poulpy/src/dft/ntt.rs
src/dft/ntt.rsRaw
1use crate::modulus::montgomery::Montgomery;
2use crate::modulus::shoup::Shoup;
3use crate::modulus::prime::Prime;
4use crate::modulus::ReduceOnce;
5use crate::modulus::WordOps;
6use crate::dft::DFT;
7use itertools::izip;
8
9pub struct Table<O>{
10 prime:Prime<O>,
11 psi_forward_rev:Vec<Shoup<u64>>,
12 psi_backward_rev: Vec<Shoup<u64>>,
13 q:O,
14 two_q:O,
15 four_q:O,
16}
17
18impl Table< u64> {
19 pub fn new(prime: Prime<u64>, nth_root: u64)->Self{
20
21 assert!(nth_root&(nth_root-1) == 0, "invalid argument: nth_root = {} is not a power of two", nth_root);
22
23 let psi: u64 = prime.primitive_nth_root(nth_root);
24
25 let psi_mont: Montgomery<u64> = prime.montgomery.prepare(psi);
26 let psi_inv_mont: Montgomery<u64> = prime.montgomery.pow(psi_mont, prime.phi-1);
27
28 let mut psi_forward_rev: Vec<Shoup<u64>> = vec![Shoup(0, 0); (nth_root >> 1) as usize];
29 let mut psi_backward_rev: Vec<Shoup<u64>> = vec![Shoup(0, 0); (nth_root >> 1) as usize];
30
31 psi_forward_rev[0] = prime.shoup.prepare(1);
32 psi_backward_rev[0] = prime.shoup.prepare(1);
33
34 let log_nth_root_half: u32 = (nth_root>>1).log2() as _;
35
36 let mut powers_forward: u64 = 1u64;
37 let mut powers_backward: u64 = 1u64;
38
39 for i in 1..(nth_root>>1) as usize{
40
41 let i_rev: usize = i.reverse_bits_msb(log_nth_root_half);
42
43 prime.montgomery.mul_external_assign(psi_mont, &mut powers_forward);
44 prime.montgomery.mul_external_assign(psi_inv_mont, &mut powers_backward);
45
46 psi_forward_rev[i_rev] = prime.shoup.prepare(powers_forward);
47 psi_backward_rev[i_rev] = prime.shoup.prepare(powers_backward);
48 }
49
50 let q: u64 = prime.q();
51
52 Self{
53 prime: prime,
54 psi_forward_rev: psi_forward_rev,
55 psi_backward_rev: psi_backward_rev,
56 q:q,
57 two_q:q<<1,
58 four_q:q<<2,
59 }
60 }
61
62 // Returns n^-1 mod q in Montgomery.
63 fn inv(&self, n:u64) -> Montgomery<u64>{
64 self.prime.montgomery.pow(self.prime.montgomery.prepare(n), self.prime.phi-1)
65 }
66}
67
68
69impl DFT<u64> for Table<u64>{
70 fn forward_inplace(&self, a: &mut [u64]){
71 self.forward_inplace(a)
72 }
73
74 fn forward_inplace_lazy(&self, a: &mut [u64]){
75 self.forward_inplace_lazy(a)
76 }
77
78 fn backward_inplace(&self, a: &mut [u64]){
79 self.backward_inplace(a)
80 }
81
82 fn backward_inplace_lazy(&self, a: &mut [u64]){
83 self.backward_inplace_lazy(a)
84 }
85}
86
87impl Table<u64>{
88
89 pub fn forward_inplace_lazy(&self, a: &mut [u64]){
90 self.forward_inplace_core::<true>(a);
91 }
92
93 pub fn forward_inplace(&self, a: &mut [u64]){
94 self.forward_inplace_core::<false>(a);
95 }
96
97 pub fn forward_inplace_core<const LAZY: bool>(&self, a: &mut [u64]) {
98
99 let n: usize = a.len();
100 assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
101 let log_n: u32 = usize::BITS - ((n as usize)-1).leading_zeros();
102
103 for layer in 0..log_n {
104 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
105 let t: usize = 2*size;
106 if layer == log_n - 1 {
107 if LAZY{
108 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
109 let (a, b) = a.split_at_mut(size);
110 self.dit::<false>(&mut a[0], &mut b[0], *psi);
111 debug_assert!(a[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", a[0], self.two_q-1);
112 debug_assert!(b[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", b[0], self.two_q-1);
113 });
114 }else{
115 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
116 let (a, b) = a.split_at_mut(size);
117 self.dit::<true>(&mut a[0], &mut b[0], *psi);
118 self.prime.shoup.reduce_assign(&mut a[0]);
119 self.prime.shoup.reduce_assign(&mut b[0]);
120 debug_assert!(a[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", a[0], self.q-1);
121 debug_assert!(b[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", b[0], self.q-1);
122 });
123 }
124
125 } else if t >= 16{
126 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
127 let (a, b) = a.split_at_mut(size);
128 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
129 self.dit::<true>(&mut a[0], &mut b[0], *psi);
130 self.dit::<true>(&mut a[1], &mut b[1], *psi);
131 self.dit::<true>(&mut a[2], &mut b[2], *psi);
132 self.dit::<true>(&mut a[3], &mut b[3], *psi);
