wip

Cargo.toml

@@ -1,20 +1,2 @@
-[package]
-name = "math"
-version = "0.1.0"
-edition = "2021"
-
-[dependencies]
-primality-test = "0.3.0"
-num-bigint = "0.4.6"
-num-traits = "0.2.19"
-prime_factorization = "1.0.5"
-itertools = "0.13.0"
-criterion = "0.5.1"
-
-[[bench]]
-name = "ntt"
-harness = false
-
-[[bench]]
-name = "operations"
-harness = false
+[workspace]
+members = ["math"]

README.md

@@ -1 +1 @@
-# math
+# app

math/Cargo.toml

@@ -0,0 +1,20 @@
+[package]
+name = "math"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+primality-test = "0.3.0"
+num-bigint = "0.4.6"
+num-traits = "0.2.19"
+prime_factorization = "1.0.5"
+itertools = "0.13.0"
+criterion = "0.5.1"
+
+[[bench]]
+name = "ntt"
+harness = false
+
+[[bench]]
+name = "operations"
+harness = false

math/benches/operations.rs

@@ -2,9 +2,8 @@ use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
 use math::ring::Ring;
 use math::modulus::VecOperations;
 use math::modulus::montgomery::Montgomery;
-use math::modulus::{BARRETT, ONCE};
-
-const CHUNK: usize= 8;
+use math::modulus::ONCE;
+use math::CHUNK;
 
 fn vec_add_unary(c: &mut Criterion) {
     fn runner(r: Ring<u64>) -> Box<dyn FnMut()> {

math/examples/main.rs

@@ -1,4 +1,3 @@
-extern crate math;
 use math::ring::Ring;
 use math::modulus::prime::Prime;
 use math::dft::ntt::Table;

math/src/dft/ntt.rs

@@ -7,6 +7,7 @@ use crate::modulus::ONCE;
 use crate::dft::DFT;
 use itertools::izip;
 
+#[allow(dead_code)]
 pub struct Table<O>{
     prime:Prime<O>,
     psi: O,

math/src/lib.rs

@@ -6,6 +6,8 @@ pub mod dft;
 pub mod ring;
 pub mod poly;
 
+pub const CHUNK: usize= 8;
+
 pub mod macros{
     
     #[macro_export]

math/src/modulus.rs

@@ -72,7 +72,10 @@ pub trait WordOperations<O>{
     fn word_sub_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut O);
 
     // Assigns -a to a.
-    fn word_neg_assign<const REDUCE:REDUCEMOD>(&self, a:&mut O);
+    fn word_neg_unary_assign<const REDUCE:REDUCEMOD>(&self, a:&mut O);
+
+    // Assigns -a to b.
+    fn word_neg_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b:&mut O);
 
     // Assigns a * 2^64 to b.
     fn word_prepare_montgomery_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut montgomery::Montgomery<O>);
@@ -102,7 +105,10 @@ pub trait VecOperations<O>{
     fn vec_sub_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
 
     // Assigns -a[i] to a[i].
-    fn vec_neg_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [O]);
+    fn vec_neg_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [O]);
+
+    // Assigns -a[i] to a[i].
+    fn vec_neg_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
 
     // Assigns a * 2^64 to b.
     fn vec_prepare_montgomery_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [montgomery::Montgomery<O>]);

math/src/modulus/impl_u64/operations.rs

@@ -44,11 +44,17 @@ impl WordOperations<u64> for Prime<u64>{
     }
 
     #[inline(always)]
-    fn word_neg_assign<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
+    fn word_neg_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
         *a = self.q.wrapping_sub(*a);
         self.word_reduce_assign::<REDUCE>(a)
     }
 
+    #[inline(always)]
+    fn word_neg_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
+        *b = self.q.wrapping_sub(*a);
+        self.word_reduce_assign::<REDUCE>(b)
+    }
+
     #[inline(always)]
     fn word_prepare_montgomery_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut Montgomery<u64>){
         self.montgomery.prepare_assign::<REDUCE>(*a, b);
@@ -100,8 +106,13 @@ impl VecOperations<u64> for Prime<u64>{
     }
 
     #[inline(always)]
-    fn vec_neg_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
-        apply_unary!(self, Self::word_neg_assign::<REDUCE>, a, CHUNK);
+    fn vec_neg_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
+        apply_unary!(self, Self::word_neg_unary_assign::<REDUCE>, a, CHUNK);
+    }
+
+    #[inline(always)]
+    fn vec_neg_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &mut [u64]){
+        apply_binary!(self, Self::word_neg_binary_assign::<REDUCE>, a, b, CHUNK);
     }
 
