diff --git a/math/src/ring.rs b/math/src/ring.rs
index a335421..f8ef639 100644
--- a/math/src/ring.rs
+++ b/math/src/ring.rs
@@ -33,6 +33,10 @@ impl<O: Unsigned> RingRNS<O> {
         PolyRNS::<u64>::new(self.n(), self.level())
     }
 
+    pub fn new_poly(&self) -> Poly<u64> {
+        Poly::<u64>::new(self.n())
+    }
+
     pub fn max_level(&self) -> usize {
         self.0.len() - 1
     }
diff --git a/math/src/ring/impl_u64/rescaling_rns.rs b/math/src/ring/impl_u64/rescaling_rns.rs
index d1c9690..0de8059 100644
--- a/math/src/ring/impl_u64/rescaling_rns.rs
+++ b/math/src/ring/impl_u64/rescaling_rns.rs
@@ -1,6 +1,6 @@
 use crate::modulus::barrett::Barrett;
 use crate::modulus::{BARRETT, NONE, ONCE};
-use crate::poly::PolyRNS;
+use crate::poly::{Poly, PolyRNS};
 use crate::ring::Ring;
 use crate::ring::RingRNS;
 use crate::scalar::ScalarRNS;
@@ -8,18 +8,19 @@ extern crate test;
 
 impl RingRNS<u64> {
     /// Updates b to floor(a / q[b.level()]).
+    /// buf is unused if <ROUND=false,NTT=false>
     pub fn div_by_last_modulus<const ROUND: bool, const NTT: bool>(
         &self,
         a: &PolyRNS<u64>,
-        buf: &mut PolyRNS<u64>,
+        buf: &mut [Poly<u64>; 2],
         b: &mut PolyRNS<u64>,
     ) {
         debug_assert!(self.level() != 0, "invalid call: self.level()=0");
         debug_assert!(
-            self.level() <= a.level(),
-            "invalid input a: self.level()={} > a.level()={}",
-            self.level(),
-            a.level()
+            a.level() >= self.level(),
+            "invalid input a:  a.level()={} < self.level()={}",
+            a.level(),
+            self.level()
         );
         debug_assert!(
             b.level() >= self.level() - 1,
@@ -35,7 +36,7 @@ impl RingRNS<u64> {
         if ROUND {
             let q_level_half: u64 = r_last.modulus.q >> 1;
 
-            let (buf_q_scaling, buf_qi_scaling) = buf.0.split_at_mut(1);
+            let (buf_q_scaling, buf_qi_scaling) = buf.split_at_mut(1);
 
             if NTT {
                 r_last.intt::<false>(a.at(level), &mut buf_q_scaling[0]);
@@ -76,7 +77,7 @@ impl RingRNS<u64> {
             }
         } else {
             if NTT {
-                let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.0.split_at_mut(1);
+                let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.split_at_mut(1);
                 self.0[level].intt::<false>(a.at(level), &mut buf_ntt_q_scaling[0]);
                 for (i, r) in self.0[0..level].iter().enumerate() {
                     r.ntt::<true>(&buf_ntt_q_scaling[0], &mut buf_ntt_qi_scaling[0]);
@@ -104,12 +105,12 @@ impl RingRNS<u64> {
     /// Expects a to be in the NTT domain.
     pub fn div_by_last_modulus_inplace<const ROUND: bool, const NTT: bool>(
         &self,
-        buf: &mut PolyRNS<u64>,
+        buf: &mut [Poly<u64>; 2],
         a: &mut PolyRNS<u64>,
     ) {
         debug_assert!(
             self.level() <= a.level(),
-            "invalid input a: self.level()={} > a.level()={}",
+            "invalid input a: a.level()={} < self.level()={}",
             self.level(),
             a.level()
         );
@@ -120,7 +121,7 @@ impl RingRNS<u64> {
 
         if ROUND {
             let q_level_half: u64 = r_last.modulus.q >> 1;
-            let (buf_q_scaling, buf_qi_scaling) = buf.0.split_at_mut(1);
+            let (buf_q_scaling, buf_qi_scaling) = buf.split_at_mut(1);
 
