added spqlios as submodule

rns/src/ring/impl_u64/utils.rs

@@ -0,0 +1,38 @@
+use crate::modulus::ONCE;
+use crate::poly::Poly;
+use crate::ring::Ring;
+
+impl Ring<u64> {
+    // Generates a vector storing {X^{2^0}, X^{2^1}, .., X^{2^log_n}}.
+    pub fn gen_x_pow_2<const NTT: bool, const INV: bool>(&self, log_n: usize) -> Vec<Poly<u64>> {
+        let mut x_pow: Vec<Poly<u64>> = Vec::<Poly<u64>>::with_capacity(log_n);
+
+        (0..log_n).for_each(|i| {
+            let mut idx: usize = 1 << i;
+
+            if INV {
+                idx = self.n() - idx;
+            }
+
+            x_pow.push(self.new_poly());
+
+            if i == 0 {
+                x_pow[i].0[idx] = self.modulus.montgomery.one();
+                self.ntt_inplace::<false>(&mut x_pow[i]);
+            } else {
+                let (left, right) = x_pow.split_at_mut(i);
+                self.a_mul_b_montgomery_into_c::<ONCE>(&left[i - 1], &left[i - 1], &mut right[0]);
+            }
+        });
+
+        if INV {
+            self.a_neg_into_a::<1, ONCE>(&mut x_pow[0]);
+        }
+
+        if !NTT {
+            x_pow.iter_mut().for_each(|x| self.intt_inplace::<false>(x));
+        }
+
+        x_pow
+    }
+}