Project: Function Fitting Calculator

In many of my microcontroller projects, I often need a function to correlate a raw ADC reading with a proper value. The math required to accurately convert something like a thermistor reading to a temperature often involves complex calculations, which can be computationally intensive and not very accurate on a microcontroller.

I discovered that by completing the entire circuit and then plotting the ADC values against known values from a reliable source, I can create a function using a two- or three-dimensional polynomial. This method is significantly more accurate and allows the microcontroller to use only addition, subtraction, multiplication, and bit shifting operations, which are much faster.

For my latest project, I decided to create a calculator that can handle all the heavy lifting when it comes to fitting an equation to these plots. I am not a professional and I understand there is always a better way to do something. This is my journey in creating that application.

09/09/2024

Whenever I am using an ADC on my microcontrollers (that’s the part that takes an analog voltage and gives you a digital value), you have to map it to known values. So, if I have it hooked up to a thermistor, I take an actual thermometer and take multiple sample measurements. Then, I either use linear regression or a parabola to find a function that I can use to map these values to a temperature or, in this case, a voltage. I do this a lot, and I thought it would be nice to have a calculator to do so, so I built one. I was in the flow state working on this for almost 2 hours; it was wonderful.

Now, I enter the raw read values and the actual measurements to match them. As I’m entering the data, it calculates everything. It will automatically fill out the calculated value for the raw data using the found function and give a percentage of how close it is. Getting an average of those percentages gives me an idea of how accurate my measurements likely are because all values should either be linear or based on a parabola.

09/10/2024

This took me way too long to figure out how to add the points to the graph, but after about 3 hours of banging my head, I got it! I think tomorrow I can go back to building my mapping calculations tab in the settings window.

09/12/2024

So… I tried to cheat. I gave Copilot my calculation functions for the linear and parabolic equations and asked it to make the next iteration cubic, and it did. It looked great, even included the same suboptimal way I calculated the first two. But when I ran the function on some data… Nope, not even close. I gave up. I really don’t need anything but parabolic equations. I don’t even need linear, to be honest, but if I can use linear, it’s several times faster to calculate than parabolic. Anyway, that was tonight’s journey. I feel like HAL trying to change a lightbulb.

09/25/2024

Okay, I got stuck on the calculator again. The functions it generates are precise, but that means long float numbers. So, I added a float precision control so you can simplify the equation and see with each change how it affects its accuracy. Then… long story short, microcontrollers hate float math or even dividing. There are some really fast tricks to divide by 10 that can be faster in some controllers than a bit shift, but I often use a bit shift to divide by multiples of 2. That’s pretty quick. That allows me to make my equation all integers and really speed up the calculations. Now I can do both (10^x) and (2^x) on all integers and see with each change how that affects the precision of the equation. This is a real tool to me now. I am super excited about this.

I have plans to add a place to input your maximum expected raw value. With that, I will also be able to report the maximum number of bits needed for the variables in use and whether they need to be signed. This way, I can determine if most controllers can keep it as an integer or if I need to use a long, a long long, or, in very rare circumstances, keep it as a byte (8 bits).

09/26/2024

I’ve been working on it more and added some new features:

Added arbitrary decimals (e.g., 10012 = 100.12) for doing fixed-point math with integer variables.
Included a max raw value so the entire range of the raw data can be considered, even if your plots don’t include it.
Added precision control for spreadsheets when plots are being calculated. You can set it to 0 to assume absolute integer math only, or to keep the chart from filling up with a lot of fractional numbers.
When using integer math, it will tell you what size in bits will be required for the variables in the calculation and if they need to be signed. This way, when you’re shaping your equation, you can target a certain variable type. This helps you determine if you can achieve the accuracy you need using only integers or if you need to use longs to get the required accuracy.

Right now, I can’t think of anything else I do to these equations when I am making them by hand. What is amazing is that with this, you can experiment with and check so many different combinations to get what you need out of it and see it all live and how it affects your plots.

This program is actually quite complicated, and some of these controls aren’t very self-explanatory. Down the road, I might not remember what they were supposed to do. So, I added a tooltip box that can display more text than a standard tooltip and provided a description for each control as you hover over it. I think future Andy will appreciate this clarity because sometimes the things past Andy wrote make no sense to me at all.

09/27/2024

I’ve got an idea. What if I added a new editable column between the reading and calculated columns that represents the weight as a percentage? This way, the plots can be weighted for importance during calculation. If you have an outlier that is less important, you can have it weigh less, or more if it’s more important. I think I’ll also include a button that will automatically calculate the weights of all the plots so that their accuracy is more even. Instead of nine plots being perfect and one plot being only 20%, it might make all plots really close to 80%. That could be very useful. Maybe another slider would be better to adjust from all being 100% to the accuracy being as equal as possible. I like this idea; I think this will be what I’ll do next.

I’ve finished the balance and weight system for this. There’s now a new column where you can input the weight of each plot. Also, I’ve built in an auto-balancing feature that performs numerous calculations to determine the best weight solution. The original generation is excellent for identifying outliers in the data. However, if you decide the outliers are correct, auto-balancing will help integrate everything and improve accuracy for that extra 0.01%.