             if NTT {
                 r_last.intt::<false>(a.at(level), &mut buf_q_scaling[0]);
@@ -152,7 +153,7 @@ impl RingRNS<u64> {
             }
         } else {
             if NTT {
-                let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.0.split_at_mut(1);
+                let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.split_at_mut(1);
                 r_last.intt::<false>(a.at(level), &mut buf_ntt_q_scaling[0]);
                 for (i, r) in self.0[0..level].iter().enumerate() {
                     r.ntt::<true>(&buf_ntt_q_scaling[0], &mut buf_ntt_qi_scaling[0]);
@@ -178,104 +179,106 @@ impl RingRNS<u64> {
     /// Updates b to floor(a / prod_{level - nb_moduli}^{level} q[i])
     pub fn div_by_last_moduli<const ROUND: bool, const NTT: bool>(
         &self,
-        nb_moduli: usize,
+        nb_moduli_dropped: usize,
         a: &PolyRNS<u64>,
-        buf: &mut PolyRNS<u64>,
+        buf0: &mut [Poly<u64>; 2],
+        buf1: &mut PolyRNS<u64>,
         c: &mut PolyRNS<u64>,
     ) {
         debug_assert!(
-            nb_moduli <= self.level(),
-            "invalid input nb_moduli: nb_moduli={} > a.level()={}",
-            nb_moduli,
-            a.level()
+            nb_moduli_dropped <= self.level(),
+            "invalid input nb_moduli_dropped: nb_moduli_dropped={} > self.level()={}",
+            nb_moduli_dropped,
+            self.level()
         );
         debug_assert!(
-            a.level() <= self.level(),
-            "invalid input a: self.level()={} > a.level()={}",
-            self.level(),
-            a.level()
+            a.level() >= self.level(),
+            "invalid input a: a.level()={} < self.level()={}",
+            a.level(),
+            self.level()
         );
         debug_assert!(
-            buf.level() >= self.level() - 1,
-            "invalid input buf: buf.level()={} < a.level()-1={}",
-            buf.level(),
-            a.level() - 1
+            buf1.level() >= self.level(),
+            "invalid input buf: buf.level()={} < self.level()={}",
+            buf1.level(),
+            self.level()
         );
         debug_assert!(
-            c.level() >= self.level() - nb_moduli,
-            "invalid input c: c.level()={} < c.level()-nb_moduli={}",
+            c.level() >= self.level() - nb_moduli_dropped,
+            "invalid input c: c.level()={} < self.level()-nb_moduli_dropped={}",
             c.level(),
-            a.level() - nb_moduli
+            self.level() - nb_moduli_dropped
         );
 
-        if nb_moduli == 0 {
+        if nb_moduli_dropped == 0 {
             if a != c {
                 c.copy(a);
             }
         } else {
             if NTT {
-                self.intt::<false>(a, buf);
-                (0..nb_moduli).for_each(|i| {
+                self.intt::<false>(a, buf1);
+                (0..nb_moduli_dropped).for_each(|i| {
                     self.at_level(self.level() - i)
-                        .div_by_last_modulus_inplace::<ROUND, false>(
-                            &mut PolyRNS::<u64>::default(),
-                            buf,
-                        )
+                        .div_by_last_modulus_inplace::<ROUND, false>(buf0, buf1)
                 });
-                self.at_level(self.level() - nb_moduli).ntt::<false>(buf, c);
+                self.at_level(self.level() - nb_moduli_dropped)
+                    .ntt::<false>(buf1, c);
             } else {
-                println!("{} {:?}", self.level(), buf.level());
-                self.div_by_last_modulus::<ROUND, false>(a, buf, c);
+                self.div_by_last_modulus::<ROUND, false>(a, buf0, buf1);
 
-                (1..nb_moduli - 1).for_each(|i| {
-                    println!("{} {:?}", self.level() - i, buf.level());
+                (1..nb_moduli_dropped - 1).for_each(|i| {
                     self.at_level(self.level() - i)
-                        .div_by_last_modulus_inplace::<ROUND, false>(buf, c);
+                        .div_by_last_modulus_inplace::<ROUND, false>(buf0, buf1);
                 });
 
