s after all a mobile phone operating system/software.
Sigh !! Yes I did not like Android to begin with, as well - for use on an Embedded System. But sometimes I think the market and needs decide what has to be used and what should not be. This is one such thing. Over the past few years, I have learned to love Android as an embedded operating system....
Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm
The last two articles were on discrete logarithms in finite fields — in practical terms, how to take the state \( S \) of an LFSR and its characteristic polynomial \( p(x) \) and figure out how many shift steps are required to go from the state 000...001 to \( S \). If we consider \( S \) as a polynomial bit vector such that \( S = x^k \bmod p(x) \), then this is equivalent to the task of figuring out \( k \) from \( S \) and \( p(x) \).
This time we’re tackling something...
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Last time we talked about discrete logarithms which are easy when the group in question has an order which is a smooth number, namely the product of small prime factors. Just as a reminder, the goal here is to find \( k \) if you are given some finite multiplicative group (or a finite field, since it has a multiplicative group) with elements \( y \) and \( g \), and you know you can express \( y = g^k \) for some unknown integer \( k \). The value \( k \) is the discrete logarithm of \( y \)...
Introduction to Deep Insight Analysis for RTOS Based Applications
Over the past several years, embedded systems have become extremely complex. As systems become more complex, they become harder and more time consuming to debug. It isn’t uncommon for development teams to spend more than 40% development cycle time just debugging their systems. This is where deep insight analysis has the potential to dramatically decrease costs and time to market.
Defining Deep Insight Analysis
Deep insight analysis is a set of tools and techniques that can be...
Linear Feedback Shift Registers for the Uninitiated, Part IV: Easy Discrete Logarithms and the Silver-Pohlig-Hellman Algorithm
Last time we talked about the multiplicative inverse in finite fields, which is rather boring and mundane, and has an easy solution with Blankinship’s algorithm.
Discrete logarithms, on the other hand, are much more interesting, and this article covers only the tip of the iceberg.
What is a Discrete Logarithm, Anyway?Regular logarithms are something that you’re probably familiar with: let’s say you have some number \( y = b^x \) and you know \( y \) and \( b \) but...
Linear Feedback Shift Registers for the Uninitiated, Part III: Multiplicative Inverse, and Blankinship's Algorithm
Last time we talked about basic arithmetic operations in the finite field \( GF(2)[x]/p(x) \) — addition, multiplication, raising to a power, shift-left and shift-right — as well as how to determine whether a polynomial \( p(x) \) is primitive. If a polynomial \( p(x) \) is primitive, it can be used to define an LFSR with coefficients that correspond to the 1 terms in \( p(x) \), that has maximal length of \( 2^N-1 \), covering all bit patterns except the all-zero...
Continuous Integration for Embedded Systems
It is no secret that anyone who wants to streamline project management, reduce risk and improve the quality needs some form of "automation" in SW development processes. What is commonly used in most companies as a tool for such automation is called Continuous Integration (CI). It is a good practice for embedded systems as well even though it is much harder to use CI for embedded systems compared to pure software development because embedded systems mostly depend on...
Finally got a drone!
As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process. When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video). Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...
Oscilloscope Dreams
My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.
When I was in college in the early 1990's, our oscilloscopes looked like this:
Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:
Oscilloscopes are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...
New book on Elliptic Curve Cryptography
New book on Elliptic Curve Cryptography now online. Deep discount for early purchase. Will really appreciate comments on how to improve the book because physical printing won't happen for a few more months. Check it out here: http://mng.bz/D9NA
Introduction to Microcontrollers - More Timers and Displays
Building Your World Around Timers
By now you have seen four different ways to use timers in your programs. Next we will look at some ways to produce the effect of multiple parallel streams of work in your program with the help of timers. This effect is only an appearance, not a reality, since a single microcontroller (one core) can only run a single thread of code. However, since microcontrollers are so fast in relation to a great many of the tasks to...
Ten Little Algorithms, Part 4: Topological Sort
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection
Today we’re going to take a break from my usual focus on signal processing or numerical algorithms, and focus on...
Modulation Alternatives for the Software Engineer
Before I get to talking about modulation, here's a brief diversion.
A long time ago -- 1993, to be precise -- I took my first course on digital electronics and processors. In that class, we had to buy a copy of the TTL Data Book* from Texas Instruments.
If you have any experience in digital logic design you probably know that TTL stands for Transistor-transistor logic (thereby making the phrase "TTL Logic" an example of RAS...
Vintage robotics!
The town we live in had it's yearly Spring Fesitval last weekend. There are vendor booths, food, rides, etc - it's a fun event put on by the town. The town shuts main street down each year for one day for the festival. All of the shops in this downtown strip have been converted into an Antique and art district.
While walking down the street, I spotted a cart full of robot arms in front of one of the antique shops! Quite an assortment - two with some type of...
Ten Little Algorithms, Part 7: Continued Fraction Approximation
In this article we explore the use of continued fractions to approximate any particular real number, with practical applications.
Wye Delta Tee Pi: Observations on Three-Terminal Networks
Today I’m going to talk a little bit about three-terminal linear passive networks. These generally come in two flavors, wye and delta.
