From d235de63e2a62a0768e3f1de69282b4244bb29d3 Mon Sep 17 00:00:00 2001
From: Miccah <m.castorina93@gmail.com>
Date: Mon, 16 Aug 2021 03:49:50 -0500
Subject: [PATCH] math: add egcd function implementing the extended Euclidean
 algorithm (#11203)

---
 vlib/math/math.v      | 15 +++++++++++++++
 vlib/math/math_test.v | 13 +++++++++++++
 2 files changed, 28 insertions(+)

diff --git a/vlib/math/math.v b/vlib/math/math.v
index 5e36425b6a..917998d8c1 100644
--- a/vlib/math/math.v
+++ b/vlib/math/math.v
@@ -89,6 +89,21 @@ pub fn gcd(a_ i64, b_ i64) i64 {
 	return a
 }
 
+// egcd returns (gcd(a, b), x, y) such that |a*x + b*y| = gcd(a, b)
+pub fn egcd(a i64, b i64) (i64, i64, i64) {
+	mut old_r, mut r := a, b
+	mut old_s, mut s := i64(1), i64(0)
+	mut old_t, mut t := i64(0), i64(1)
+
+	for r != 0 {
+		quot := old_r / r
+		old_r, r = r, old_r % r
+		old_s, s = s, old_s - quot * s
+		old_t, t = t, old_t - quot * t
+	}
+	return if old_r < 0 { -old_r } else { old_r }, old_s, old_t
+}
+
 // lcm calculates least common (non-negative) multiple.
 pub fn lcm(a i64, b i64) i64 {
 	if a == 0 {
diff --git a/vlib/math/math_test.v b/vlib/math/math_test.v
index 2f99353fa6..5a847278c5 100644
--- a/vlib/math/math_test.v
+++ b/vlib/math/math_test.v
@@ -764,3 +764,16 @@ fn test_large_tan() {
 		assert soclose(f1, f2, 4e-9)
 	}
 }
+
+fn test_egcd() {
+	helper := fn (a i64, b i64, expected_g i64) {
+		g, x, y := egcd(a, b)
+		assert g == expected_g
+		assert abs(a * x + b * y) == g
+	}
+
+	helper(6, 9, 3)
+	helper(6, -9, 3)
+	helper(-6, -9, 3)
+	helper(0, 0, 0)
+}