@@ -1,7 +1,7 @@
 use base2k::{
-    AddNormal, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps,
-    ScratchOwned, VecZnx, VecZnxAlloc, VecZnxBig, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc,
-    VecZnxDftOps, VecZnxOps, ZnxInfos,
+    AddNormal, Decoding, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc,
+    ScalarZnxDftOps, ScratchOwned, VecZnx, VecZnxAlloc, VecZnxBig, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft,
+    VecZnxDftAlloc, VecZnxDftOps, VecZnxOps, ZnxInfos,
 };
 use itertools::izip;
 use sampling::source::Source;

@@ -17,6 +17,20 @@ /// * `data`: data to encode on the receiver.
     /// * `log_max`: base two logarithm of the infinity norm of the input data.
     fn encode_vec_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize);
 
+    /// encodes a single i64 on the receiver at the given index.
+    ///
+    /// # Arguments
+    ///
+    /// * `col_i`: the index of the poly where to encode the data.
+    /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
+    /// * `log_k`: base two negative logarithm of the scaling of the data.
+    /// * `i`: index of the coefficient on which to encode the data.
+    /// * `data`: data to encode on the receiver.
+    /// * `log_max`: base two logarithm of the infinity norm of the input data.
+    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, data: i64, log_max: usize);
+}
+
+pub trait Decoding {
     /// decode a vector of i64 from the receiver.
     ///
     /// # Arguments
@@ -35,18 +49,6 @@ /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `data`: data to decode from the receiver.
     fn decode_vec_float(&self, col_i: usize, log_base2k: usize, data: &mut [Float]);
 
-    /// encodes a single i64 on the receiver at the given index.
-    ///
-    /// # Arguments
-    ///
-    /// * `col_i`: the index of the poly where to encode the data.
-    /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
-    /// * `log_k`: base two negative logarithm of the scaling of the data.
-    /// * `i`: index of the coefficient on which to encode the data.
-    /// * `data`: data to encode on the receiver.
-    /// * `log_max`: base two logarithm of the infinity norm of the input data.
-    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, data: i64, log_max: usize);
-
     /// decode a single of i64 from the receiver at the given index.
     ///
     /// # Arguments
@@ -64,6 +66,12 @@ fn encode_vec_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize) {
         encode_vec_i64(self, col_i, log_base2k, log_k, data, log_max)
     }
 
+    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
+        encode_coeff_i64(self, col_i, log_base2k, log_k, i, value, log_max)
+    }
+}
+
+impl<D: AsRef<[u8]>> Decoding for VecZnx<D> {
     fn decode_vec_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
         decode_vec_i64(self, col_i, log_base2k, log_k, data)
     }
@@ -72,10 +80,6 @@ fn decode_vec_float(&self, col_i: usize, log_base2k: usize, data: &mut [Float]) {
         decode_vec_float(self, col_i, log_base2k, data)
     }
 
-    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
-        encode_coeff_i64(self, col_i, log_base2k, log_k, i, value, log_max)
-    }
-
     fn decode_coeff_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
         decode_coeff_i64(self, col_i, log_base2k, log_k, i)
     }
@@ -139,7 +143,7 @@ })
     }
 }
 
-fn decode_vec_i64<D: AsMut<[u8]> + AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
+fn decode_vec_i64<D: AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
     let size: usize = (log_k + log_base2k - 1) / log_base2k;
     #[cfg(debug_assertions)]
     {
@@ -167,7 +171,7 @@ }
     })
 }
 
-fn decode_vec_float<D: AsMut<[u8]> + AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, data: &mut [Float]) {
+fn decode_vec_float<D: AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, data: &mut [Float]) {
     let size: usize = a.size();
     #[cfg(debug_assertions)]
     {
@@ -252,7 +256,7 @@ })
     }
 }
 
-fn decode_coeff_i64<D: AsMut<[u8]> + AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
+fn decode_coeff_i64<D: AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
     #[cfg(debug_assertions)]
     {
         assert!(i < a.n());
@@ -280,7 +284,7 @@ #[cfg(test)]
 mod tests {
     use crate::vec_znx_ops::*;
     use crate::znx_base::*;
-    use crate::{Encoding, FFT64, Module, VecZnx, znx_base::ZnxInfos};
+    use crate::{Decoding, Encoding, FFT64, Module, VecZnx, znx_base::ZnxInfos};
     use itertools::izip;
     use sampling::source::Source;
 

@@ -305,7 +305,7 @@ }
 #[cfg(test)]
 mod tests {
     use crate::{
-        Encoding, FFT64, FillUniform, MatZnxDft, MatZnxDftOps, Module, ScratchOwned, VecZnx, VecZnxAlloc, VecZnxBig,
+        Decoding, FFT64, FillUniform, MatZnxDft, MatZnxDftOps, Module, ScratchOwned, VecZnx, VecZnxAlloc, VecZnxBig,
         VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, ZnxInfos, ZnxView, ZnxViewMut,
     };
     use sampling::source::Source;

