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...
How to Estimate Encoder Velocity Without Making Stupid Mistakes: Part II (Tracking Loops and PLLs)
Yeeehah! Finally we're ready to tackle some more clever ways to figure out the velocity of a position encoder. In part I, we looked at the basics of velocity estimation. Then in my last article, I talked a little about what's necessary to evaluate different kinds of algorithms. Now it's time to start describing them. We'll cover tracking loops and phase-locked loops in this article, and Luenberger observers in part III.
But first we need a moderately simple, but interesting, example...
Important Programming Concepts (Even on Embedded Systems) Part V: State Machines
Other articles in this series:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part VI: Abstraction
Oh, hell, this article just had to be about state machines, didn’t it? State machines! Those damned little circles and arrows and q’s.
Yeah, I know you don’t like them. They bring back bad memories from University, those Mealy and Moore machines with their state transition tables, the ones you had to write up...
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...
VHDL tutorial - A practical example - part 2 - VHDL coding
In part 1 of this series we focused on the hardware design, including some of the VHDL definitions of the I/O characteristics of the CPLD part. In part 2, we will describe the VHDL logic of the CPLD for this design.
With any design, the first step to gather the requirements for the job at hand. From part 1 of this article, I have copied two sections that address some of the requirements for the CPLD design.
The data acquisition engine has the...
An overview of Linux Boot Process for Embedded Systems
This Text provides an insight in to the Embedded Linux Boot Process. Reader should have a basic Knowledge of Boot Process in general and should be familiar with Embedded Linux Boot Process.
.................PART-A................(1) Software components Involved in Embedded Linux Boot Process (a) Bootloader (b) kernel Image (c) root file system - either an initrd image or a NFS location(2) Steps during Booting process of a conventional...Using the C language to program the am335x PRU
Introduction
Some weeks ago, I published an article on how we used the PRU to implement a power supply control loop having hard realtime constraints:
//www.embeddedrelated.com/showarticle/586.php
Writing this kind of logic in assembly language is not easy. First the assembly language itself may be difficult to learn depending on your background. Then, fixed and floating point arithmetics require lot of code. While macros help to handle the complexity, they still are error prone as you...
Digital PLL's -- Part 1
1. Introduction
Figure 1.1 is a block diagram of a digital PLL (DPLL). The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal. The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance. The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.
One application of the DPLL is to recover the timing in a digital...
Unit Tests for Embedded Code
I originate from an electrical engineering background and my first industry experience was in a large, staid defense contractor. Both of these experiences contributed to a significant lack of knowledge with regards to software development best practices. Electrical engineers often have a backwards view of software in general; large defense contractors have similar views of software and couple it with a general disdain for any sort of automation or ‘immature’ practices. While there...
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....
Endianness and Serial Communication
Endianness is a consideration that is easily overlooked in the design of embedded systems. I myself am amply guilty of this oversight. It’s something you don’t ever have to worry about if you’re only working with a single processor or two processors that have the same endianness. You can even avoid it if you have two processors that have different endianness but never transmit data between themselves that consists of more than one byte. It’s easy to lull...
Zebras Hate You For No Reason: Why Amdahl's Law is Misleading in a World of Cats (And Maybe in Ours Too)
I’ve been wasting far too much of my free time lately on this stupid addicting game called the Kittens Game. It starts so innocently. You are a kitten in a catnip forest. Gather catnip.
And you click on Gather catnip and off you go. Soon you’re hunting unicorns and building Huts and studying Mathematics and Theology and so on. AND IT’S JUST A TEXT GAME! HTML and Javascript, that’s it, no pictures. It’s an example of an
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow.
In the world of floating-point arithmetic, overflow is possible but not particularly common. You can get it when numbers become too large; IEEE double-precision floating-point numbers support a range of just under 21024, and if you go beyond that you have problems:
for k in [10, 100, 1000, 1020, 1023, 1023.9, 1023.9999, 1024]: try: ...10 Circuit Components You Should Know
Chefs have their miscellaneous ingredients, like condensed milk, cream of tartar, and xanthan gum. As engineers, we too have quite our pick of circuits, and a good circuit designer should know what's out there. Not just the bread and butter ingredients like resistors, capacitors, op-amps, and comparators, but the miscellaneous "gadget" components as well.
Here are ten circuit components you may not have heard of, but which are occasionally quite useful.
