@polkadot/util/bn/sqrt.js

// Copyright 2017-2022 @polkadot/util authors & contributors
// SPDX-License-Identifier: Apache-2.0
import { assert } from "../assert.js";
import { BN } from "./bn.js";
import { BN_MAX_INTEGER, BN_ONE, BN_ZERO } from "./consts.js";
import { bnToBn } from "./toBn.js";
const SQRT_MAX_SAFE_INTEGER = new BN(94906265);
/**
 * @name bnSqrt
 * @summary Calculates the integer square root of a BN
 * @example
 * <BR>
 *
 * ```javascript
 * import BN from 'bn.js';
 * import { bnSqrt } from '@polkadot/util';
 *
 * bnSqrt(new BN(16)).toString(); // => '4'
 * ```
 */

export function bnSqrt(value) {
  const n = bnToBn(value);
  assert(n.gte(BN_ZERO), '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.lte(BN_MAX_INTEGER)) {
    return new BN(Math.floor(Math.sqrt(n.toNumber())));
  } // 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 = SQRT_MAX_SAFE_INTEGER.clone();

  while (true) {
    const x1 = n.div(x0).iadd(x0).ishrn(1);

    if (x0.eq(x1) || x0.eq(x1.sub(BN_ONE))) {
      return x0;
    }

    x0 = x1;
  }
}