//... UNO. so use the universal pin names
# define frequency_output 6   // PD2 (2) is not a PWM pin on the UNO. Use 3, 5, 6, 9, 10 or 11
# define coil_neg A4          // PC4
# define pot_in A3            // PC3

//... deserves a name
# define inputPulse A5    //... anywhere, I avoid pin 13 (SCK)

double df;          // Default Rpm base output  //... is zero by default
double rt;          // Rpm time / Pure engine Rpm  //... is zero by default
int pot;            //... is zero by default

float potcorrect= 0.001;  //... must use a float, and what means: to turn the pot from -1 to 1

//... this global is unused, as you define it locally
// unsigned long pulse_time(0);

void setup() {
  //... remove this gratuitous comment: put your setup code here, to run once:

  Serial.begin(115200);
  Serial.println("\nhello, world");

  pinMode(frequency_output, OUTPUT);
  pinMode(coil_neg, INPUT);

//... unecessary  pinMode(pot_in, INPUT);
//... it's already LOW by deafaut  digitalWrite(frequency_output, LOW);
}

void loop() {
//  noInterrupts();
  //... remove this gratuitous comment: put your main code here, to run repeatedly:
  // Voltage measuring

  long pulse_time;

//... SCK? WTF. that's pin 13, just use that

//... true: SCK false pulseIn, does the same thing better
//...
  bool byHand = false;   //... try both. pulseIn will not hang like your while/while/while can. Will.
  
  if (byHand) {
//... you actually need to read the pin
    while (digitalRead(inputPulse) == LOW)
      ;  //wait for High on Pin2 of PORTB
    unsigned long start = micros();
    while (digitalRead(inputPulse) == HIGH)
      ;  //wait for Low
    while (digitalRead(inputPulse) == LOW)
      ;  //wait for High
    pulse_time = micros() - start;
  }
  else {  // use pulseIn
    pulse_time = pulseIn(inputPulse, HIGH);
    pulse_time += pulseIn(inputPulse, LOW);
  }

  // Rpm interpolation
//.. valid variable definition and initialisation but
//... you don't often see this around here
//  double rt(60 * (1000 / (pulse_time * 4)));
//  double df(pulse_time * (potcorrect * pot));

//... use floating point in you expressions or the caculation is done w/ integer maths
// double is the same as float on the UNO; using float is more honest
  double rt = 60.0 * (1000000.0 / (pulse_time * 4));  // 1000000 for microseconds

  pot = analogRead(pot_in);   //... this comes before the next line, otherwise your pot is stale.
  double df = pulse_time * (potcorrect * pot);



  //Output  //... formatting and additional variables
  analogWrite(frequency_output, df);  // Output PWM

  Serial.print("df (PWM):  ");
  Serial.print(df, 2);

  Serial.print("  rt: ");
  Serial.print(rt, 2);

  Serial.print("  pot: ");
  Serial.print(pot);

  Serial.println("");
}