Arduino:
Rounding numbers

How to:

In Arduino, you can round numbers using built-in functions. Key players are round, ceil, and floor. Here’s a quick demo:

void setup() {
  Serial.begin(9600);
  
  float myNumber = 123.4567;

  // Round to the nearest whole number
  Serial.println(round(myNumber)); // Outputs: 123

  // Always rounds up
  Serial.println(ceil(myNumber));  // Outputs: 124

  // Always rounds down
  Serial.println(floor(myNumber)); // Outputs: 123
}

void loop() {
  // Nothing to loop through.
}

Deep Dive:

Rounding algorithms have a long history; they’ve been around long before digital computers. In analog computing, rounding was a physical process. In digital computing, it’s a mathematical one.

Rounding is needed when we convert from a type with more precision (like float or double) to a type with less precision (like int). But how we round can vary:

1. round(): Standard rounding. If the fraction is 0.5 or higher, it goes up; else, it goes down.
2. ceil(): Short for “ceiling”, always rounds up to the nearest whole number, even if it’s closer to the lower number.
3. floor(): Opposite of ceiling; always rounds down.

Choosing between these functions hinges on what the rounded value is for. Measurements might need standard rounding, money often uses floor, while inventory systems might use ceil to ensure everything’s accounted for.

Arduino’s implementation of these functions is straightforward; they don’t handle extra cases like rounding to specific decimal places. For that, a custom function or deeper mathematics comes into play—think of multiplying to shift the decimal, rounding, then dividing back.

Round-off errors can accumulate, significantly impacting long calculations or iterative processes. Programmers need to be cautious when running numerous operations on rounded values.

See Also:

2. In-depth look at the pitfalls and strategies for rounding: Floating Point Guide
3. For advanced techniques, including custom rounding functions and handling round-off error, you might check academic resources or detailed programming guides.