continued fraction for sqrt(n)

continuedFractionForSqrt.js

function* continuedFractionForSqrt(n) {
  // https://trizenx.blogspot.com/2018/10/continued-fraction-factorization-method.html
  function floorDiv(a, b) {
    return typeof a === "bigint" && typeof b === "bigint" ? a / b : Math.floor(a / b);
  }
  n = BigInt(n);
  if (n < 0n) {
    throw new RangeError();
  }
  const root = BigInt(sqrt(n));
  const remainder = n - root * root;
  const i = Number(root) * 2 <= Number.MAX_SAFE_INTEGER ? Number(root) : root;
  yield i;
  if (remainder !== 0n) {
    // sqrt(n) = floor(sqrt(n)) + 1 / x
    // expand continued fraction:
    // x_k = floor(x_k) + 1 / x_(k+1)
    // each x_k will have form x_k = (sqrt(n) + y_k) / z_k
    const one = i / i;
    let zprev = one;
    let z = typeof i === "number" ? Number(remainder) : remainder;
    let y = i;
    do {
      const q = floorDiv((i + y), z);
      const ynew = q * z - y;
      const znew = zprev + q * (y - ynew);
      y = ynew;
      zprev = z;
      z = znew;
      console.assert(one <= q && q <= i + i);
      console.assert(one <= y && y <= i);
      console.assert(one <= z && z <= i + i);
      yield q;
    } while (zprev !== one); //TODO: why is it cycling here - ?
    console.assert(y === i && BigInt(z) === remainder && zprev === one);
  }
}