diff --git a/src/field/fft.rs b/src/field/fft.rs
index 35b11852..3fd37b1c 100644
--- a/src/field/fft.rs
+++ b/src/field/fft.rs
@@ -67,7 +67,7 @@ fn fft_unrolled_root_table<F: Field>(n: usize) -> FftRootTable<F> {
 
 #[inline]
 fn fft_dispatch<F: Field>(
-    input: Vec<F>,
+    input: &[F],
     zero_factor: Option<usize>,
     root_table: Option<FftRootTable<F>>,
 ) -> Vec<F> {
@@ -87,13 +87,13 @@ fn fft_dispatch<F: Field>(
 }
 
 #[inline]
-pub fn fft<F: Field>(poly: PolynomialCoeffs<F>) -> PolynomialValues<F> {
+pub fn fft<F: Field>(poly: &PolynomialCoeffs<F>) -> PolynomialValues<F> {
     fft_with_options(poly, None, None)
 }
 
 #[inline]
 pub fn fft_with_options<F: Field>(
-    poly: PolynomialCoeffs<F>,
+    poly: &PolynomialCoeffs<F>,
     zero_factor: Option<usize>,
     root_table: Option<FftRootTable<F>>,
 ) -> PolynomialValues<F> {
@@ -104,12 +104,12 @@ pub fn fft_with_options<F: Field>(
 }
 
 #[inline]
-pub fn ifft<F: Field>(poly: PolynomialValues<F>) -> PolynomialCoeffs<F> {
+pub fn ifft<F: Field>(poly: &PolynomialValues<F>) -> PolynomialCoeffs<F> {
     ifft_with_options(poly, None, None)
 }
 
 pub fn ifft_with_options<F: Field>(
-    poly: PolynomialValues<F>,
+    poly: &PolynomialValues<F>,
     zero_factor: Option<usize>,
     root_table: Option<FftRootTable<F>>,
 ) -> PolynomialCoeffs<F> {
@@ -139,11 +139,7 @@ pub fn ifft_with_options<F: Field>(
 /// The parameter r signifies that the first 1/2^r of the entries of
 /// input may be non-zero, but the last 1 - 1/2^r entries are
 /// definitely zero.
-pub(crate) fn fft_classic<F: Field>(
-    input: Vec<F>,
-    r: usize,
-    root_table: FftRootTable<F>,
-) -> Vec<F> {
+pub(crate) fn fft_classic<F: Field>(input: &[F], r: usize, root_table: FftRootTable<F>) -> Vec<F> {
     let mut values = reverse_index_bits(input);
 
     let n = values.len();
@@ -196,7 +192,7 @@ pub(crate) fn fft_classic<F: Field>(
 /// The parameter r signifies that the first 1/2^r of the entries of
 /// input may be non-zero, but the last 1 - 1/2^r entries are
 /// definitely zero.
-fn fft_unrolled<F: Field>(input: Vec<F>, r_orig: usize, root_table: FftRootTable<F>) -> Vec<F> {
+fn fft_unrolled<F: Field>(input: &[F], r_orig: usize, root_table: FftRootTable<F>) -> Vec<F> {
     let n = input.len();
     let lg_n = log2_strict(input.len());
 
@@ -325,10 +321,10 @@ mod tests {
         }
         let coefficients = PolynomialCoeffs::new_padded(coefficients);
 
-        let points = fft(coefficients.clone());
+        let points = fft(&coefficients);
         assert_eq!(points, evaluate_naive(&coefficients));
 
-        let interpolated_coefficients = ifft(points);
+        let interpolated_coefficients = ifft(&points);
         for i in 0..degree {
             assert_eq!(interpolated_coefficients.coeffs[i], coefficients.coeffs[i]);
         }
@@ -337,12 +333,9 @@ mod tests {
         }
 
         for r in 0..4 {
-            // expand ceofficients by factor 2^r by filling with zeros
-            let zero_tail = coefficients.clone().lde(r);
-            assert_eq!(
-                fft(zero_tail.clone()),
-                fft_with_options(zero_tail, Some(r), None)
-            );
+            // expand coefficients by factor 2^r by filling with zeros
+            let zero_tail = coefficients.lde(r);
+            assert_eq!(fft(&zero_tail), fft_with_options(&zero_tail, Some(r), None));
         }
     }
 