     #[inline(always)]

math/src/poly.rs

@@ -0,0 +1,58 @@
+pub mod poly;
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Poly<O>(pub Vec<O>);
+
+impl<O> Poly<O>where
+    O: Default + Clone,
+    {
+    pub fn new(n: usize) -> Self{
+        Self(vec![O::default();n])
+    }
+
+    pub fn buffer_size(&self) -> usize{
+        return self.0.len()
+    }
+
+    pub fn from_buffer(&mut self, n: usize, buf: &mut [O]){
+        assert!(buf.len() >= n, "invalid buffer: buf.len()={} < n={}", buf.len(), n);
+        self.0 = Vec::from(&buf[..n]);
+    }
+
+    pub fn n(&self) -> usize{
+        return self.0.len()
+    }
+}
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct PolyRNS<O>(pub Vec<Poly<O>>);
+
+impl<O> PolyRNS<O>where
+    O: Default + Clone,
+    {
+    pub fn new(n: usize) -> Self{
+        Self(vec![Poly::<O>::new(n);n])
+    }
+
+    pub fn n(&self) -> usize{
+        self.0[0].n()
+    }
+
+    pub fn level(&self) -> usize{
+        self.0.len()-1
+    }
+
+    pub fn buffer_size(&self) -> usize{
+        self.n() * (self.level()+1)
+    }
+
+    pub fn from_buffer(&mut self, n: usize, level: usize, buf: &mut [O]){
+        assert!(buf.len() >= n * (level+1), "invalid buffer: buf.len()={} < n * (level+1)={}", buf.len(), level+1);
+        self.0.clear();
+        for chunk in buf.chunks_mut(n).take(level+1) {
+            let mut poly: Poly<O> = Poly(Vec::new());
+            poly.from_buffer(n, chunk);
+            self.0.push(poly);
+        }
+    }
+}

math/src/ring.rs

@@ -8,4 +8,7 @@ pub struct Ring<O>{
     pub n:usize,
     pub modulus:Prime<O>,
     pub dft:Box<dyn DFT<O>>,
-}
+}
+
+
+pub struct RingRNS<O>(pub Vec<Ring<O>>);

math/src/ring/impl_u64/mod.rs

@@ -0,0 +1,3 @@
+pub mod automorphism;
+pub mod ring;
+pub mod ring_rns;

