// note the simulation speed is about one third of real time
// adjust timings if using on real hardware.

const int buttonPin = 5;
unsigned long inStateAtMs = millis() ;
int buttonState ;  // 0 = waiting for press, 1= waiting for release 2= differentiate single or double 3= wait button release (double)

void setup() {
  pinMode(buttonPin, INPUT_PULLUP);
  Serial.begin(9600);
}

void loop() {

  if ( buttonState == 0 ) {
    // wait for button press
    if ( millis() - inStateAtMs > 100 ) {
      if (!digitalRead(buttonPin)) {
        buttonState = 1 ;
        inStateAtMs = millis();
      }
    }
  }
  else if ( buttonState == 1 ) {
    // wait for stable button release 1
    if ( millis() - inStateAtMs > 100 && digitalRead(buttonPin) ) {
      buttonState = 2 ;
      inStateAtMs = millis();
    }
  }
  else if ( buttonState == 2 ) {
    // differentiate between single and double press
    if ( millis() - inStateAtMs > 400 ) {
      // timeout - is a single press
      Serial.println("single");
      buttonState = 0 ;
      inStateAtMs = millis() ;
    }
    else if (  ( ! digitalRead(buttonPin) ) && (millis() - inStateAtMs > 100 ) ) {
      // got second press within timeout - double
      Serial.println("double");
      buttonState = 3 ;
      inStateAtMs = millis() ;
    }
  }
  else if ( buttonState == 3 ) {
    // wait for stable button release 2
    if ( millis() - inStateAtMs > 100 && digitalRead(buttonPin) ) {
      buttonState = 0 ;
      inStateAtMs = millis();
    }
  }
}