poulpy/src/dft/ntt.rs
src/dft/ntt.rsRaw
1use crate::modulus::montgomery::Montgomery;
2use crate::modulus::barrett::Barrett;
3use crate::modulus::prime::Prime;
4use crate::modulus::ReduceOnce;
5use crate::modulus::WordOps;
6use crate::modulus::ONCE;
7use crate::dft::DFT;
8use itertools::izip;
9
10pub struct Table<O>{
11 prime:Prime<O>,
12 psi: O,
13 psi_forward_rev:Vec<Barrett<u64>>,
14 psi_backward_rev: Vec<Barrett<u64>>,
15 q:O,
16 two_q:O,
17 four_q:O,
18}
19
20impl Table< u64> {
21 pub fn new(prime: Prime<u64>, nth_root: u64)->Self{
22
23 assert!(nth_root&(nth_root-1) == 0, "invalid argument: nth_root = {} is not a power of two", nth_root);
24
25 let psi: u64 = prime.primitive_nth_root(nth_root);
26
27 let psi_mont: Montgomery<u64> = prime.montgomery.prepare::<ONCE>(psi);
28 let psi_inv_mont: Montgomery<u64> = prime.montgomery.pow(psi_mont, prime.phi-1);
29
30 let mut psi_forward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
31 let mut psi_backward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
32
33 psi_forward_rev[0] = prime.barrett.prepare(1);
34 psi_backward_rev[0] = prime.barrett.prepare(1);
35
36 let log_nth_root_half: u32 = (nth_root>>1).log2() as _;
37
38 let mut powers_forward: u64 = 1u64;
39 let mut powers_backward: u64 = 1u64;
40
41 for i in 1..(nth_root>>1) as usize{
42
43 let i_rev: usize = i.reverse_bits_msb(log_nth_root_half);
44
45 prime.montgomery.mul_external_assign::<ONCE>(psi_mont, &mut powers_forward);
46 prime.montgomery.mul_external_assign::<ONCE>(psi_inv_mont, &mut powers_backward);
47
48 psi_forward_rev[i_rev] = prime.barrett.prepare(powers_forward);
49 psi_backward_rev[i_rev] = prime.barrett.prepare(powers_backward);
50 }
51
52 let q: u64 = prime.q();
53
54 Self{
55 prime: prime,
56 psi:psi,
57 psi_forward_rev: psi_forward_rev,
58 psi_backward_rev: psi_backward_rev,
59 q:q,
60 two_q:q<<1,
61 four_q:q<<2,
62 }
63 }
64}
65
66
67impl DFT<u64> for Table<u64>{
68
69 fn forward_inplace(&self, a: &mut [u64]){
70 self.forward_inplace::<false>(a)
71 }
72
73 fn forward_inplace_lazy(&self, a: &mut [u64]){
74 self.forward_inplace::<true>(a)
75 }
76
77 fn backward_inplace(&self, a: &mut [u64]){
78 self.backward_inplace::<false>(a)
79 }
80
81 fn backward_inplace_lazy(&self, a: &mut [u64]){
82 self.backward_inplace::<true>(a)
83 }
84}
85
86impl Table<u64>{
87
88 pub fn forward_inplace<const LAZY:bool>(&self, a: &mut [u64]){
89 self.forward_inplace_core::<LAZY, 0, 0>(a);
90 }
91
92 pub fn forward_inplace_core<const LAZY: bool, const SKIPSTART: u8, const SKIPEND: u8>(&self, a: &mut [u64]) {
93
94 let n: usize = a.len();
95 assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
96 let log_n: u32 = usize::BITS - ((n as usize)-1).leading_zeros();
97
98 let start: u32 = SKIPSTART as u32;
99 let end: u32 = log_n - (SKIPEND as u32);
100
101 for layer in start..end {
102 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
103 let t: usize = 2*size;
104 if layer == log_n - 1 {
105 if LAZY{
106 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
107 let (a, b) = a.split_at_mut(size);
108 self.dit_inplace::<false>(&mut a[0], &mut b[0], *psi);
