farey.ts

const farey = (x: number, N: number): [number, number] => {
  if (x > 1) {
    const units = Math.floor(x);
    const [a, d] = farey(x - units, N);

    return [a + units * d, d];
  }
  let [a, b] = [0, 1];
  let [c, d] = [1, 1];

  while (b <= N && d <= N) {
    const mediant = (a + c) / (b + d);
    if (x == mediant) {
      if (b + d <= N) {
        return [a + c, b + d];
      } else if (d > b) {
        return [c, d];
      } else {
        return [a, b];
      }
    } else if (x > mediant) {
      [a, b] = [a + c, b + d];
    } else {
      [c, d] = [a + c, b + d];
    }
  }
  if (b > N) {
    return [c, d];
  } else {
    return [a, b];
  }
};

farey(563 / 337, 1000);