/**
* @module sequences
*/
/**
* Calculates the square root of a number.
* @param {number} n - The number to calculate the square root of.
* @returns {number} The square root of n.
* @see {@link https://instacode.app/run/FASwtgDg9gTgLgAgN4IM4EcCuBDGBTAJSikQF8EAzGKMBAIgAEBzAa0wGMwQ8YAvAekxwQAG1R0A3MGAYc+IiSlA|▶ Try it live in Instacode}
*/
export const squareRoot = n => n ** 0.5;
/**
* Calculates the integer square root of a BigInt using Newton's method.
* @param {bigint} n - The BigInt to calculate the square root of.
* @returns {bigint} The integer square root of n.
* @see {@link https://instacode.app/run/FASwtgDg9gTgLgAgN4IM4EcCuBDGBTAJSijgCEBJBAXwQDMYowEAiAAQHMBrTAYzBDwwAXgHpMcEABtUzANzBgGHPiIkK8oA|▶ Try it live in Instacode}
*/
export const squareRootBI = n => {
if (n < 0n) throw new RangeError('Square root of negative numbers is not supported');
if (n === 0n) return 0n;
if (n < 4n) return 1n;
if (n < 9n) return 2n;
if (n < 16n) return 3n;
let res = BigInt(n.toString().substr(0, n.toString().length / 2));
let last;
while (true) {
last = res;
res = (res + n / res) / 2n;
const p = res * res;
if (p === n) return res;
if (last === res) return res;
const next = p + res * 2n - 1n;
if (n > next) return res;
}
return res;
};