@@ -13,14 +13,14 @@ pub const BARRETT: REDUCEMOD = 4;
 pub const BARRETTLAZY: REDUCEMOD = 5;
 
 pub trait WordOps<O> {
-    fn log2(self) -> O;
+    fn log2(self) -> usize;
     fn reverse_bits_msb(self, n: u32) -> O;
     fn mask(self) -> O;
 }
 
 impl WordOps<u64> for u64 {
     #[inline(always)]
-    fn log2(self) -> u64 {
+    fn log2(self) -> usize {
         (u64::BITS - (self - 1).leading_zeros()) as _
     }
     #[inline(always)]
@@ -188,17 +188,17 @@ d: &barrett::Barrett<u64>,
         a: &mut u64,
     );
 
-    fn sa_rsh_sb_mask_sc_into_sa(&self, c: &u64, b: &u64, a: &mut u64);
+    fn sa_rsh_sb_mask_sc_into_sa(&self, c: &usize, b: &u64, a: &mut u64);
 
-    fn sa_rsh_sb_mask_sc_into_sd(&self, a: &u64, b: &u64, c: &u64, d: &mut u64);
+    fn sa_rsh_sb_mask_sc_into_sd(&self, a: &u64, b: &usize, c: &u64, d: &mut u64);
 
-    fn sa_rsh_sb_mask_sc_add_sd_into_sd(&self, a: &u64, b: &u64, c: &u64, d: &mut u64);
+    fn sa_rsh_sb_mask_sc_add_sd_into_sd(&self, a: &u64, b: &usize, c: &u64, d: &mut u64);
 
     fn sa_signed_digit_into_sb<const CARRYOVERWRITE: bool, const BALANCED: bool>(
         &self,
         a: &u64,
         base: &u64,
-        shift: &u64,
+        shift: &usize,
         mask: &u64,
         carry: &mut u64,
         b: &mut u64,
@@ -372,13 +372,13 @@ va: &mut [u64],
     );
 
     // vec(a) <- (vec(a)>>scalar(b)) & scalar(c).
-    fn va_rsh_sb_mask_sd_into_va<const CHUNK: usize>(&self, sb: &u64, sc: &u64, va: &mut [u64]);
+    fn va_rsh_sb_mask_sc_into_va<const CHUNK: usize>(&self, sb: &usize, sc: &u64, va: &mut [u64]);
 
     // vec(d) <- (vec(a)>>scalar(b)) & scalar(c).
     fn va_rsh_sb_mask_sc_into_vd<const CHUNK: usize>(
         &self,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         sc: &u64,
         vd: &mut [u64],
     );
@@ -387,7 +387,7 @@ // vec(d) <- vec(d) + (vec(a)>>scalar(b)) & scalar(c).
     fn va_rsh_sb_mask_sc_add_vd_into_vd<const CHUNK: usize>(
         &self,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         sc: &u64,
         vd: &mut [u64],
     );
@@ -398,7 +398,7 @@ fn va_ith_digit_unsigned_base_sb_into_vc<const CHUNK: usize>(
         &self,
         i: usize,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         vc: &mut [u64],
     );
 
@@ -410,7 +410,7 @@ fn va_ith_digit_signed_base_sb_into_vc<const CHUNK: usize, const BALANCED: bool>(
         &self,
         i: usize,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         carry: &mut [u64],
         vc: &mut [u64],
     );

@@ -22,7 +22,7 @@ for _i in 0..63 {
             q_inv = q_inv.wrapping_mul(q_pow);
             q_pow = q_pow.wrapping_mul(q_pow);
         }
-        let mut precomp = Self {
+        let mut precomp: MontgomeryPrecomp<u64> = Self {
             q: q,
             two_q: q << 1,
             four_q: q << 2,

@@ -213,17 +213,17 @@ self.barrett.mul_external_assign::<REDUCE>(*d, a);
     }
 
     #[inline(always)]
-    fn sa_rsh_sb_mask_sc_into_sa(&self, b: &u64, c: &u64, a: &mut u64) {
+    fn sa_rsh_sb_mask_sc_into_sa(&self, b: &usize, c: &u64, a: &mut u64) {
         *a = (*a >> b) & c
     }
 
     #[inline(always)]
-    fn sa_rsh_sb_mask_sc_into_sd(&self, a: &u64, b: &u64, c: &u64, d: &mut u64) {
+    fn sa_rsh_sb_mask_sc_into_sd(&self, a: &u64, b: &usize, c: &u64, d: &mut u64) {
         *d = (*a >> b) & c
     }
 
