Initial rebrand: @polkadot -> @pezkuwi (14 packages)

- Package namespace: @polkadot/* -> @pezkuwi/*
- Repository: polkadot-js/common -> pezkuwichain/pezkuwi-common
- Author: Pezkuwi Team <team@pezkuwichain.io>

Core packages:
- @pezkuwi/util (utilities)
- @pezkuwi/util-crypto (crypto primitives)
- @pezkuwi/keyring (account management)
- @pezkuwi/networks (chain metadata)
- @pezkuwi/hw-ledger (Ledger hardware wallet)
- @pezkuwi/x-* (10 polyfill packages)

Total: 14 packages
Upstream: polkadot-js/common v14.0.1

packages/util/src/bn/sqrt.ts

@@ -0,0 +1,50 @@
+// Copyright 2017-2025 @polkadot/util authors & contributors
+// SPDX-License-Identifier: Apache-2.0
+
+import type { ToBn } from '../types.js';
+
+import { BN } from './bn.js';
+import { BN_MAX_INTEGER, BN_ONE, BN_SQRT_MAX_INTEGER } from './consts.js';
+import { bnToBn } from './toBn.js';
+
+/**
+ * @name bnSqrt
+ * @summary Calculates the integer square root of a BN
+ * @example
+ * <BR>
+ *
+ * ```javascript
+ * import BN from 'bn.js';
+ * import { bnSqrt } from '@pezkuwi/util';
+ *
+ * bnSqrt(new BN(16)).toString(); // => '4'
+ * ```
+ */
+export function bnSqrt <ExtToBn extends ToBn> (value: ExtToBn | BN | bigint | string | number | null): BN {
+  const n = bnToBn(value);
+
+  if (n.isNeg()) {
+    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.lte(BN_MAX_INTEGER)) {
+    // ~~ More performant version of Math.floor
+    return new BN(~~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 = BN_SQRT_MAX_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;
+  }
+}