From 3881eb19c523220e618d2daf60314087a103d7f1 Mon Sep 17 00:00:00 2001
From: pnezis <pnezis@gmail.com>
Date: Mon, 9 Mar 2026 22:01:57 +0200
Subject: [PATCH] Fix `Integer.extended_gcd/2` returning negative GCD for zero
 base cases

When one argument is 0 and the other is negative, `extended_gcd/2`
was returning a negative GCD, violating both the @spec (which
declares `non_neg_integer`) and consistency with `gcd/2`.
---
 lib/elixir/lib/integer.ex               | 10 ++++++++--
 lib/elixir/test/elixir/integer_test.exs |  9 ++++++++-
 2 files changed, 16 insertions(+), 3 deletions(-)

diff --git a/lib/elixir/lib/integer.ex b/lib/elixir/lib/integer.ex
index 7dd894d6860..a3f05fcc1ab 100644
--- a/lib/elixir/lib/integer.ex
+++ b/lib/elixir/lib/integer.ex
@@ -532,8 +532,12 @@ defmodule Integer do
 
       iex> Integer.extended_gcd(10, 0)
       {10, 1, 0}
+      iex> Integer.extended_gcd(-10, 0)
+      {10, -1, 0}
       iex> Integer.extended_gcd(0, 10)
       {10, 0, 1}
+      iex> Integer.extended_gcd(0, -10)
+      {10, 0, -1}
       iex> Integer.extended_gcd(0, 0)
       {0, 0, 0}
 
@@ -541,8 +545,10 @@ defmodule Integer do
   @doc since: "1.12.0"
   @spec extended_gcd(integer, integer) :: {non_neg_integer, integer, integer}
   def extended_gcd(0, 0), do: {0, 0, 0}
-  def extended_gcd(0, b), do: {b, 0, 1}
-  def extended_gcd(a, 0), do: {a, 1, 0}
+  def extended_gcd(0, b) when b > 0, do: {b, 0, 1}
+  def extended_gcd(0, b) when b < 0, do: {-b, 0, -1}
+  def extended_gcd(a, 0) when a > 0, do: {a, 1, 0}
+  def extended_gcd(a, 0) when a < 0, do: {-a, -1, 0}
 
   def extended_gcd(integer1, integer2) when is_integer(integer1) and is_integer(integer2) do
     extended_gcd(integer2, integer1, 0, 1, 1, 0)
diff --git a/lib/elixir/test/elixir/integer_test.exs b/lib/elixir/test/elixir/integer_test.exs
index db94d6b07a9..a9ba693cc52 100644
--- a/lib/elixir/test/elixir/integer_test.exs
+++ b/lib/elixir/test/elixir/integer_test.exs
@@ -282,7 +282,7 @@ defmodule IntegerTest do
   end
 
   test "extended_gcd" do
-    # Poor's man properby based testing
+    # Poor's man property based testing
     for _ <- 1..100 do
       left = :rand.uniform(1000)
       right = :rand.uniform(1000)
@@ -290,5 +290,12 @@ defmodule IntegerTest do
       assert Integer.gcd(left, right) == gcd
       assert m * left + n * right == gcd
     end
+
+    # zero cases
+    for {left, right} <- [{10, 0}, {0, 10}, {0, -10}, {-10, 0}] do
+      {gcd, m, n} = Integer.extended_gcd(left, right)
+      assert Integer.gcd(left, right) == gcd
+      assert m * left + n * right == gcd
+    end
   end
 end