     #[inline(always)]
-    fn sa_rsh_sb_mask_sc_add_sd_into_sd(&self, a: &u64, b: &u64, c: &u64, d: &mut u64) {
+    fn sa_rsh_sb_mask_sc_add_sd_into_sd(&self, a: &u64, b: &usize, c: &u64, d: &mut u64) {
         *d += (*a >> b) & c
     }
 
@@ -232,7 +232,7 @@ fn sa_signed_digit_into_sb<const CARRYOVERWRITE: bool, const BALANCED: bool>(
         &self,
         a: &u64,
         base: &u64,
-        shift: &u64,
+        shift: &usize,
         mask: &u64,
         carry: &mut u64,
         b: &mut u64,
@@ -246,7 +246,7 @@
         let c: u64 = if BALANCED && *carry == base >> 1 {
             a & 1
         } else {
-            ((*carry | (*carry << 1)) >> base) & 1
+            ((*carry | (*carry << 1)) >> shift) & 1
         };
 
         *b = *carry + (self.q - base) * c;
@@ -561,7 +561,7 @@ );
     }
 
     // vec(a) <- (vec(a)>>scalar(b)) & scalar(c).
-    fn va_rsh_sb_mask_sd_into_va<const CHUNK: usize>(&self, sb: &u64, sc: &u64, va: &mut [u64]) {
+    fn va_rsh_sb_mask_sc_into_va<const CHUNK: usize>(&self, sb: &usize, sc: &u64, va: &mut [u64]) {
         apply_ssv!(self, Self::sa_rsh_sb_mask_sc_into_sa, sb, sc, va, CHUNK);
     }
 
@@ -569,7 +569,7 @@ // vec(d) <- (vec(a)>>scalar(b)) & scalar(c).
     fn va_rsh_sb_mask_sc_into_vd<const CHUNK: usize>(
         &self,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         sc: &u64,
         vd: &mut [u64],
     ) {
@@ -580,7 +580,7 @@ // vec(d) <- vec(d) + (vec(a)>>scalar(b)) & scalar(c).
     fn va_rsh_sb_mask_sc_add_vd_into_vd<const CHUNK: usize>(
         &self,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         sc: &u64,
         vd: &mut [u64],
     ) {
@@ -601,10 +601,10 @@ fn va_ith_digit_unsigned_base_sb_into_vc<const CHUNK: usize>(
         &self,
         i: usize,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         vc: &mut [u64],
     ) {
-        self.va_rsh_sb_mask_sc_into_vd::<CHUNK>(va, &((i as u64) * sb), &((1 << sb) - 1), vc);
+        self.va_rsh_sb_mask_sc_into_vd::<CHUNK>(va, &(i * sb), &((1 << sb) - 1), vc);
     }
 
     // vec(c) <- i-th signed digit base 2^{w} of vec(a).
@@ -615,7 +615,7 @@ fn va_ith_digit_signed_base_sb_into_vc<const CHUNK: usize, const BALANCED: bool>(
         &self,
         i: usize,
         va: &[u64],
-        sb: &u64,
+        sb: &usize,
         carry: &mut [u64],
         vc: &mut [u64],
     ) {
@@ -627,7 +627,7 @@ self,
                 Self::sa_signed_digit_into_sb::<true, BALANCED>,
                 va,
                 &base,
-                &(i as u64 * sb),
+                &(i * sb),
                 &mask,
                 carry,
                 vc,
@@ -639,7 +639,7 @@ self,
                 Self::sa_signed_digit_into_sb::<false, BALANCED>,
                 va,
                 &base,
-                &(i as u64 * sb),
+                &(i * sb),
                 &mask,
                 carry,
                 vc,

