@@ -179,6 +179,12 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "60b1af1c220855b6ceac025d3f6ecdd2b7c4894bfe9cd9bda4fbb4bc7c0d4cf0"
 
 [[package]]
+name = "equivalent"
+version = "1.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5443807d6dff69373d433ab9ef5378ad8df50ca6298caf15de6e52e24aaf54d5"
+
+[[package]]
 name = "getrandom"
 version = "0.2.15"
 source = "registry+https://github.com/rust-lang/crates.io-index"
@@ -200,10 +206,26 @@ "crunchy",
 ]
 
 [[package]]
+name = "hashbrown"
+version = "0.15.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bf151400ff0baff5465007dd2f3e717f3fe502074ca563069ce3a6629d07b289"
+
+[[package]]
 name = "hermit-abi"
 version = "0.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "fbf6a919d6cf397374f7dfeeea91d974c7c0a7221d0d0f4f20d859d329e53fcc"
+
+[[package]]
+name = "indexmap"
+version = "2.7.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "62f822373a4fe84d4bb149bf54e584a7f4abec90e072ed49cda0edea5b95471f"
+dependencies = [
+ "equivalent",
+ "hashbrown",
+]
 
 [[package]]
 name = "is-terminal"
@@ -273,6 +295,7 @@ name = "math"
 version = "0.1.0"
 dependencies = [
  "criterion",
+ "indexmap",
  "itertools 0.14.0",
  "num",
  "num-bigint",

@@ -13,6 +13,7 @@ prime_factorization = "1.0.5"
 itertools = "0.14.0"
 criterion = "0.5.1"
 rand_distr = "0.4.3"
+indexmap = "2.7.0"
 sampling = { path = "../sampling" }
 
 [[bench]]

@@ -9,6 +9,7 @@ pub mod ring;
 pub mod scalar;
 
 pub const CHUNK: usize = 8;
+pub const GALOISGENERATOR: usize = 5;
 
 pub mod macros {
 

@@ -4,6 +4,7 @@ use crate::ring::Ring;
 use crate::modulus::{ONCE, WordOps};
 use crate::modulus::barrett::Barrett;
 use std::cmp::min;
+use std::mem::transmute;
 
 
 impl Ring<u64>{
@@ -41,11 +42,13 @@
         x_pow
     }
 
-    pub fn pack<const ZEROGARBAGE: bool, const NTT: bool>(&self, polys: &mut HashMap<usize, Poly<u64>>, log_gap: usize) -> Poly<u64>{
+    pub fn pack<'a, const ZEROGARBAGE: bool, const NTT: bool>(&self, polys: &'a mut HashMap<usize, &'a mut Poly<u64>>, log_gap: usize) -> &'a Poly<u64>{
         
-        let log_n = self.log_n();
-        let log_start = log_n - log_gap;
-        let mut log_end = log_n;
+        let log_n: usize = self.log_n();
+        let log_nth_root: usize = log_n+1;
+        let nth_root: usize = 1<<log_nth_root;
+        let log_start: usize = log_n - log_gap;
+        let mut log_end: usize = log_n;
 
         let mut keys: Vec<usize> = polys.keys().copied().collect();
         keys.sort();
@@ -76,9 +79,99 @@
             self.a_mul_b_scalar_barrett_into_a::<ONCE>(&n_inv,  poly);
         }
 