-                self.at_level(self.level() - nb_moduli + 1)
-                    .div_by_last_modulus_inplace::<ROUND, false>(buf, c);
+                self.at_level(self.level() - nb_moduli_dropped + 1)
+                    .div_by_last_modulus::<ROUND, false>(buf1, buf0, c);
             }
         }
     }
 
-    /// Updates a to floor(a / prod_{level - nb_moduli}^{level} q[i])
+    /// Updates a to floor(a / prod_{level - nb_moduli_dropped}^{level} q[i])
     pub fn div_by_last_moduli_inplace<const ROUND: bool, const NTT: bool>(
         &self,
-        nb_moduli: usize,
-        buf: &mut PolyRNS<u64>,
+        nb_moduli_dropped: usize,
+        buf0: &mut [Poly<u64>; 2],
+        buf1: &mut PolyRNS<u64>,
         a: &mut PolyRNS<u64>,
     ) {
         debug_assert!(
-            self.level() <= a.level(),
-            "invalid input a: self.level()={} > a.level()={}",
-            self.level(),
-            a.level()
+            nb_moduli_dropped <= self.level(),
+            "invalid input nb_moduli_dropped: nb_moduli_dropped={} > self.level()={}",
+            nb_moduli_dropped,
+            self.level()
         );
         debug_assert!(
-            nb_moduli <= a.level(),
-            "invalid input nb_moduli: nb_moduli={} > a.level()={}",
-            nb_moduli,
-            a.level()
+            a.level() >= self.level(),
+            "invalid input a: a.level()={} < self.level()={}",
+            a.level(),
+            self.level()
         );
-        if nb_moduli == 0 {
+        debug_assert!(
+            buf1.level() >= self.level(),
+            "invalid input buf: buf.level()={} < self.level()={}",
+            buf1.level(),
+            self.level()
+        );
+        if nb_moduli_dropped == 0 {
             return;
         }
 
         if NTT {
-            self.intt::<false>(a, buf);
-            (0..nb_moduli).for_each(|i| {
+            self.intt::<false>(a, buf1);
+            (0..nb_moduli_dropped).for_each(|i| {
                 self.at_level(self.level() - i)
-                    .div_by_last_modulus_inplace::<ROUND, false>(
-                        &mut PolyRNS::<u64>::default(),
-                        buf,
-                    )
+                    .div_by_last_modulus_inplace::<ROUND, false>(buf0, buf1)
             });
-            self.at_level(self.level() - nb_moduli).ntt::<false>(buf, a);
+            self.at_level(self.level() - nb_moduli_dropped)
+                .ntt::<false>(buf1, a);
         } else {
-            (0..nb_moduli).for_each(|i| {
+            (0..nb_moduli_dropped).for_each(|i| {
                 self.at_level(self.level() - i)
-                    .div_by_last_modulus_inplace::<ROUND, false>(buf, a)
+                    .div_by_last_modulus_inplace::<ROUND, false>(buf0, a)
             });
         }
     }
diff --git a/math/tests/rescaling_rns.rs b/math/tests/rescaling_rns.rs
index cba05bc..35b4bce 100644
--- a/math/tests/rescaling_rns.rs
+++ b/math/tests/rescaling_rns.rs
@@ -1,6 +1,6 @@
 use itertools::izip;
 use math::num_bigint::Div;
-use math::poly::PolyRNS;
+use math::poly::{Poly, PolyRNS};
 use math::ring::RingRNS;
 use num_bigint::BigInt;
 use sampling::source::Source;
@@ -44,8 +44,34 @@ fn rescaling_rns_u64() {
         "test_div_by_last_modulus_inplace::<ROUND:true, NTT:false>",
         || test_div_by_last_modulus_inplace::<true, false>(&ring_rns),
     );
-
-    //sub_test("test_div_by_last_moduli::<ROUND:false, NTT:false>", ||{test_div_by_last_moduli::<false, false>(&ring_rns)});
+    sub_test("test_div_by_last_moduli::<ROUND:false, NTT:false>", || {
+        test_div_by_last_moduli::<false, false>(&ring_rns)
+    });
+    sub_test("test_div_by_last_moduli::<ROUND:false, NTT:true>", || {
+        test_div_by_last_moduli::<false, true>(&ring_rns)
+    });
+    sub_test("test_div_by_last_moduli::<ROUND:true, NTT:false>", || {
+        test_div_by_last_moduli::<true, false>(&ring_rns)
+    });
+    sub_test("test_div_by_last_moduli::<ROUND:true, NTT:true>", || {
+        test_div_by_last_moduli::<true, true>(&ring_rns)
+    });
+    sub_test(
+        "test_div_by_last_moduli_inplace::<ROUND:false, NTT:false>",
+        || test_div_by_last_moduli_inplace::<false, false>(&ring_rns),
+    );
+    sub_test(
+        "test_div_by_last_moduli_inplace::<ROUND:false, NTT:true>",
+        || test_div_by_last_moduli_inplace::<false, true>(&ring_rns),
+    );
+    sub_test(
+        "test_div_by_last_moduli_inplace::<ROUND:true, NTT:false>",
+        || test_div_by_last_moduli_inplace::<true, false>(&ring_rns),
+    );
+    sub_test(
+        "test_div_by_last_moduli_inplace::<ROUND:true, NTT:true>",
+        || test_div_by_last_moduli_inplace::<true, true>(&ring_rns),
+    );
 }
 
