From 631cd72f59a5cfa70abc08330f6688cf96fec1fb Mon Sep 17 00:00:00 2001
From: Danylo Kanievskyi <danylokaniev@gmail.com>
Date: Wed, 30 Oct 2024 16:52:50 +0200
Subject: [PATCH] fix: perform more precise `sqrt` on bignumbers in `FluidDex`

---
 src/dex/fluid-dex/fluid-dex.ts | 17 +++++++----------
 src/dex/fluid-dex/utils.ts     | 15 +++++++++++++++
 2 files changed, 22 insertions(+), 10 deletions(-)
 create mode 100644 src/dex/fluid-dex/utils.ts

diff --git a/src/dex/fluid-dex/fluid-dex.ts b/src/dex/fluid-dex/fluid-dex.ts
index b0704e119..be13c52fa 100644
--- a/src/dex/fluid-dex/fluid-dex.ts
+++ b/src/dex/fluid-dex/fluid-dex.ts
@@ -32,6 +32,7 @@ import { extractReturnAmountPosition } from '../../executor/utils';
 import { MultiResult } from '../../lib/multi-wrapper';
 import { generalDecoder } from '../../lib/decoders';
 import { BigNumber } from 'ethers';
+import { sqrt } from './utils';
 
 export class FluidDex extends SimpleExchange implements IDex<FluidDexData> {
   eventPools: { [id: string]: FluidDexEventPool } = {};
@@ -610,18 +611,14 @@ export class FluidDex extends SimpleExchange implements IDex<FluidDexData> {
   ): bigint {
     // Adding 1e18 precision
 
-    const xyRoot = BigInt(Math.floor(Math.sqrt(Number(x * y * BigInt(1e18)))));
-    const x2y2Root = BigInt(
-      Math.floor(Math.sqrt(Number(x2 * y2 * BigInt(1e18)))),
-    );
+    const xyRoot = sqrt(BigNumber.from(x).mul(y).mul(BigInt(1e18))).toBigInt();
+    const x2y2Root = sqrt(
+      BigNumber.from(x2).mul(y2).mul(BigInt(1e18)),
+    ).toBigInt();
 
     // Calculating 'a' using the given formula
-    const a =
-      (Number(y2) * Number(xyRoot) +
-        Number(t) * Number(xyRoot) -
-        Number(y) * Number(x2y2Root)) /
-      (Number(xyRoot) + Number(x2y2Root));
-    return BigInt(Math.floor(a));
+    const a = (y2 * xyRoot + t * xyRoot - y * x2y2Root) / (xyRoot + x2y2Root);
+    return a;
   }
 
   /**
diff --git a/src/dex/fluid-dex/utils.ts b/src/dex/fluid-dex/utils.ts
new file mode 100644
index 000000000..ff9dd3620
--- /dev/null
+++ b/src/dex/fluid-dex/utils.ts
@@ -0,0 +1,15 @@
+import { BigNumber } from 'ethers';
+
+const ONE = BigNumber.from(1);
+const TWO = BigNumber.from(2);
+
+export function sqrt(value: BigNumber) {
+  let x = value;
+  let z = x.add(ONE).div(TWO);
+  let y = x;
+  while (z.sub(y).isNegative()) {
+    y = z;
+    z = x.div(z).add(z).div(TWO);
+  }
+  return y;
+}