-        Poly::<u64>::default()
+        let x_pow2: Vec<Poly<u64>> = self.gen_x_pow_2::<true, false>(log_n);
+        let mut tmpa: Poly<u64> = self.new_poly();
+        let mut tmpb: Poly<u64> = self.new_poly();
+
+        for i in log_start..log_end{
+
+            let t: usize = 1<<(log_n-1-i);
+
+            for j in 0..t{
+
+                let option_lo: Option<&&mut Poly<u64>> = polys.get(&i);
+                let option_hi: Option<&&mut Poly<u64>> = polys.get(&(i+t));
+                let mut hi_exists: bool = false;
+
+                match option_hi{
+                    Some(hi) =>{
+
+                            // Unsafe code is necessary because two mutables references are
+                            // accessed from the map.
+                            unsafe{
+                                self.a_mul_b_montgomery_into_a::<ONCE>(&x_pow2[log_n-i-1],  transmute(*hi as *const Poly<u64> as *mut Poly<u64>));
+                            }
+
+                            hi_exists = true;
+
+                            match option_lo{
+                                Some(lo) =>{
+
+                                    self.a_sub_b_into_c::<1, ONCE>(lo, hi, &mut tmpa);
+                                    
+                                    // Ensures unsafe blocks are "safe".
+                                    let ptr_hi: *mut Poly<u64> = *hi as *const Poly<u64> as *mut Poly<u64>;
+                                    let ptr_lo: *mut Poly<u64> = *lo as *const Poly<u64> as *mut Poly<u64>;
+                                    assert!(ptr_hi != ptr_lo, "something went seriously wrong");
+
+                                    unsafe{
+                                        self.a_add_b_into_b::<ONCE>(hi, transmute(ptr_lo));
+                                    }
+                                }
+                                None =>{
+                                    unsafe{
+                                        polys.insert(j, transmute(*hi as *const Poly<u64> as *mut Poly<u64>));
+                                    }
+                                },
+                            }
+
+                            polys.remove(&(j+t));
+                        }
+
+                    None =>{},  
+                }
+
+                let option_lo: Option<&&mut Poly<u64>> = polys.get(&i);
+                let option_hi: Option<&&mut Poly<u64>> = polys.get(&(i+t));
+
+                match option_lo{
+                    Some(lo) =>{
+                        
+                        let gal_el: usize = self.galois_element(1<<(i-1), i == 0, log_nth_root);
+
+                        if hi_exists{
+                            self.automorphism::<true>(&tmpa, gal_el, 2<<self.log_n(), &mut tmpb);
+                        }else{
+                            self.automorphism::<true>(*lo, gal_el, nth_root, &mut tmpa);
+                        }
+                        unsafe{
+                            self.a_add_b_into_b::<ONCE>(&tmpa, transmute(*lo as *const Poly<u64> as *mut Poly<u64>));
+                        }
+                    }
+
+                    None =>{
+                        match option_hi{
+                            Some(hi) =>{
+                                let gal_el: usize = self.galois_element(1<<(i-1), i == 0, log_nth_root);
+
+                                self.automorphism::<true>(*hi, gal_el, nth_root, &mut tmpa);
+
+                                unsafe{
+                                    self.a_sub_b_into_a::<1, ONCE>(&tmpa, transmute(*hi as *const Poly<u64> as *mut Poly<u64>))
+                                }
+                            }
+
+                            None =>{}
+                        }
+                    }
+                }
+            }
+        }
+
+        *polys.get(&0).unwrap()
     }
 }
+
 
 // Returns the largest
 fn max_pow2_gap(vec: &[usize]) -> usize{

@@ -7,6 +7,7 @@ use crate::modulus::{BARRETT, REDUCEMOD};
 use crate::poly::Poly;
 use crate::ring::Ring;
 use crate::CHUNK;
+use crate::GALOISGENERATOR;
 use num_bigint::BigInt;
 use num_traits::ToPrimitive;
 
@@ -38,6 +39,29 @@ a.0.iter_mut()
             .step_by(step)
             .enumerate()
             .for_each(|(i, v)| *v = (&coeffs[i] % &q_big).to_u64().unwrap());
+    }
+
+    // Returns GALOISGENERATOR^gen_1 * (-1)^gen_2 mod 2^log_nth_root.
+    pub fn galois_element(&self, gen_1: usize, gen_2: bool, log_nth_root: usize) -> usize{
+        let mut gal_el: usize = 1;
+        let mut gen_1_pow: usize = GALOISGENERATOR;
+        let mut e: usize = gen_1;
+        while e > 0{
+            if e & 1 == 1{
+                gal_el = gal_el.wrapping_mul(gen_1_pow);
+            }
+
+            gen_1_pow *= gen_1_pow;
+            e>>=1;
+        }
+
+        let nth_root = 1<<log_nth_root;
+        gal_el &= (nth_root-1);
+
+        if gen_2{
+            return nth_root - gal_el
+        }
+        gal_el
     }
 }