math/src/ring/impl_u64/ring.rs

@@ -0,0 +1,102 @@
+use crate::ring::Ring;
+use crate::dft::ntt::Table;
+use crate::modulus::prime::Prime;
+use crate::modulus::montgomery::Montgomery;
+use crate::poly::Poly;
+use crate::modulus::REDUCEMOD;
+use crate::modulus::VecOperations;
+use crate::CHUNK;
+
+impl Ring<u64>{
+    pub fn new(n:usize, q_base:u64, q_power:usize) -> Self{
+        let prime: Prime<u64> = Prime::<u64>::new(q_base, q_power);
+        Self {
+            n: n,
+            modulus: prime.clone(),
+            dft: Box::new(Table::<u64>::new(prime, (2 * n) as u64)),
+        }
+    }
+
+    pub fn n(&self) -> usize{
+        return self.n
+    }
+
+    pub fn new_poly(&self) -> Poly<u64>{
+        Poly::<u64>::new(self.n())
+    }
+}
+
+impl Ring<u64>{
+    pub fn ntt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
+        match LAZY{
+            true => self.dft.forward_inplace_lazy(&mut poly.0),
+            false => self.dft.forward_inplace(&mut poly.0)
+        }
+    }
+
+    pub fn intt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
+        match LAZY{
+            true => self.dft.forward_inplace_lazy(&mut poly.0),
+            false => self.dft.forward_inplace(&mut poly.0)
+        }
+    }
+
+    pub fn ntt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
+        poly_out.0.copy_from_slice(&poly_in.0);
+        match LAZY{
+            true => self.dft.backward_inplace_lazy(&mut poly_out.0),
+            false => self.dft.backward_inplace(&mut poly_out.0)
+        }
+    }
+
+    pub fn intt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
+        poly_out.0.copy_from_slice(&poly_in.0);
+        match LAZY{
+            true => self.dft.backward_inplace_lazy(&mut poly_out.0),
+            false => self.dft.backward_inplace(&mut poly_out.0)
+        }
+    }
+}
+
+impl Ring<u64>{
+
+    #[inline(always)]
+    pub fn add_inplace<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &mut Poly<u64>){
+        self.modulus.vec_add_unary_assign::<CHUNK, REDUCE>(&a.0, &mut b.0);
+    }
+
+    #[inline(always)]
+    pub fn add<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &Poly<u64>, c: &mut Poly<u64>){
+        self.modulus.vec_add_binary_assign::<CHUNK, REDUCE>(&a.0, &b.0, &mut c.0);
+    }
+
+    #[inline(always)]
+    pub fn sub_inplace<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &mut Poly<u64>){
+        self.modulus.vec_sub_unary_assign::<CHUNK, REDUCE>(&a.0, &mut b.0);
+    }
+
+    #[inline(always)]
+    pub fn sub<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &Poly<u64>, c: &mut Poly<u64>){
+        self.modulus.vec_sub_binary_assign::<CHUNK, REDUCE>(&a.0, &b.0, &mut c.0);
+    }
+
+    #[inline(always)]
+    pub fn neg<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &mut Poly<u64>){
+        self.modulus.vec_neg_binary_assign::<CHUNK, REDUCE>(&a.0, &mut b.0);
+    }
+
+    #[inline(always)]
+    pub fn neg_inplace<const REDUCE: REDUCEMOD>(&self, a: &mut Poly<u64>){
+        self.modulus.vec_neg_unary_assign::<CHUNK, REDUCE>(&mut a.0);
+    }
+
+    #[inline(always)]
+    pub fn  mul_montgomery_external<const REDUCE:REDUCEMOD>(&self, a:&Poly<Montgomery<u64>>, b:&Poly<u64>, c: &mut Poly<u64>){
+        self.modulus.vec_mul_montgomery_external_binary_assign::<CHUNK, REDUCE>(&a.0, &b.0, &mut c.0);
+    }
+
+    #[inline(always)]
+    pub fn mul_montgomery_external_inplace<const REDUCE:REDUCEMOD>(&self, a:&Poly<Montgomery<u64>>, b:&mut Poly<u64>){
+        self.modulus.vec_mul_montgomery_external_unary_assign::<CHUNK, REDUCE>(&a.0, &mut b.0);
+    }
+}

math/src/ring/impl_u64/ring_rns.rs

@@ -0,0 +1,114 @@
+use crate::ring::{Ring, RingRNS};
+use crate::poly::PolyRNS;
+use crate::modulus::montgomery::Montgomery;
+use crate::modulus::REDUCEMOD;
+
+impl RingRNS<u64>{
+    pub fn new(n:usize, moduli: Vec<u64>) -> Self{
+        assert!(!moduli.is_empty(), "moduli cannot be empty");
+        let rings: Vec<Ring<u64>> = moduli
+            .into_iter()
+            .map(|prime: u64| Ring::new(n, prime, 1))
+            .collect();
+        RingRNS(rings)
+    }
+
+    pub fn n(&self) -> usize{
+        self.0[0].n()
+    }
+
+    pub fn max_level(&self) -> usize{
+        self.0.len()-1
+    }
+}
+
+impl RingRNS<u64>{
+    
+}
+
+impl RingRNS<u64>{
+    
+    #[inline(always)]
+    pub fn add<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &PolyRNS<u64>, c: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(c.n() >= self.n(), "c.n()={} < n={}", c.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        debug_assert!(c.level() >= LEVEL, "c.level()={} < LEVEL={}", c.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.add::<REDUCE>(&a.0[i], &b.0[i], &mut c.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn add_inplace<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.add_inplace::<REDUCE>(&a.0[i], &mut b.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn sub<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &PolyRNS<u64>, c: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(c.n() >= self.n(), "c.n()={} < n={}", c.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        debug_assert!(c.level() >= LEVEL, "c.level()={} < LEVEL={}", c.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.sub::<REDUCE>(&a.0[i], &b.0[i], &mut c.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn sub_inplace<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.sub_inplace::<REDUCE>(&a.0[i], &mut b.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn neg<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.neg::<REDUCE>(&a.0[i], &mut b.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn neg_inplace<const LEVEL:usize, const REDUCE: REDUCEMOD>(&self, a: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.neg_inplace::<REDUCE>(&mut a.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn  mul_montgomery_external<const LEVEL:usize, const REDUCE:REDUCEMOD>(&self, a:&PolyRNS<Montgomery<u64>>, b:&PolyRNS<u64>, c: &mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(c.n() >= self.n(), "c.n()={} < n={}", c.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        debug_assert!(c.level() >= LEVEL, "c.level()={} < LEVEL={}", c.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.mul_montgomery_external::<REDUCE>(&a.0[i], &b.0[i], &mut c.0[i]));
+    }
+
+    #[inline(always)]
+    pub fn mul_montgomery_external_inplace<const LEVEL:usize, const REDUCE:REDUCEMOD>(&self, a:&PolyRNS<Montgomery<u64>>, b:&mut PolyRNS<u64>){
+        debug_assert!(self.max_level() <= LEVEL, "max_level={} < LEVEL={}", self.max_level(), LEVEL);
+        debug_assert!(a.n() >= self.n(), "a.n()={} < n={}", a.n(), self.n());
+        debug_assert!(b.n() >= self.n(), "b.n()={} < n={}", b.n(), self.n());
+        debug_assert!(a.level() >= LEVEL, "a.level()={} < LEVEL={}", a.level(), LEVEL);
+        debug_assert!(b.level() >= LEVEL, "b.level()={} < LEVEL={}", b.level(), LEVEL);
+        self.0.iter().take(LEVEL + 1).enumerate().for_each(|(i, ring)| ring.mul_montgomery_external_inplace::<REDUCE>(&a.0[i], &mut b.0[i]));
+    }
+}