@@ -350,10 +343,7 @@ mod tests {
         let degree = coefficients.len();
         let degree_padded = 1 << log2_ceil(degree);
 
-        let mut coefficients_padded = coefficients.clone();
-        for _i in degree..degree_padded {
-            coefficients_padded.coeffs.push(F::ZERO);
-        }
+        let coefficients_padded = coefficients.padded(degree_padded);
         evaluate_naive_power_of_2(&coefficients_padded)
     }
 
diff --git a/src/field/interpolation.rs b/src/field/interpolation.rs
index 3d5e609c..83414f1b 100644
--- a/src/field/interpolation.rs
+++ b/src/field/interpolation.rs
@@ -18,7 +18,7 @@ pub(crate) fn interpolant<F: Field>(points: &[(F, F)]) -> PolynomialCoeffs<F> {
         .map(|x| interpolate(points, x, &barycentric_weights))
         .collect();
 
-    let mut coeffs = ifft(PolynomialValues {
+    let mut coeffs = ifft(&PolynomialValues {
         values: subgroup_evals,
     });
     coeffs.trim();
diff --git a/src/fri/prover.rs b/src/fri/prover.rs
index 1c642d17..c7717d03 100644
--- a/src/fri/prover.rs
+++ b/src/fri/prover.rs
@@ -91,8 +91,7 @@ fn fri_committed_trees<F: Field + Extendable<D>, const D: usize>(
                 .collect::<Vec<_>>(),
         );
         shift = shift.exp_u32(arity as u32);
-        // TODO: Is it faster to interpolate?
-        values = coeffs.clone().coset_fft(shift.into())
+        values = coeffs.coset_fft(shift.into())
     }
 
     coeffs.trim();
diff --git a/src/permutation_argument.rs b/src/permutation_argument.rs
index 3c98c801..7bad6d8d 100644
--- a/src/permutation_argument.rs
+++ b/src/permutation_argument.rs
@@ -90,7 +90,7 @@ impl<F: Fn(Target) -> usize> TargetPartition<Target, F> {
         }
 
         let mut indices = HashMap::new();
-        // // Here we keep just the Wire targets, filtering out everything else.
+        // Here we keep just the Wire targets, filtering out everything else.
         let partition = partition
             .into_values()
             .map(|v| {
diff --git a/src/polynomial/commitment.rs b/src/polynomial/commitment.rs
index e50839e7..93ef631f 100644
--- a/src/polynomial/commitment.rs
+++ b/src/polynomial/commitment.rs
@@ -34,10 +34,7 @@ impl<F: Field> ListPolynomialCommitment<F> {
     /// Creates a list polynomial commitment for the polynomials interpolating the values in `values`.
     pub fn new(values: Vec<PolynomialValues<F>>, rate_bits: usize, blinding: bool) -> Self {
         let degree = values[0].len();
-        let polynomials = values
-            .par_iter()
-            .map(|v| v.clone().ifft())
-            .collect::<Vec<_>>();
+        let polynomials = values.par_iter().map(|v| v.ifft()).collect::<Vec<_>>();
         let lde_values = timed!(
             Self::lde_values(&polynomials, rate_bits, blinding),
             "to compute LDE"
@@ -92,7 +89,7 @@ impl<F: Field> ListPolynomialCommitment<F> {
             .par_iter()
             .map(|p| {
                 assert_eq!(p.len(), degree, "Polynomial degree invalid.");
-                p.clone().lde(rate_bits).coset_fft(F::coset_shift()).values
+                p.lde(rate_bits).coset_fft(F::coset_shift()).values
             })
             .chain(if blinding {
                 // If blinding, salt with two random elements to each leaf vector.
@@ -182,7 +179,7 @@ impl<F: Field> ListPolynomialCommitment<F> {
         final_poly += zs_quotient;
 