 fn sub_test<F: FnOnce()>(name: &str, f: F) {
@@ -58,7 +84,7 @@ fn test_div_by_last_modulus<const ROUND: bool, const NTT: bool>(ring_rns: &RingR
     let mut source: Source = Source::new(seed);
 
     let mut a: PolyRNS<u64> = ring_rns.new_polyrns();
-    let mut b: PolyRNS<u64> = ring_rns.new_polyrns();
+    let mut buf: [Poly<u64>; 2] = [ring_rns.new_poly(), ring_rns.new_poly()];
     let mut c: PolyRNS<u64> = ring_rns.at_level(ring_rns.level() - 1).new_polyrns();
 
     // Allocates a random PolyRNS
@@ -75,7 +101,7 @@ fn test_div_by_last_modulus<const ROUND: bool, const NTT: bool>(ring_rns: &RingR
         ring_rns.ntt_inplace::<false>(&mut a);
     }
 
-    ring_rns.div_by_last_modulus::<ROUND, NTT>(&a, &mut b, &mut c);
+    ring_rns.div_by_last_modulus::<ROUND, NTT>(&a, &mut buf, &mut c);
 
     if NTT {
         ring_rns.at_level(c.level()).intt_inplace::<false>(&mut c);
@@ -105,7 +131,7 @@ fn test_div_by_last_modulus_inplace<const ROUND: bool, const NTT: bool>(ring_rns
     let mut source: Source = Source::new(seed);
 
     let mut a: PolyRNS<u64> = ring_rns.new_polyrns();
-    let mut buf: PolyRNS<u64> = ring_rns.new_polyrns();
+    let mut buf: [Poly<u64>; 2] = [ring_rns.new_poly(), ring_rns.new_poly()];
 
     // Allocates a random PolyRNS
     ring_rns.fill_uniform(&mut source, &mut a);
@@ -152,12 +178,13 @@ fn test_div_by_last_moduli<const ROUND: bool, const NTT: bool>(ring_rns: &RingRN
     let seed: [u8; 32] = [0; 32];
     let mut source: Source = Source::new(seed);
 
-    let nb_moduli: usize = ring_rns.level();
+    let nb_moduli_dropped: usize = ring_rns.level();
 
     let mut a: PolyRNS<u64> = ring_rns.new_polyrns();
-    let mut buf: PolyRNS<u64> = ring_rns.new_polyrns();
+    let mut buf0: [Poly<u64>; 2] = [ring_rns.new_poly(), ring_rns.new_poly()];
+    let mut buf1: PolyRNS<u64> = ring_rns.new_polyrns();
     let mut c: PolyRNS<u64> = ring_rns
-        .at_level(ring_rns.level() - nb_moduli)
+        .at_level(ring_rns.level() - nb_moduli_dropped)
         .new_polyrns();
 
     // Allocates a random PolyRNS
@@ -174,7 +201,7 @@ fn test_div_by_last_moduli<const ROUND: bool, const NTT: bool>(ring_rns: &RingRN
         ring_rns.ntt_inplace::<false>(&mut a);
     }
 