@@ -349,4 +349,69 @@ debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
         self.modulus
             .vb_sub_va_add_sc_mul_sd_into_va::<CHUNK, BRANGE, REDUCE>(&b.0, c, d, &mut a.0);
     }
+
+    pub fn a_rsh_scalar_b_mask_scalar_c_into_d(
+        &self,
+        a: &Poly<u64>,
+        b: &usize,
+        c: &u64,
+        d: &mut Poly<u64>,
+    ) {
+        debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
+        debug_assert!(d.n() == self.n(), "d.n()={} != n={}", d.n(), self.n());
+        self.modulus
+            .va_rsh_sb_mask_sc_into_vd::<CHUNK>(&a.0, b, c, &mut d.0);
+    }
+
+    pub fn a_rsh_scalar_b_mask_scalar_c_add_d_into_d(
+        &self,
+        a: &Poly<u64>,
+        b: &usize,
+        c: &u64,
+        d: &mut Poly<u64>,
+    ) {
+        debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
+        debug_assert!(d.n() == self.n(), "d.n()={} != n={}", d.n(), self.n());
+        self.modulus
+            .va_rsh_sb_mask_sc_add_vd_into_vd::<CHUNK>(&a.0, b, c, &mut d.0);
+    }
+
+    pub fn a_ith_digit_unsigned_base_scalar_b_into_c(
+        &self,
+        i: usize,
+        a: &Poly<u64>,
+        b: &usize,
+        c: &mut Poly<u64>,
+    ) {
+        debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
+        debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
+        self.modulus
+            .va_ith_digit_unsigned_base_sb_into_vc::<CHUNK>(i, &a.0, b, &mut c.0);
+    }
+
+    pub fn a_ith_digit_signed_base_scalar_b_into_c<const BALANCED: bool>(
+        &self,
+        i: usize,
+        a: &Poly<u64>,
+        b: &usize,
+        carry: &mut Poly<u64>,
+        c: &mut Poly<u64>,
+    ) {
+        debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
+        debug_assert!(
+            carry.n() == self.n(),
+            "carry.n()={} != n={}",
+            carry.n(),
+            self.n()
+        );
+        debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
+        self.modulus
+            .va_ith_digit_signed_base_sb_into_vc::<CHUNK, BALANCED>(
+                i,
+                &a.0,
+                b,
+                &mut carry.0,
+                &mut c.0,
+            );
+    }
 }

@@ -0,0 +1,75 @@
+use itertools::izip;
+use math::modulus::{WordOps, ONCE};
+use math::poly::Poly;
+use math::ring::Ring;
+use sampling::source::Source;
+
+#[test]
+fn digit_decomposition() {
+    let n: usize = 1 << 4;
+    let q_base: u64 = 65537u64;
+    let q_power: usize = 1usize;
+    let ring: Ring<u64> = Ring::new(n, q_base, q_power);
+
+    sub_test("test_unsigned_digit_decomposition", || {
+        test_unsigned_digit_decomposition(&ring)
+    });
+
+    sub_test("test_signed_digit_decomposition::<BALANCED=false>", || {
+        test_signed_digit_decomposition::<false>(&ring)
+    });
+
+    sub_test("test_signed_digit_decomposition::<BALANCED=true>", || {
+        test_signed_digit_decomposition::<true>(&ring)
+    });
+}
+
+fn sub_test<F: FnOnce()>(name: &str, f: F) {
+    println!("Running {}", name);
+    f();
+}
+
+fn test_unsigned_digit_decomposition(ring: &Ring<u64>) {
+    let mut a: Poly<u64> = ring.new_poly();
+    let mut b: Poly<u64> = ring.new_poly();
+    let mut c: Poly<u64> = ring.new_poly();
+
+    let seed: [u8; 32] = [0; 32];
+    let mut source: Source = Source::new(seed);
+    ring.fill_uniform(&mut source, &mut a);
+
+    let base: usize = 8;
+    let log_q: usize = ring.modulus.q.log2();
+    let d: usize = ((log_q + base - 1) / base) as _;
+
+    (0..d).for_each(|i| {
+        ring.a_ith_digit_unsigned_base_scalar_b_into_c(i, &a, &base, &mut b);
+        ring.a_mul_b_scalar_into_a::<ONCE>(&(1 << (i * base)), &mut b);
+        ring.a_add_b_into_b::<ONCE>(&b, &mut c);
+    });
+
+    izip!(a.0, c.0).for_each(|(a, c)| assert_eq!(a, c));
+}
+
+fn test_signed_digit_decomposition<const BALANCED: bool>(ring: &Ring<u64>) {
+    let mut a: Poly<u64> = ring.new_poly();
+    let mut b: Poly<u64> = ring.new_poly();
+    let mut carry: Poly<u64> = ring.new_poly();
+    let mut c: Poly<u64> = ring.new_poly();
+
+    let seed: [u8; 32] = [0; 32];
+    let mut source: Source = Source::new(seed);
+    ring.fill_uniform(&mut source, &mut a);
+
+    let base: usize = 8;
+    let log_q: usize = ring.modulus.q.log2();
+    let d: usize = ((log_q + base - 1) / base) as _;
+
+    (0..d).for_each(|i| {
+        ring.a_ith_digit_signed_base_scalar_b_into_c::<BALANCED>(i, &a, &base, &mut carry, &mut b);
+        ring.a_mul_b_scalar_into_a::<ONCE>(&(1 << (i * base)), &mut b);
+        ring.a_add_b_into_b::<ONCE>(&b, &mut c);
+    });
+
+    izip!(a.0, c.0).for_each(|(a, c)| assert_eq!(a, c));
+}