         let lde_final_poly = final_poly.lde(config.rate_bits);
-        let lde_final_values = lde_final_poly.clone().coset_fft(F::coset_shift().into());
+        let lde_final_values = lde_final_poly.coset_fft(F::coset_shift().into());
 
         let fri_proof = fri_proof(
             &commitments
diff --git a/src/polynomial/division.rs b/src/polynomial/division.rs
index 50e1f8a6..6fa636ea 100644
--- a/src/polynomial/division.rs
+++ b/src/polynomial/division.rs
@@ -88,7 +88,7 @@ impl<F: Field> PolynomialCoeffs<F> {
 
         let root = F::primitive_root_of_unity(log2_strict(a.len()));
         // Equals to the evaluation of `a` on `{g.w^i}`.
-        let mut a_eval = fft(a);
+        let mut a_eval = fft(&a);
         // Compute the denominators `1/(g^n.w^(n*i) - 1)` using batch inversion.
         let denominator_g = g.exp(n as u64);
         let root_n = root.exp(n as u64);
@@ -112,7 +112,7 @@ impl<F: Field> PolynomialCoeffs<F> {
                 *x *= d;
             });
         // `p` is the interpolating polynomial of `a_eval` on `{w^i}`.
-        let mut p = ifft(a_eval);
+        let mut p = ifft(&a_eval);
         // We need to scale it by `g^(-i)` to get the interpolating polynomial of `a_eval` on `{g.w^i}`,
         // a.k.a `a/Z_H`.
         let g_inv = g.inverse();
diff --git a/src/polynomial/polynomial.rs b/src/polynomial/polynomial.rs
index 5f9bccd9..3e11f200 100644
--- a/src/polynomial/polynomial.rs
+++ b/src/polynomial/polynomial.rs
@@ -33,12 +33,12 @@ impl<F: Field> PolynomialValues<F> {
         self.values.len()
     }
 
-    pub fn ifft(self) -> PolynomialCoeffs<F> {
+    pub fn ifft(&self) -> PolynomialCoeffs<F> {
         ifft(self)
     }
 
     /// Returns the polynomial whose evaluation on the coset `shift*H` is `self`.
-    pub fn coset_ifft(self, shift: F) -> PolynomialCoeffs<F> {
+    pub fn coset_ifft(&self, shift: F) -> PolynomialCoeffs<F> {
         let mut shifted_coeffs = self.ifft();
         shifted_coeffs
             .coeffs
@@ -54,9 +54,9 @@ impl<F: Field> PolynomialValues<F> {
         polys.into_iter().map(|p| p.lde(rate_bits)).collect()
     }
 
-    pub fn lde(self, rate_bits: usize) -> Self {
+    pub fn lde(&self, rate_bits: usize) -> Self {
         let coeffs = ifft(self).lde(rate_bits);
-        fft_with_options(coeffs, Some(rate_bits), None)
+        fft_with_options(&coeffs, Some(rate_bits), None)
     }
 
     pub fn degree(&self) -> usize {
@@ -66,7 +66,7 @@ impl<F: Field> PolynomialValues<F> {
     }
 
     pub fn degree_plus_one(&self) -> usize {
-        self.clone().ifft().degree_plus_one()
+        self.ifft().degree_plus_one()
     }
 }
 
@@ -136,7 +136,7 @@ impl<F: Field> PolynomialCoeffs<F> {
             .fold(F::ZERO, |acc, &c| acc * x + c)
     }
 
-    pub fn lde_multiple(polys: Vec<Self>, rate_bits: usize) -> Vec<Self> {
+    pub fn lde_multiple(polys: Vec<&Self>, rate_bits: usize) -> Vec<Self> {
         polys.into_iter().map(|p| p.lde(rate_bits)).collect()
     }
 