109 debug_assert!(a[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", a[0], self.two_q-1);
110 debug_assert!(b[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", b[0], self.two_q-1);
111 });
112 }else{
113 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
114 let (a, b) = a.split_at_mut(size);
115 self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
116 self.prime.barrett.reduce_assign(&mut a[0]);
117 self.prime.barrett.reduce_assign(&mut b[0]);
118 debug_assert!(a[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", a[0], self.q-1);
119 debug_assert!(b[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", b[0], self.q-1);
120 });
121 }
122
123 } else if t >= 16{
124 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
125 let (a, b) = a.split_at_mut(size);
126 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
127 self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
128 self.dit_inplace::<true>(&mut a[1], &mut b[1], *psi);
129 self.dit_inplace::<true>(&mut a[2], &mut b[2], *psi);
130 self.dit_inplace::<true>(&mut a[3], &mut b[3], *psi);
131 self.dit_inplace::<true>(&mut a[4], &mut b[4], *psi);
132 self.dit_inplace::<true>(&mut a[5], &mut b[5], *psi);
133 self.dit_inplace::<true>(&mut a[6], &mut b[6], *psi);
134 self.dit_inplace::<true>(&mut a[7], &mut b[7], *psi);
135 });
136 });
137 }else{
138 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
139 let (a, b) = a.split_at_mut(size);
140 izip!(a, b).for_each(|(a, b)| self.dit_inplace::<true>(a, b, *psi));
141 });
142 }
143 }
144 }
145
146 #[inline(always)]
147 fn dit_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
148 debug_assert!(*a < self.four_q, "a:{} q:{}", a, self.four_q);
149 debug_assert!(*b < self.four_q, "b:{} q:{}", b, self.four_q);
150 a.reduce_once_assign(self.two_q);
151 let bt: u64 = self.prime.barrett.mul_external_lazy(t, *b);
152 *b = a.wrapping_add(self.two_q-bt);
153 *a = a.wrapping_add(bt);
154 if !LAZY {
155 a.reduce_once_assign(self.two_q);
156 b.reduce_once_assign(self.two_q);
157 }
158 }
159
160 pub fn backward_inplace<const LAZY:bool>(&self, a: &mut [u64]){
161 self.backward_inplace_core::<LAZY, 0, 0>(a);
162 }
163
164 pub fn backward_inplace_core<const LAZY:bool, const SKIPSTART: u8, const SKIPEND: u8>(&self, a: &mut [u64]) {
165 let n: usize = a.len();
166 assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
167 let log_n = usize::BITS - ((n as usize)-1).leading_zeros();
168
169 let start: u32 = SKIPEND as u32;
170 let end: u32 = log_n - (SKIPSTART as u32);
171
172 for layer in (start..end).rev() {
173 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
174 let t: usize = 2*size;
175 if layer == 0 {
176
177 let n_inv: Barrett<u64> = self.prime.barrett.prepare(self.prime.inv(n as u64));
178 let psi: Barrett<u64> = self.prime.barrett.prepare(self.prime.barrett.mul_external(n_inv, self.psi_backward_rev[1].0));
179
180 izip!(a.chunks_exact_mut(2 * size)).for_each(
181 |a| {
182 let (a, b) = a.split_at_mut(size);
183 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
184 self.dif_last_inplace::<LAZY>(&mut a[0], &mut b[0], psi, n_inv);