src/poly.rs

@@ -1,29 +0,0 @@
-pub mod poly;
-
-#[derive(Clone, Debug, PartialEq, Eq)]
-pub struct Poly<O>(pub Vec<O>);
-
-impl<O> Poly<O>where
-    O: Default + Clone,
-    {
-    pub fn new(n: usize) -> Self{
-        Self(vec![O::default();n])
-    }
-
-    pub fn new_montgomery(n: usize) -> Self{
-        Self(vec![O::default();n])
-    }
-
-    pub fn buffer_size(&self) -> usize{
-        return self.0.len()
-    }
-
-    pub fn from_buffer(&mut self, n: usize, buf: &mut [O]){
-        assert!(buf.len() >= n, "invalid buffer: buf.len()={} < n={}", buf.len(), n);
-        self.0 = Vec::from(&buf[..n]);
-    }
-
-    pub fn n(&self) -> usize{
-        return self.0.len()
-    }
-}

src/ring/impl_u64/mod.rs

@@ -1,2 +0,0 @@
-pub mod automorphism;
-pub mod ring;

src/ring/impl_u64/ring.rs

@@ -1,53 +0,0 @@
-use crate::ring::Ring;
-use crate::dft::ntt::Table;
-use crate::modulus::prime::Prime;
-use crate::poly::Poly;
-
-impl Ring<u64>{
-    pub fn new(n:usize, q_base:u64, q_power:usize) -> Self{
-        let prime: Prime<u64> = Prime::<u64>::new(q_base, q_power);
-        Self {
-            n: n,
-            modulus: prime.clone(),
-            dft: Box::new(Table::<u64>::new(prime, (2 * n) as u64)),
-        }
-    }
-
-    pub fn n(&self) -> usize{
-        return self.n
-    }
-
-    pub fn new_poly(&self) -> Poly<u64>{
-        Poly::<u64>::new(self.n())
-    }
-
-    pub fn ntt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
-        match LAZY{
-            true => self.dft.forward_inplace_lazy(&mut poly.0),
-            false => self.dft.forward_inplace(&mut poly.0)
-        }
-    }
-
-    pub fn intt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
-        match LAZY{
-            true => self.dft.forward_inplace_lazy(&mut poly.0),
-            false => self.dft.forward_inplace(&mut poly.0)
-        }
-    }
-
-    pub fn ntt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
-        poly_out.0.copy_from_slice(&poly_in.0);
-        match LAZY{
-            true => self.dft.backward_inplace_lazy(&mut poly_out.0),
-            false => self.dft.backward_inplace(&mut poly_out.0)
-        }
-    }
-
-    pub fn intt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
-        poly_out.0.copy_from_slice(&poly_in.0);
-        match LAZY{
-            true => self.dft.backward_inplace_lazy(&mut poly_out.0),
-            false => self.dft.backward_inplace(&mut poly_out.0)
-        }
-    }
-}