pezkuwi-common/packages/util/bi/sqrt.js

import { BigInt } from '@pezkuwi/x-bigint';
import { _0n, _1n, _2pow53n, _sqrt2pow53n } from './consts.js';
import { nToBigInt } from './toBigInt.js';
/**
 * @name nSqrt
 * @summary Calculates the integer square root of a bigint
 */
export function nSqrt(value) {
    const n = nToBigInt(value);
    if (n < _0n) {
        throw new Error('square root of negative numbers is not supported');
    }
    // https://stackoverflow.com/questions/53683995/javascript-big-integer-square-root/
    // shortcut <= 2^53 - 1 to use the JS utils
    if (n <= _2pow53n) {
        // ~~ is more performant that Math.floor
        return BigInt(~~Math.sqrt(Number(n)));
    }
    // Use sqrt(MAX_SAFE_INTEGER) as starting point. since we already know the
    // output will be larger than this, we expect this to be a safe start
    let x0 = _sqrt2pow53n;
    while (true) {
        const x1 = ((n / x0) + x0) >> _1n;
        if (x0 === x1 || (x0 === (x1 - _1n))) {
            return x0;
        }
        x0 = x1;
    }
}