From d37137070076314e042f1926df055235ee479a27 Mon Sep 17 00:00:00 2001
From: malatrax <simon.malatrait@grenoble-inp.org>
Date: Mon, 29 Apr 2024 13:17:00 +0200
Subject: [PATCH] feat: add felt division based on binary exponentiation

---
 src/primitives/felt.test.ts | 21 ++++++++-------------
 src/primitives/felt.ts      | 27 ++++++++++++++++++++++++++-
 2 files changed, 34 insertions(+), 14 deletions(-)

diff --git a/src/primitives/felt.test.ts b/src/primitives/felt.test.ts
index 41bb3839..2b27db46 100644
--- a/src/primitives/felt.test.ts
+++ b/src/primitives/felt.test.ts
@@ -107,19 +107,14 @@ describe('Felt', () => {
   });
 
   describe('div', () => {
-    test('should divide two felts properly', () => {
-      const a = new Felt(10n);
-      const b = new Felt(2n);
-      const result = a.div(b);
-      const expected = new Felt(5n);
-      expect(result.eq(expected)).toBeTrue();
-    });
-    test('should go to 0 if a < b in a/b', () => {
-      const a = new Felt(5n);
-      const b = new Felt(10n);
-      const result = a.div(b);
-      const expected = new Felt(0n);
-      expect(result.eq(expected)).toBeTrue();
+    test.each([
+      [new Felt(10n), new Felt(2n)],
+      [new Felt(5n), new Felt(10n)],
+      [new Felt(Felt.PRIME - 10n), new Felt(10n)],
+      [new Felt(10n), new Felt(Felt.PRIME - 10n)],
+    ])('should divide two felts properly', (a: Felt, b: Felt) => {
+      const result = a.div(b).mul(b);
+      expect(result).toStrictEqual(a);
     });
   });
 });
diff --git a/src/primitives/felt.ts b/src/primitives/felt.ts
index 24b4570e..4a229aa4 100644
--- a/src/primitives/felt.ts
+++ b/src/primitives/felt.ts
@@ -42,7 +42,8 @@ export class Felt {
     if (!isFelt(other) || other.inner === 0n) {
       throw new ForbiddenOperation();
     }
-    return new Felt(this.inner / other.inner);
+
+    return this.mul(other.inv());
   }
 
   eq(other: MaybeRelocatable): boolean {
@@ -60,4 +61,28 @@ export class Felt {
   toHexString(): string {
     return this.inner.toString(16);
   }
+
+  /**
+   * @dev Compute modular multiplicative inverse with
+   * Euler totient's function and Fermat's little theorem
+   */
+  private inv(): Felt {
+    return this.pow(Felt.PRIME - 2n);
+  }
+
+  /** @dev Binary Exponentiation - Iterative version */
+  private pow(exp: bigint): Felt {
+    if (exp === 0n) return new Felt(1n);
+    if (exp === 1n) return this;
+    let res = 1n;
+    let inner = this.inner;
+    while (exp !== 0n) {
+      if (exp & 1n) {
+        res = (res * inner) % Felt.PRIME;
+      }
+      inner = (inner * inner) % Felt.PRIME;
+      exp >>= 1n;
+    }
+    return new Felt(res);
+  }
 }