diff --git a/src/backend.rs b/src/backend.rs
index 32021c5..845db22 100644
--- a/src/backend.rs
+++ b/src/backend.rs
@@ -42,10 +42,9 @@ impl Modulus for u64 {
         0
     }
     fn map_element_to_i64(&self, v: &Self::Element) -> i64 {
-        assert!(v < self);
-
+        assert!(v <= self, "{v} must be <= {self}");
         if *v > (self >> 1) {
-            ToPrimitive::to_i64(&(self - v)).unwrap()
+            -ToPrimitive::to_i64(&(self - v)).unwrap()
         } else {
             ToPrimitive::to_i64(v).unwrap()
         }
diff --git a/src/decomposer.rs b/src/decomposer.rs
index 2db3f58..a490019 100644
--- a/src/decomposer.rs
+++ b/src/decomposer.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use num_traits::{AsPrimitive, Num, One, PrimInt, ToPrimitive, WrappingSub, Zero};
+use num_traits::{AsPrimitive, FromPrimitive, Num, One, PrimInt, ToPrimitive, WrappingSub, Zero};
 use std::{fmt::Debug, marker::PhantomData, ops::Rem};
 
 use crate::backend::{ArithmeticOps, ModularOpsU64};
@@ -92,7 +92,9 @@ impl<T: PrimInt + NumInfo + Debug> DefaultDecomposer<T> {
     }
 }
 
-impl<T: PrimInt + WrappingSub + Debug + NumInfo> Decomposer for DefaultDecomposer<T> {
+impl<T: PrimInt + ToPrimitive + FromPrimitive + WrappingSub + Debug + NumInfo> Decomposer
+    for DefaultDecomposer<T>
+{
     type Element = T;
 
     fn new(q: T, logb: usize, d: usize) -> DefaultDecomposer<T> {
@@ -117,45 +119,34 @@ impl<T: PrimInt + WrappingSub + Debug + NumInfo> Decomposer for DefaultDecompose
         }
     }
 
+    /// Signed BNAF decomposition. Only returns most significant `d`
+    /// decomposition limbs
+    ///
+    /// Implements algorithm 3 of https://eprint.iacr.org/2021/1161.pdf
     fn decompose(&self, value: &T) -> Vec<T> {
-        let value = round_value(*value, self.ignore_bits);
+        let mut value = round_value(*value, self.ignore_bits);
 
         let q = self.q;
-        // if value >= (q >> 1) {
-        //     value = value.wrapping_sub(&q);
-        // }
-
         let logb = self.logb;
-        let b = T::one() << logb; // base
-        let b_by2 = T::one() << (logb - 1);
-        // let neg_b_by2_modq = q - b_by2;
-        let full_mask = (T::one() << logb) - T::one();
-        // let half_mask = b_by2 - T::one();
-        let mut carry = T::zero();
-        let mut out = Vec::<T>::with_capacity(self.d);
-        for i in 0..self.d {
-            let mut limb = ((value >> (logb * i)) & full_mask) + carry;
-            carry = T::zero();
-            if limb >= b_by2 {
-                limb = (q + limb) - b;
-                carry = T::one();
-            }
-
-            // carry = ((q + g - limb) % q) >> logb;
+        let b = T::one() << logb;
+        let full_mask = b - T::one();
+        let bby2 = b >> 1;
 
-            // carry = limb & b_by2;
-            // limb = (q + limb) - (carry << 1);
-            // if limb > q {
-            //     limb = limb - q;
-            // }
-            out.push(limb);
-
-            // carry = carry >> (logb - 1);
+        if value > (q >> 1) {
+            value = !(q - value) + T::one()
         }
 
-        out[self.d - 1] = out[self.d - 1] + (carry << logb);
-        if out[self.d - 1] > q {
-            out[self.d - 1] = out[self.d - 1] - q;
+        let mut out = Vec::with_capacity(self.d);
+        for _ in 0..self.d {
+            let k_i = value & full_mask;
+            value = (value - k_i) >> logb;
+
+            if k_i > bby2 || (k_i == bby2 && ((value & full_mask) >= bby2)) {
+                out.push(q - (b - k_i));
+                value = value + T::one();
+            } else {
+                out.push(k_i)
+            }
         }
 
         return out;
@@ -215,27 +206,29 @@ fn round_value<T: PrimInt>(value: T, ignore_bits: usize) -> T {
 
 #[cfg(test)]
 mod tests {
+    use num_traits::Float;
     use rand::{thread_rng, Rng};
 
     use crate::{
         backend::{ModInit, ModularOpsU64},
         decomposer::round_value,
-        utils::generate_prime,
+        utils::{generate_prime, Stats, TryConvertFrom1},
     };
 
     use super::{Decomposer, DefaultDecomposer};
 
     #[test]
     fn decomposition_works() {
-        let logq = 55;
-        let logb = 9;
-        let d = 6;
+        let logq = 50;
+        let logb = 5;
+        let d = 10;
 
         let mut rng = thread_rng();
+        let mut stats = Stats { samples: vec![] };
 
         // q is prime of bits logq and i is true, other q = 1<<logq
         // FIXME: Test fails when q is prime, albeit the difference is minute
-        for i in [true, false] {
+        for i in [false] {
             let q = if i {
                 generate_prime(logq, 1 << 4, 1u64 << logq).unwrap()
             } else {
@@ -249,12 +242,14 @@ mod tests {
                 let value_back = decomposer.recompose(&limbs, &modq_op);
                 let rounded_value =
                     round_value(value, decomposer.ignore_bits) << decomposer.ignore_bits;
-                // dbg!(&limbs, q);
+                stats.add_more(&Vec::<i64>::try_convert_from(&limbs, &q));
                 assert_eq!(
                     rounded_value, value_back,
                     "Expected {rounded_value} got {value_back} for q={q}"
                 );
             }
         }
+        println!("Mean: {}", stats.mean());
+        println!("Std: {}", stats.std_dev());
     }
 }
diff --git a/src/rgsw.rs b/src/rgsw.rs
index 02c2079..a2eea9d 100644
--- a/src/rgsw.rs
+++ b/src/rgsw.rs
@@ -2122,7 +2122,7 @@ pub(crate) mod tests {
     #[test]
     fn some_work() {
         let logq = 50;
-        let ring_size = 1 << 10;
+        let ring_size = 1 << 11;
         let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
         let d_rgsw = 10;
         let logb = 5;