-    ring_rns.div_by_last_moduli::<ROUND, NTT>(nb_moduli, &a, &mut buf, &mut c);
+    ring_rns.div_by_last_moduli::<ROUND, NTT>(nb_moduli_dropped, &a, &mut buf0, &mut buf1, &mut c);
 
     if NTT {
         ring_rns.at_level(c.level()).intt_inplace::<false>(&mut c);
@@ -188,7 +215,7 @@ fn test_div_by_last_moduli<const ROUND: bool, const NTT: bool>(ring_rns: &RingRN
 
     // Performs floor division on a
     let mut scalar_big = BigInt::from(1);
-    (0..nb_moduli)
+    (0..nb_moduli_dropped)
         .for_each(|i| scalar_big *= BigInt::from(ring_rns.0[ring_rns.level() - i].modulus.q));
     coeffs_a.iter_mut().for_each(|a| {
         if ROUND {
@@ -201,15 +228,15 @@ fn test_div_by_last_moduli<const ROUND: bool, const NTT: bool>(ring_rns: &RingRN
     izip!(coeffs_a, coeffs_c).for_each(|(a, b)| assert_eq!(a, b));
 }
 
-/*
-fn test_div_floor_by_last_moduli_inplace<const NTT: bool>(ring_rns: &RingRNS<u64>) {
+fn test_div_by_last_moduli_inplace<const ROUND: bool, const NTT: bool>(ring_rns: &RingRNS<u64>) {
     let seed: [u8; 32] = [0; 32];
     let mut source: Source = Source::new(seed);
 
-    let nb_moduli: usize = ring_rns.level();
+    let nb_moduli_dropped: usize = ring_rns.level();
 
     let mut a: PolyRNS<u64> = ring_rns.new_polyrns();
-    let mut b: PolyRNS<u64> = ring_rns.new_polyrns();
+    let mut buf0: [Poly<u64>; 2] = [ring_rns.new_poly(), ring_rns.new_poly()];
+    let mut buf1: PolyRNS<u64> = ring_rns.new_polyrns();
 
     // Allocates a random PolyRNS
     ring_rns.fill_uniform(&mut source, &mut a);
@@ -225,23 +252,36 @@ fn test_div_floor_by_last_moduli_inplace<const NTT: bool>(ring_rns: &RingRNS<u64
         ring_rns.ntt_inplace::<false>(&mut a);
     }
 
-    ring_rns.div_floor_by_last_moduli_inplace::<NTT>(nb_moduli, &mut b, &mut a);
+    ring_rns.div_by_last_moduli_inplace::<ROUND, NTT>(
+        nb_moduli_dropped,
+        &mut buf0,
+        &mut buf1,
+        &mut a,
+    );
 
     if NTT {
-        ring_rns.at_level(a.level()-nb_moduli).intt_inplace::<false>(&mut a);
+        ring_rns
+            .at_level(a.level() - nb_moduli_dropped)
+            .intt_inplace::<false>(&mut a);
     }
 
     // Exports c to coeffs_c
     let mut coeffs_c = vec![BigInt::from(0); a.n()];
     ring_rns
-        .at_level(a.level()-nb_moduli)
+        .at_level(a.level() - nb_moduli_dropped)
         .to_bigint_inplace(&a, 1, &mut coeffs_c);
 
     // Performs floor division on a
     let mut scalar_big = BigInt::from(1);
-    (0..nb_moduli).for_each(|i|{scalar_big *= BigInt::from(ring_rns.0[ring_rns.level()-i].modulus.q)});
-    coeffs_a.iter_mut().for_each(|a| {a.div_floor(&scalar_big)});
+    (0..nb_moduli_dropped)
+        .for_each(|i| scalar_big *= BigInt::from(ring_rns.0[ring_rns.level() - i].modulus.q));
+    coeffs_a.iter_mut().for_each(|a| {
+        if ROUND {
+            *a = a.div_round(&scalar_big);
+        } else {
+            *a = a.div_floor(&scalar_big);
+        }
+    });
 
-    assert!(coeffs_a == coeffs_c, "test_div_floor_by_last_moduli_inplace");
+    izip!(coeffs_a, coeffs_c).for_each(|(a, b)| assert_eq!(a, b));
 }
-*/