From 6a6414163a677065df1c7576c4d26395e8f09c60 Mon Sep 17 00:00:00 2001
From: wborgeaud <williamborgeaud@gmail.com>
Date: Sun, 20 Mar 2022 07:23:51 +0100
Subject: [PATCH 1/3] Fix `inv_mod_xn`

---
 field/src/polynomial/division.rs | 6 ++++++
 field/src/polynomial/mod.rs      | 9 +++++++--
 2 files changed, 13 insertions(+), 2 deletions(-)

diff --git a/field/src/polynomial/division.rs b/field/src/polynomial/division.rs
index d761ab50..c394b4b1 100644
--- a/field/src/polynomial/division.rs
+++ b/field/src/polynomial/division.rs
@@ -86,8 +86,14 @@ impl<F: Field> PolynomialCoeffs<F> {
 
     /// Computes the inverse of `self` modulo `x^n`.
     pub fn inv_mod_xn(&self, n: usize) -> Self {
+        assert!(n > 0, "`n` needs to be nonzero");
         assert!(self.coeffs[0].is_nonzero(), "Inverse doesn't exist.");
 
+        // If polynomial is constant, return the inverse of the constant.
+        if self.degree_plus_one() == 1 {
+            return Self::new(vec![self.coeffs[0].inverse()]);
+        }
+
         let h = if self.len() < n {
             self.padded(n)
         } else {
diff --git a/field/src/polynomial/mod.rs b/field/src/polynomial/mod.rs
index 33db6a87..85f982e4 100644
--- a/field/src/polynomial/mod.rs
+++ b/field/src/polynomial/mod.rs
@@ -528,10 +528,15 @@ mod tests {
         let mut rng = thread_rng();
         let a_deg = rng.gen_range(1..1_000);
         let n = rng.gen_range(1..1_000);
-        let a = PolynomialCoeffs::new(F::rand_vec(a_deg));
+        let mut a = PolynomialCoeffs::new(F::rand_vec(a_deg));
+        if a.coeffs[0].is_zero() {
+            a.coeffs[0] = F::ONE; // First coefficient needs to be nonzero.
+        }
         let b = a.inv_mod_xn(n);
         let mut m = &a * &b;
-        m.coeffs.drain(n..);
+        if m.coeffs.len() > n {
+            m.coeffs.drain(n..);
+        }
         m.trim();
         assert_eq!(
             m,

From 3b767ca42f7a42fa87a518cbababee905057c9bb Mon Sep 17 00:00:00 2001
From: wborgeaud <williamborgeaud@gmail.com>
Date: Sun, 20 Mar 2022 07:26:40 +0100
Subject: [PATCH 2/3] `a_deg` should be degree of `a`

---
 field/src/polynomial/mod.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/field/src/polynomial/mod.rs b/field/src/polynomial/mod.rs
index 85f982e4..10394f52 100644
--- a/field/src/polynomial/mod.rs
+++ b/field/src/polynomial/mod.rs
@@ -526,9 +526,9 @@ mod tests {
     fn test_inv_mod_xn() {
         type F = GoldilocksField;
         let mut rng = thread_rng();
-        let a_deg = rng.gen_range(1..1_000);
+        let a_deg = rng.gen_range(0..1_000);
         let n = rng.gen_range(1..1_000);
-        let mut a = PolynomialCoeffs::new(F::rand_vec(a_deg));
+        let mut a = PolynomialCoeffs::new(F::rand_vec(a_deg + 1));
         if a.coeffs[0].is_zero() {
             a.coeffs[0] = F::ONE; // First coefficient needs to be nonzero.
         }

From 163053b8fa60b53ea99cc115f655e67daa000cab Mon Sep 17 00:00:00 2001
From: wborgeaud <williamborgeaud@gmail.com>
Date: Mon, 21 Mar 2022 05:34:36 +0100
Subject: [PATCH 3/3] Use truncate instead of drain

---
 field/src/polynomial/mod.rs | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/field/src/polynomial/mod.rs b/field/src/polynomial/mod.rs
index 10394f52..035ee724 100644
--- a/field/src/polynomial/mod.rs
+++ b/field/src/polynomial/mod.rs
@@ -534,9 +534,7 @@ mod tests {
         }
         let b = a.inv_mod_xn(n);
         let mut m = &a * &b;
-        if m.coeffs.len() > n {
-            m.coeffs.drain(n..);
-        }
+        m.coeffs.truncate(n);
         m.trim();
         assert_eq!(
             m,