@@ -194,16 +194,16 @@ impl<F: Field> PolynomialCoeffs<F> {
         Self::new(self.trimmed().coeffs.into_iter().rev().collect())
     }
 
-    pub fn fft(self) -> PolynomialValues<F> {
+    pub fn fft(&self) -> PolynomialValues<F> {
         fft(self)
     }
 
     /// Returns the evaluation of the polynomial on the coset `shift*H`.
-    pub fn coset_fft(self, shift: F) -> PolynomialValues<F> {
+    pub fn coset_fft(&self, shift: F) -> PolynomialValues<F> {
         let modified_poly: Self = shift
             .powers()
-            .zip(self.coeffs)
-            .map(|(r, c)| r * c)
+            .zip(&self.coeffs)
+            .map(|(r, &c)| r * c)
             .collect::<Vec<_>>()
             .into();
         modified_poly.fft()
@@ -262,8 +262,7 @@ impl<F: Field> Sub for &PolynomialCoeffs<F> {
 
     fn sub(self, rhs: Self) -> Self::Output {
         let len = max(self.len(), rhs.len());
-        let mut coeffs = self.coeffs.clone();
-        coeffs.resize(len, F::ZERO);
+        let mut coeffs = self.padded(len).coeffs;
         for (i, &c) in rhs.coeffs.iter().enumerate() {
             coeffs[i] -= c;
         }
@@ -343,7 +342,7 @@ impl<F: Field> Mul for &PolynomialCoeffs<F> {
             .zip(b_evals.values)
             .map(|(pa, pb)| pa * pb)
             .collect();
-        ifft(mul_evals.into())
+        ifft(&mul_evals.into())
     }
 }
 
@@ -390,7 +389,7 @@ mod tests {
         let n = 1 << k;
         let poly = PolynomialCoeffs::new(F::rand_vec(n));
         let shift = F::rand();
-        let coset_evals = poly.clone().coset_fft(shift).values;
+        let coset_evals = poly.coset_fft(shift).values;
 
         let generator = F::primitive_root_of_unity(k);
         let naive_coset_evals = F::cyclic_subgroup_coset_known_order(generator, shift, n)
@@ -411,7 +410,7 @@ mod tests {
         let n = 1 << k;
         let evals = PolynomialValues::new(F::rand_vec(n));
         let shift = F::rand();
-        let coeffs = evals.clone().coset_ifft(shift);
+        let coeffs = evals.coset_ifft(shift);
 
         let generator = F::primitive_root_of_unity(k);
         let naive_coset_evals = F::cyclic_subgroup_coset_known_order(generator, shift, n)
diff --git a/src/util/mod.rs b/src/util/mod.rs
index bfebe058..83a97881 100644
--- a/src/util/mod.rs
+++ b/src/util/mod.rs
@@ -51,7 +51,7 @@ pub(crate) fn transpose<T: Clone>(matrix: &[Vec<T>]) -> Vec<Vec<T>> {
 }
 
 /// Permutes `arr` such that each index is mapped to its reverse in binary.
-pub(crate) fn reverse_index_bits<T: Copy>(arr: Vec<T>) -> Vec<T> {
+pub(crate) fn reverse_index_bits<T: Copy>(arr: &[T]) -> Vec<T> {
     let n = arr.len();
     let n_power = log2_strict(n);
 
@@ -99,12 +99,9 @@ mod tests {
 
     #[test]
     fn test_reverse_index_bits() {
+        assert_eq!(reverse_index_bits(&[10, 20, 30, 40]), vec![10, 30, 20, 40]);
         assert_eq!(
-            reverse_index_bits(vec![10, 20, 30, 40]),
-            vec![10, 30, 20, 40]
-        );
-        assert_eq!(
-            reverse_index_bits(vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),
+            reverse_index_bits(&[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),
             vec![0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]
         );
     }