add sqrt function

src/utils/index.ts

@@ -1,4 +1,5 @@
 import sortedInsert from './sortedInsert'
 import validateAndParseAddress from './validateAndParseAddress'
+import sqrt from './sqrt'
 
-export { sortedInsert, validateAndParseAddress }
+export { sortedInsert, validateAndParseAddress, sqrt }

src/utils/sqrt.test.ts

@@ -0,0 +1,24 @@
+import JSBI from 'jsbi'
+import { MaxUint256 } from '../constants'
+import sqrt from './sqrt'
+
+describe('#sqrt', () => {
+  it('correct for 0-1000', () => {
+    for (let i = 0; i < 1000; i++) {
+      expect(sqrt(JSBI.BigInt(i))).toEqual(JSBI.BigInt(Math.floor(Math.sqrt(i))))
+    }
+  })
+
+  it('correct for all even powers of 2', async () => {
+    for (let i = 0; i < 1000; i++) {
+      const root = JSBI.exponentiate(JSBI.BigInt(2), JSBI.BigInt(i))
+      const rootSquared = JSBI.multiply(root, root)
+
+      expect(sqrt(rootSquared)).toEqual(root)
+    }
+  })
+
+  it('correct for MaxUint256', () => {
+    expect(sqrt(MaxUint256)).toEqual(JSBI.BigInt('340282366920938463463374607431768211455'))
+  })
+})

src/utils/sqrt.ts

@@ -0,0 +1,31 @@
+import JSBI from 'jsbi'
+import invariant from 'tiny-invariant'
+
+export const MAX_SAFE_INTEGER = JSBI.BigInt(Number.MAX_SAFE_INTEGER)
+
+const ZERO = JSBI.BigInt(0)
+const ONE = JSBI.BigInt(1)
+const TWO = JSBI.BigInt(2)
+
+/**
+ * Computes floor(sqrt(value))
+ * @param value the value for which to compute the square root, rounded down
+ */
+export default function sqrt(value: JSBI): JSBI {
+  invariant(JSBI.greaterThanOrEqual(value, ZERO), 'NEGATIVE')
+
+  // rely on built in sqrt if possible
+  if (JSBI.lessThan(value, MAX_SAFE_INTEGER)) {
+    return JSBI.BigInt(Math.floor(Math.sqrt(JSBI.toNumber(value))))
+  }
+
+  let z: JSBI
+  let x: JSBI
+  z = value
+  x = JSBI.add(JSBI.divide(value, TWO), ONE)
+  while (JSBI.lessThan(x, z)) {
+    z = x
+    x = JSBI.divide(JSBI.add(JSBI.divide(value, x), x), TWO)
+  }
+  return z
+}