## You Don't Need an RTOS (Part 2)

In this second article, we'll tweak the simple superloop in three critical ways that will improve it's worst-case response time (WCRT) to be nearly as good as a preemptive RTOS ("real-time operating system"). We'll do this by adding task priorities, interrupts, and finite state machines. Additionally, we'll discuss how to incorporate a sleep mode when there's no work to be done and I'll also share with you a different variation on the superloop that can help schedule even the toughest of task sets.

## Unuglify C++ FSM with DSL

Domain Specific Languages (DSL) are an effective way to avoid boilerplate or repetitive code. Using DSLs lets the programmer focus on the problem domain, rather than the mechanisms used to solve it. Here I show how to design and implement a DSL using the C++ preprocessor, using the FSM library, and the examples I presented in my previous articles.

## Linear Feedback Shift Registers for the Uninitiated

In 2017 and 2018 I wrote an eighteen-part series of articles about linear feedback shift registers, or LFSRs:

div.jms-article-content ol > li { list-style-type: upper-roman } Ex-Pralite Monks and Finite Fields, in which we describe what an LFSR is as a digital circuit; its cyclic behavior over time; the definition of groups, rings, and fields; the isomorphism between N-bit LFSRs and the field \( GF(2^N) \); and the reason why I wrote this series## You Don't Need an RTOS (Part 1)

In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.

## Unraveling the Enigma: Object Detection in the World of Pixels

Exploring the realm of embedded systems co-design for object recognition, this blog navigates the convergence of hardware and software in revolutionizing industries. Delving into real-time image analysis and environmental sensing, the discussion highlights advanced object detection and image segmentation techniques. With insights into Convolutional Neural Networks (CNNs) decoding pixel data and autonomously extracting features, the blog emphasizes their pivotal role in modern computer vision. Practical examples, including digit classification using TensorFlow and Keras on the MNIST dataset, underscore the power of CNNs. Through industry insights and visualization aids, the blog unveils a tapestry of innovation, charting a course towards seamless interaction between intelligent embedded systems and the world.

## There's a State in This Machine!

An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.

## 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.

## Elliptic Curve Cryptography - Multiple Signatures

The use of point pairing becomes very useful when many people are required to sign one document. This is typical in a contract situation when several people are agreeing to a set of requirements. If we used the method described in the blog on signatures, each person would sign the document, and then the verification process would require checking every single signature. By using pairings, only one check needs to be performed. The only requirement is the ability to verify the...

## Flood Fill, or: The Joy of Resource Constraints

When transferred from the PC world to a microcontroller, a famous, tried-and-true graphics algorithm is no longer viable. The challenge of creating an alternative under severe resource constraints is an intriguing puzzle, the kind that keeps embedded development fun and interesting.

## Elliptic Curve Cryptography - Extension Fields

An introduction to the pairing of points on elliptic curves. Point pairing normally requires curves over an extension field because the structure of an elliptic curve has two independent sets of points if it is large enough. The rules of pairings are described in a general way to show they can be useful for verification purposes.

## You Don't Need an RTOS (Part 2)

In this second article, we'll tweak the simple superloop in three critical ways that will improve it's worst-case response time (WCRT) to be nearly as good as a preemptive RTOS ("real-time operating system"). We'll do this by adding task priorities, interrupts, and finite state machines. Additionally, we'll discuss how to incorporate a sleep mode when there's no work to be done and I'll also share with you a different variation on the superloop that can help schedule even the toughest of task sets.

## You Don't Need an RTOS (Part 1)

In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.

## Unuglify C++ FSM with DSL

Domain Specific Languages (DSL) are an effective way to avoid boilerplate or repetitive code. Using DSLs lets the programmer focus on the problem domain, rather than the mechanisms used to solve it. Here I show how to design and implement a DSL using the C++ preprocessor, using the FSM library, and the examples I presented in my previous articles.

## Square root in fixed point VHDL

In this blog we will design and implement a fixed point square root function in VHDL. The algorithm is based on the recursive Newton Raphson inverse square root algorithm and the implementation offers parametrizable pipeline depth, word length and the algorithm is built with VHDL records and procedures for easy use.

## Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

I’m writing this article in a room with a bunch of other people talking, and while sometimes I wish they would just SHUT UP, it would be...

## There's a State in This Machine!

An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.

## Linear Feedback Shift Registers for the Uninitiated

In 2017 and 2018 I wrote an eighteen-part series of articles about linear feedback shift registers, or LFSRs:

div.jms-article-content ol > li { list-style-type: upper-roman } Ex-Pralite Monks and Finite Fields, in which we describe what an LFSR is as a digital circuit; its cyclic behavior over time; the definition of groups, rings, and fields; the isomorphism between N-bit LFSRs and the field \( GF(2^N) \); and the reason why I wrote this series## Ten Little Algorithms, Part 3: Welford's Method (and Friends)

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

Last time we talked about a low-pass filter, and we saw that a one-line...

## Practical CRCs for Embedded Systems

CRCs are a very practical tool for embedded systems: you're likely to need to use one as part of a communications protocol or to verify the integrity of a program image before writing it to flash. But CRCs can be difficult to understand and tricky to implement. The first time I attempted to write CRC code from scratch I failed once. Then twice. Then three times. Eventually I gave up and used an existing library. I consider myself intelligent: I got A's...

## Elliptic Curve Cryptography - Basic Math

An introduction to the math of elliptic curves for cryptography. Covers the basic equations of points on an elliptic curve and the concept of point addition as well as multiplication.

## Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

I’m writing this article in a room with a bunch of other people talking, and while sometimes I wish they would just SHUT UP, it would be...

## Ten Little Algorithms, Part 1: Russian Peasant Multiplication

This blog needs some short posts to balance out the long ones, so I thought I’d cover some of the algorithms I’ve used over the years. Like the Euclidean algorithm and Extended Euclidean algorithm and Newton’s method — except those you should know already, and if not, you should be locked in a room until you do. Someday one of them may save your life. Well, you never know.

Other articles in this series:

- Part 1:

## Ten Little Algorithms, Part 3: Welford's Method (and Friends)

Other articles in this series:

- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection

Last time we talked about a low-pass filter, and we saw that a one-line...

## From Baremetal to RTOS: A review of scheduling techniques

Transitioning from bare-metal embedded software development to a real-time operating system (RTOS) can be a difficult endeavor. Many developers struggle with the question of whether they should use an RTOS or simply use a bare-metal scheduler. One of the goals of this series is to walk developers through the transition and decision making process of abandoning bare-metal thinking and getting up to speed quickly with RTOSes. Before diving into the details of RTOSes, the appropriate first step...

## 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...

## Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method

Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of the waveform they were sampled from.

## Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection

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 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method

This article is mainly an excuse to scribble down some cryptic-looking mathematics — Don’t panic! Close your eyes and scroll down if you feel nauseous — and...

## Practical CRCs for Embedded Systems

CRCs are a very practical tool for embedded systems: you're likely to need to use one as part of a communications protocol or to verify the integrity of a program image before writing it to flash. But CRCs can be difficult to understand and tricky to implement. The first time I attempted to write CRC code from scratch I failed once. Then twice. Then three times. Eventually I gave up and used an existing library. I consider myself intelligent: I got A's...

## 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.

## Elliptic Curve Cryptography

Secure online communications require encryption. One standard is AES (Advanced Encryption Standard) from NIST. But for this to work, both sides need the same key for encryption and decryption. This is called Private Key encryption.