@@ -80,7 +80,7 @@ (bound.log2().ceil() as i64)
         );
 
         let limb: usize = (log_k + log_base2k - 1) / log_base2k - 1;
-        let log_base2k_rem: usize = log_k % log_base2k;
+        let log_base2k_rem: usize = (limb + 1) * log_base2k - log_k;
 
         if log_base2k_rem != 0 {
             a.at_mut(col_i, limb).iter_mut().for_each(|a| {
@@ -123,7 +123,7 @@ (bound.log2().ceil() as i64)
         );
 
         let limb: usize = (log_k + log_base2k - 1) / log_base2k - 1;
-        let log_base2k_rem: usize = log_k % log_base2k;
+        let log_base2k_rem: usize = (limb + 1) * log_base2k - log_k;
 
         if log_base2k_rem != 0 {
             a.at_mut(col_i, limb).iter_mut().for_each(|a| {
@@ -198,7 +198,7 @@ (bound.log2().ceil() as i64)
         );
 
         let limb: usize = (log_k + log_base2k - 1) / log_base2k - 1;
-        let log_base2k_rem: usize = log_k % log_base2k;
+        let log_base2k_rem: usize = (limb + 1) * log_base2k - log_k;
 
         if log_base2k_rem != 0 {
             a.at_mut(col_i, limb).iter_mut().for_each(|a| {
@@ -241,7 +241,7 @@ (bound.log2().ceil() as i64)
         );
 
         let limb: usize = (log_k + log_base2k - 1) / log_base2k - 1;
-        let log_base2k_rem: usize = log_k % log_base2k;
+        let log_base2k_rem: usize = (limb + 1) * log_base2k - log_k;
 
         if log_base2k_rem != 0 {
             a.at_mut(col_i, limb).iter_mut().for_each(|a| {

@@ -1,5 +1,5 @@
 use crate::znx_base::ZnxInfos;
-use crate::{Encoding, VecZnx};
+use crate::{Decoding, VecZnx};
 use rug::Float;
 use rug::float::Round;
 use rug::ops::{AddAssignRound, DivAssignRound, SubAssignRound};
@@ -9,7 +9,7 @@ /// Returns the standard devaition of the i-th polynomial.
     fn std(&self, col_i: usize, log_base2k: usize) -> f64;
 }
 
-impl<D: AsMut<[u8]> + AsRef<[u8]>> Stats for VecZnx<D> {
+impl<D: AsRef<[u8]>> Stats for VecZnx<D> {
     fn std(&self, col_i: usize, log_base2k: usize) -> f64 {
         let prec: u32 = (self.size() * log_base2k) as u32;
         let mut data: Vec<Float> = (0..self.n()).map(|_| Float::with_val(prec, 0)).collect();

@@ -1,8 +1,8 @@
 use crate::ffi::vec_znx_big;
 use crate::znx_base::{ZnxInfos, ZnxView};
 use crate::{Backend, DataView, DataViewMut, FFT64, Module, ZnxSliceSize, alloc_aligned};
+use std::fmt;
 use std::marker::PhantomData;
-use std::{cmp::min, fmt};
 
 pub struct VecZnxBig<D, B: Backend> {
     data: D,
@@ -168,7 +168,7 @@ impl<D: AsRef<[u8]>> fmt::Display for VecZnxBig<D, FFT64> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         writeln!(
             f,
-            "VecZnx(n={}, cols={}, size={})",
+            "VecZnxBig(n={}, cols={}, size={})",
             self.n, self.cols, self.size
         )?;
 

@@ -3,6 +3,7 @@
 use crate::ffi::vec_znx_dft;
 use crate::znx_base::ZnxInfos;
 use crate::{Backend, DataView, DataViewMut, FFT64, Module, ZnxSliceSize, ZnxView, alloc_aligned};
+use std::fmt;
 
 pub struct VecZnxDft<D, B: Backend> {
     data: D,
@@ -163,3 +164,38 @@ _phantom: PhantomData,
         }
     }
 }
+
+impl<D: AsRef<[u8]>> fmt::Display for VecZnxDft<D, FFT64> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        writeln!(
+            f,
+            "VecZnxDft(n={}, cols={}, size={})",
+            self.n, self.cols, self.size
+        )?;
+
+        for col in 0..self.cols {
+            writeln!(f, "Column {}:", col)?;
+            for size in 0..self.size {
+                let coeffs = self.at(col, size);
+                write!(f, "  Size {}: [", size)?;
+
+                let max_show = 100;
+                let show_count = coeffs.len().min(max_show);
+
+                for (i, &coeff) in coeffs.iter().take(show_count).enumerate() {
+                    if i > 0 {
+                        write!(f, ", ")?;
+                    }
+                    write!(f, "{}", coeff)?;
+                }
+
+                if coeffs.len() > max_show {
+                    write!(f, ", ... ({} more)", coeffs.len() - max_show)?;
+                }
+
+                writeln!(f, "]")?;
+            }
+        }
+        Ok(())
+    }
+}