impl/typescript.ts

/**
 * The largest whole number whose square does not exceed `n`.
 *
 * The floating-point square root is only a first guess: it is corrected with
 * exact bigint arithmetic, so a number just below a perfect square never rounds
 * up to its root.
 */
export function integerSqrt(n: number): number {
  if (!Number.isSafeInteger(n) || n < 0) {
    throw new RangeError(`n must be a whole number from 0 to 2^53 - 1, received ${n}`);
  }
  const target = BigInt(n);
  let r = BigInt(Math.floor(Math.sqrt(n)));
  while (r * r > target) r -= 1n;
  while ((r + 1n) * (r + 1n) <= target) r += 1n;
  return Number(r);
}