1. Multifunction gate (
Analog-to-Digital Confusion: Pitfalls of Driving an ADC
Imagine the following scenario:You're a successful engineer (sounds nice, doesn't it!) working on a project with three or four circuit boards. More than even you can handle, so you give one of them over to your coworker Wayne to design. Wayne graduated two years ago from college. He's smart, he's a quick learner, and he's really fast at designing schematics and laying out circuit boards. It's just that sometimes he takes some shortcuts... but in this case the circuit board is just something...
Byte and Switch (Part 1)
Imagine for a minute you have an electromagnet, and a microcontroller, and you want to use the microcontroller to turn the electromagnet on and off. Sounds pretty typical, right?We ask this question on our interviews of entry-level electrical engineers: what do you put between the microcontroller and the electromagnet?We used to think this kind of question was too easy, but there are a surprising number of subtleties here (and maybe a surprising number of job candidates that were missing...
Arduino robotics #1 - motor control
Arduino Robotics
Beginner robotics is a series of article chronicling my first autonomous robot build, Clusterbot. This build is meant to be affordable, relatively easy and instructive. The total cost of the build is around $50.
1. Arduino robotics - motor control2. Arduino robotics - chassis, locomotion and power3. Arduino robotics - wiring, coding and a test run4.VHDL tutorial - Creating a hierarchical design
In earlier blog entries I introduced some of the basic VHDL concepts. First, developing a function ('VHDL tutorial') and later verifying and refining it ('VHDL tutorial - part 2 - Testbench' and 'VHDL tutorial - combining clocked and sequential logic'). In this entry I will describe how to...
Introduction to Microcontrollers - Interrupts
It's Too Soon To Talk About Interrupts!
That, at least, could be one reaction to this chapter. But over the years I've become convinced that new microcontroller programmers should understand interrupts before being introduced to any complex peripherals such as timers, UARTs, ADCs, and all the other powerful function blocks found on a modern microcontroller. Since these peripherals are commonly used with interrupts, any introduction to them that does not...
Data Hiding in C
Strictly speaking, C is not an object-oriented language. Although it provides some features that fit into the object-oriented paradigm it has never had the full object-oriented focus that its successor C++ offers. C++ introduced some very useful concepts and abilities that I miss when I’m developing in ANSI C. One such concept is protected member variables and functions.
When you declare a class in C++ you can also declare member variables and functions as part of that class. Often, these...
Boot sequence for an ARM based embedded system -2
In the last post, we discussed about the startup execution sequence on an ARM based embedded system in broader terms. In this post, we are going to cover the details of a startup code.These details are also available through various ARM resources , however for the sake of completion of our discussion , here is - the flow the startup code for an ARM based embedded system.
Step 1: The reset
On startup, the processor will jump to fixed location ,(most ARM cores support two vector...
Behold, the New Comments System!
I have just finished implementing a new system for commenting the blogs. It uses Ajax extensively, so the page won't reload if you post a comment. And it is a 'threaded' system, which means that if you post a reply to a comment, it will be attached to it.
What do you think? I personally love it. Please go ahead and test it with a quick comment.
Although it is better to be logged in to post a comment, non-registered users can also comment, but they will have...
Best Embedded Systems pdf Documents Out There
There are thousands of pdf documents related to Embedded Systems available online. In fact, when I do a search in Google for:
embedded systems filetype:pdf
I get 4,340,000 results! A huge mix of articles, promotional documents, theses, etc.
Out of these 4 millions+ documents, I suspect that there must be at least a few hundreds jewels that deserve to be given more visibility.
Today, I am asking for your help (again!) to build a directory of some of the most useful pdf files out...
New Discussion Group for Users of TI ARM based MCUs
If you are a user of an ARM based TI Microcontroller, please feel free to join the new "TI ARM processors MCUs" discussion group by sending a blank email to: tiarm-subscribe@yahoogroups.com This discussion group will be moderated, so you don't have to worry about receiving more spam than you probably already get. It usually takes a few weeks for a group to gain momentum, so don't worry if the activity level is low for a little while, but make sure to join so you don't miss the good...
New TI MCU Resource Center
I am happy to announce the publication of the new "TI MCU Resource Center" on EmbeddedRelated.com, where TI will regularly add videos and articles to keep you informed on their latest and greatest MCU related products.
To access the new section, you'll find a link in the main menu of the site at the top of the page.
Blogs Section Now Online!
I am happy to announce that the blog section is now online.
Last week, I sent an email to all the members of EmbeddedRelated.com to ask for embedded systems experts who would be interested in blogging on the site. The response was very positive and I have selected 10 highly qualified individuals who will soon be writing here about all sorts of embedded systems related subjects. I am currently in the process of receiving their info (bio, photo, username, etc) and creating their bloggers'...