Why Wye?The town of Why, Arizona has a strange name that comes from the shape of the original road junction of Arizona State Highways 85 and 86, which was shaped like the letter Y. This is no longer the case, because the state highway department reconfigured the intersection
Stairway to Thévenin
This article was inspired by a recent post on reddit asking for help on Thévenin and Norton equivalent circuits.
(With apologies to Mr. Thévenin, the rest of the e's that follow will remain unaccented.)
I still remember my introductory circuits class on the subject, roughly as follows:
(NOTE: Do not get scared of what you see in the rest of this section. We're going to point out the traditional approach for teaching linear equivalent circuits first. If you have...
Using XML to describe embedded devices (and speak to them)
This article discusses one of the typical development cycles in embedded device and communication design and presents a possible, light weight solution using the free DClib/netpp framework.
The challengeAssume we're faced with the design of an embedded device, be it a simple SoC unit or a more complex, uC controlled engine with various attached peripherals. From first prototype to the market, the following development cycle is typically walked through:
Launch of Youtube Channel: My First Videos - Embedded World 2017
I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience. I would try to make the vendors focus their pitch on the essential in order to produce a one to three minutes video per booth.
So far my experience with making videos was limited to family videos, so I knew I had lots of reading to do and lots of Youtube videos and tutorials to watch. Trade shows are...
Modulation Alternatives for the Software Engineer
Before I get to talking about modulation, here's a brief diversion.
A long time ago -- 1993, to be precise -- I took my first course on digital electronics and processors. In that class, we had to buy a copy of the TTL Data Book* from Texas Instruments.
If you have any experience in digital logic design you probably know that TTL stands for Transistor-transistor logic (thereby making the phrase "TTL Logic" an example of RAS...
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Last time we looked at spread-spectrum techniques using the output bit sequence of an LFSR as a pseudorandom bit sequence (PRBS). The main benefit we explored was increasing signal-to-noise ratio (SNR) relative to other disturbance signals in a communication system.
This time we’re going to use a PRBS from LFSR output to do something completely different: system identification. We’ll show two different methods of active system identification, one using sine waves and the other...
Embedded World 2018 - More Videos!
After the interview videos last week, this week I am very happy to release two more videos taken at Embedded World 2018 and that I am proud of.
For both videos, I made extensive use of my two new toys, a Zhiyun Crane Gimbal and a Sony a6300 camera.
The use of a gimbal like the Zhiyun makes a big difference in terms of making the footage look much more stable and cinematographic.
As for the Sony camera, it takes fantastic slow-motion footage and...
Favorite Tools - Look Up Tables
As we grow in our engineering careers, we must continually add new tools to our collective tool kits. One favorite tool in my toolkit will be obvious to many experienced embedded software engineers. I still remember learning this approach early in my career via code written by colleague David Starling. The tool in question:
Look up tablesLook up tables simplify code and improve firmware maintenance. What is a look up table? A look up table is often nothing more complex than a...
Creating a Hardware Abstraction Layer (HAL) in C
In my last post, C to C++: Using Abstract Interfaces to Create Hardware Abstraction Layers (HAL), I discussed how vital hardware abstraction layers are and how to use a C++ abstract interface to create them. You may be thinking, that’s great for C++, but I work in C! How do I create a HAL that can easily swap in and out different drivers? In today’s post, I will walk through exactly how to do that while using the I2C bus as an example.
Project Directory Organization
A recent question on Reddit’s C Programming sub asked what sort of directory structure people use for their projects. Perhaps not unsurprisingly this didn’t elicit a flood of answers - maybe there are no organizational schemes that people are happy with or perhaps few people consider it a glamorous topic (not that the C Programming subreddit is filled with glamorous people -no offense I love you all). Personally I find it to be a very interesting topic. Organization and process are...
Debugging with Heartbeat LEDs
In this article I’ll discuss one of the most basic debugging tools in an embedded system: the heartbeat LED. Picture this: you’re developing your first program for a new microcontroller. You’ve written the code, configured the programmer, downloaded the HEX file and now... what Your program is running - isn’t it?
Truth is that it’s hard to tell with most embedded software. Compared to desktop or even server applications embedded software tend not to have very many...
Embedded Systems Roadmaps
What skills should every embedded systems engineer have? What should you study next to improve yourself as an embedded systems engineer? In this article I'll share with you a few lists from well-respected sources that seek to answer these questions, with the hope of helping provide you a path to mastery. Whether you've only just finished your first Arduino project or you've been building embedded systems for decades, I believe there's something in here for everyone to help improve themselves as embedded systems engineers.
Short Takes (EE Shanty): What shall we do with a zero-ohm resistor?
In circuit board design you often need flexibility. It can cost hundreds or thousands of dollars to respin a circuit board, so I need flexibility for two main reasons:
- sometimes it's important to be able to use one circuit board design to serve more than one purpose
- risk reduction: I want to give myself the option to add in or leave out certain things when I'm not 100% sure I'll need them.
And so we have jumpers and DIP switches and zero-ohm resistors:
Jumpers and...