185 self.dif_last_inplace::<LAZY>(&mut a[1], &mut b[1], psi, n_inv);
186 self.dif_last_inplace::<LAZY>(&mut a[2], &mut b[2], psi, n_inv);
187 self.dif_last_inplace::<LAZY>(&mut a[3], &mut b[3], psi, n_inv);
188 self.dif_last_inplace::<LAZY>(&mut a[4], &mut b[4], psi, n_inv);
189 self.dif_last_inplace::<LAZY>(&mut a[5], &mut b[5], psi, n_inv);
190 self.dif_last_inplace::<LAZY>(&mut a[6], &mut b[6], psi, n_inv);
191 self.dif_last_inplace::<LAZY>(&mut a[7], &mut b[7], psi, n_inv);
192 });
193 },
194 );
195
196 } else if t >= 16{
197 izip!(a.chunks_exact_mut(t), &self.psi_backward_rev[m..]).for_each(
198 |(a, psi)| {
199 let (a, b) = a.split_at_mut(size);
200 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
201 self.dif_inplace::<true>(&mut a[0], &mut b[0], *psi);
202 self.dif_inplace::<true>(&mut a[1], &mut b[1], *psi);
203 self.dif_inplace::<true>(&mut a[2], &mut b[2], *psi);
204 self.dif_inplace::<true>(&mut a[3], &mut b[3], *psi);
205 self.dif_inplace::<true>(&mut a[4], &mut b[4], *psi);
206 self.dif_inplace::<true>(&mut a[5], &mut b[5], *psi);
207 self.dif_inplace::<true>(&mut a[6], &mut b[6], *psi);
208 self.dif_inplace::<true>(&mut a[7], &mut b[7], *psi);
209 });
210 },
211 );
212 } else {
213 izip!(a.chunks_exact_mut(2 * size), &self.psi_backward_rev[m..]).for_each(
214 |(a, psi)| {
215 let (a, b) = a.split_at_mut(size);
216 izip!(a, b).for_each(|(a, b)| self.dif_inplace::<true>(a, b, *psi));
217 },
218 );
219 }
220 }
221 }
222
223 #[inline(always)]
224 fn dif_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
225 debug_assert!(*a < self.two_q, "a:{} q:{}", a, self.four_q);
226 debug_assert!(*b < self.two_q, "b:{} q:{}", b, self.four_q);
227 let d: u64 = self.prime.barrett.mul_external_lazy(t, *a + self.two_q - *b);
228 *a = a.wrapping_add(*b);
229 a.reduce_once_assign(self.two_q);
230 *b = d;
231 if !LAZY {
232 a.reduce_once_assign(self.q);
233 b.reduce_once_assign(self.q);
234 }
235 }
236
237 fn dif_last_inplace<const LAZY:bool>(&self, a: &mut u64, b: &mut u64, psi: Barrett<u64>, n_inv: Barrett<u64>){
238 debug_assert!(*a < self.two_q);
239 debug_assert!(*b < self.two_q);
240 if LAZY{
241 let d: u64 = self.prime.barrett.mul_external_lazy(psi, *a + self.two_q - *b);
242 *a = self.prime.barrett.mul_external_lazy(n_inv, *a + *b);
243 *b = d;
244 }else{
245 let d: u64 = self.prime.barrett.mul_external(psi, *a + self.two_q - *b);
246 *a = self.prime.barrett.mul_external(n_inv, *a + *b);
247 *b = d;
248 }
249 }
250}
251
252#[cfg(test)]
253mod tests {
254 use super::*;
255
256 #[test]
257 fn test_ntt() {
258 let q_base: u64 = 0x800000000004001;
259 let q_power: usize = 1;
260 let prime_instance: Prime<u64> = Prime::<u64>::new(q_base, q_power);
261 let n: u64 = 32;
262 let two_nth_root: u64 = n<<1;
263 let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, two_nth_root);
264 let mut a: Vec<u64> = vec![0; n as usize];
265 for i in 0..a.len(){
266 a[i] = i as u64;
267 }
268
269 let b: Vec<u64> = a.clone();
270 ntt_table.forward_inplace::<false>(&mut a);
271 ntt_table.backward_inplace::<false>(&mut a);
272 assert!(a == b);
273 }
274}