133 self.dit::<true>(&mut a[4], &mut b[4], *psi);
134 self.dit::<true>(&mut a[5], &mut b[5], *psi);
135 self.dit::<true>(&mut a[6], &mut b[6], *psi);
136 self.dit::<true>(&mut a[7], &mut b[7], *psi);
137 });
138 });
139 }else{
140 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
141 let (a, b) = a.split_at_mut(size);
142 izip!(a, b).for_each(|(a, b)| self.dit::<true>(a, b, *psi));
143 });
144 }
145 }
146 }
147
148 #[inline(always)]
149 fn dit<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Shoup<u64>) {
150 debug_assert!(*a < self.four_q, "a:{} q:{}", a, self.four_q);
151 debug_assert!(*b < self.four_q, "b:{} q:{}", b, self.four_q);
152 a.reduce_once_assign(self.two_q);
153 let bt: u64 = self.prime.shoup.mul_external_lazy(t, *b);
154 *b = a.wrapping_add(self.two_q-bt);
155 *a = a.wrapping_add(bt);
156 if !LAZY {
157 a.reduce_once_assign(self.two_q);
158 b.reduce_once_assign(self.two_q);
159 }
160 }
161
162 pub fn backward_inplace_lazy(&self, a: &mut [u64]){
163 self.backward_inplace_core::<true>(a);
164 }
165
166 pub fn backward_inplace(&self, a: &mut [u64]){
167 self.backward_inplace_core::<false>(a);
168 }
169
170 pub fn backward_inplace_core<const LAZY:bool>(&self, a: &mut [u64]) {
171 let n: usize = a.len();
172 assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
173 let log_n = usize::BITS - ((n as usize)-1).leading_zeros();
174
175 for layer in (0..log_n).rev() {
176 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
177 let t: usize = 2*size;
178 if layer == 0 {
179
180 let n_inv: Shoup<u64> = self.prime.shoup.prepare(self.prime.inv(n as u64));
181 let psi: Shoup<u64> = self.prime.shoup.prepare(self.prime.shoup.mul_external(n_inv, self.psi_backward_rev[1].0));
182
183 izip!(a.chunks_exact_mut(2 * size)).for_each(
184 |a| {
185 let (a, b) = a.split_at_mut(size);
186 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
187 self.dif_last::<LAZY>(&mut a[0], &mut b[0], psi, n_inv);
188 self.dif_last::<LAZY>(&mut a[1], &mut b[1], psi, n_inv);
189 self.dif_last::<LAZY>(&mut a[2], &mut b[2], psi, n_inv);
190 self.dif_last::<LAZY>(&mut a[3], &mut b[3], psi, n_inv);
191 self.dif_last::<LAZY>(&mut a[4], &mut b[4], psi, n_inv);
192 self.dif_last::<LAZY>(&mut a[5], &mut b[5], psi, n_inv);
193 self.dif_last::<LAZY>(&mut a[6], &mut b[6], psi, n_inv);
194 self.dif_last::<LAZY>(&mut a[7], &mut b[7], psi, n_inv);
195 });
196 },
197 );
198
199 } else if t >= 16{
200 izip!(a.chunks_exact_mut(t), &self.psi_backward_rev[m..]).for_each(
201 |(a, psi)| {
202 let (a, b) = a.split_at_mut(size);
203 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
204 self.dif::<true>(&mut a[0], &mut b[0], *psi);
205 self.dif::<true>(&mut a[1], &mut b[1], *psi);
206 self.dif::<true>(&mut a[2], &mut b[2], *psi);
207 self.dif::<true>(&mut a[3], &mut b[3], *psi);
208 self.dif::<true>(&mut a[4], &mut b[4], *psi);
209 self.dif::<true>(&mut a[5], &mut b[5], *psi);
210 self.dif::<true>(&mut a[6], &mut b[6], *psi);
211 self.dif::<true>(&mut a[7], &mut b[7], *psi);
212 });
213 },
214 );
215 } else {
216 izip!(a.chunks_exact_mut(2 * size), &self.psi_backward_rev[m..]).for_each(
217 |(a, psi)| {
218 let (a, b) = a.split_at_mut(size);
219 izip!(a, b).for_each(|(a, b)| self.dif::<true>(a, b, *psi));
220 },
221 );
222 }
223 }
224 }
225
226 #[inline(always)]
227 fn dif<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Shoup<u64>) {
228 debug_assert!(*a < self.two_q);
229 debug_assert!(*b < self.two_q);
230 let d: u64 = self.prime.shoup.mul_external_lazy(t, *a + self.two_q - *b);
231 *a = a.wrapping_add(*b);
232 a.reduce_once_assign(self.two_q);
233 *b = d;
234 if !LAZY {
235 a.reduce_once_assign(self.q);
236 b.reduce_once_assign(self.q);
237 }
238 }
239
240 fn dif_last<const LAZY:bool>(&self, a: &mut u64, b: &mut u64, psi: Shoup<u64>, n_inv: Shoup<u64>){
241 debug_assert!(*a < self.two_q);
242 debug_assert!(*b < self.two_q);
243 if LAZY{
244 let d: u64 = self.prime.shoup.mul_external_lazy(psi, *a + self.two_q - *b);
245 *a = self.prime.shoup.mul_external_lazy(n_inv, *a + *b);
246 *b = d;
247 }else{
248 let d: u64 = self.prime.shoup.mul_external(psi, *a + self.two_q - *b);
249 *a = self.prime.shoup.mul_external(n_inv, *a + *b);
250 *b = d;
251 }
252 }
253}