poulpy/math/src/dft/ntt.rs
math/src/dft/ntt.rsRaw
1use crate::dft::DFT;
2use crate::modulus::barrett::Barrett;
3use crate::modulus::montgomery::Montgomery;
4use crate::modulus::prime::Prime;
5use crate::modulus::ReduceOnce;
6use crate::modulus::WordOps;
7use crate::modulus::{BARRETT, NONE, ONCE};
8use itertools::izip;
9
10#[allow(dead_code)]
11pub struct Table<O> {
12 prime: Prime<O>,
13 psi: O,
14 psi_forward_rev: Vec<Barrett<u64>>,
15 psi_backward_rev: Vec<Barrett<u64>>,
16 q: O,
17 two_q: O,
18 four_q: O,
19}
20
21impl Table<u64> {
22 pub fn new(prime: Prime<u64>, nth_root: u64) -> Table<u64> {
23 assert!(
24 nth_root & (nth_root - 1) == 0,
25 "invalid argument: nth_root = {} is not a power of two",
26 nth_root
27 );
28
29 let psi: u64 = prime.primitive_nth_root(nth_root);
30
31 let psi_mont: Montgomery<u64> = prime.montgomery.prepare::<ONCE>(psi);
32 let psi_inv_mont: Montgomery<u64> = prime.montgomery.pow(psi_mont, prime.phi - 1);
33
34 let mut psi_forward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
35 let mut psi_backward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
36
37 psi_forward_rev[0] = prime.barrett.prepare(1);
38 psi_backward_rev[0] = prime.barrett.prepare(1);
39
40 let log_nth_root_half: u32 = (nth_root >> 1).log2() as _;
41
42 let mut powers_forward: u64 = 1u64;
43 let mut powers_backward: u64 = 1u64;
44
45 for i in 1..(nth_root >> 1) as usize {
46 let i_rev: usize = i.reverse_bits_msb(log_nth_root_half);
47
48 prime
49 .montgomery
50 .mul_external_assign::<ONCE>(psi_mont, &mut powers_forward);
51 prime
52 .montgomery
53 .mul_external_assign::<ONCE>(psi_inv_mont, &mut powers_backward);
54
55 psi_forward_rev[i_rev] = prime.barrett.prepare(powers_forward);
56 psi_backward_rev[i_rev] = prime.barrett.prepare(powers_backward);
57 }
58
59 let q: u64 = prime.q();
60
61 Self {
62 prime: prime,
63 psi: psi,
64 psi_forward_rev: psi_forward_rev,
65 psi_backward_rev: psi_backward_rev,
66 q: q,
67 two_q: q << 1,
68 four_q: q << 2,
69 }
70 }
71}
72
73impl DFT<u64> for Table<u64> {
74 fn forward_inplace(&self, a: &mut [u64]) {
75 self.forward_inplace::<false>(a)
76 }
77
78 fn forward_inplace_lazy(&self, a: &mut [u64]) {
79 self.forward_inplace::<true>(a)
80 }
81
82 fn backward_inplace(&self, a: &mut [u64]) {
83 self.backward_inplace::<false>(a)
84 }
85
86 fn backward_inplace_lazy(&self, a: &mut [u64]) {
87 self.backward_inplace::<true>(a)
88 }
89}
90
91impl Table<u64> {
92 pub fn forward_inplace<const LAZY: bool>(&self, a: &mut [u64]) {
93 self.forward_inplace_core::<LAZY, 0, 0>(a);
94 }
95
96 pub fn forward_inplace_core<const LAZY: bool, const SKIPSTART: u8, const SKIPEND: u8>(
97 &self,
98 a: &mut [u64],
99 ) {
100 let n: usize = a.len();
101 assert!(
102 n & n - 1 == 0,
103 "invalid x.len()= {} must be a power of two",
104 n
105 );
106 let log_n: u32 = usize::BITS - ((n as usize) - 1).leading_zeros();
107
108 let start: u32 = SKIPSTART as u32;
109 let end: u32 = log_n - (SKIPEND as u32);
110
111 for layer in start..end {
112 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
113 let t: usize = 2 * size;
114 if layer == log_n - 1 {
115 if LAZY {
116 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(
117 |(a, psi)| {
118 let (a, b) = a.split_at_mut(size);
119 self.dit_inplace::<false>(&mut a[0], &mut b[0], *psi);
120 debug_assert!(
121 a[0] < self.two_q,
122 "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)",
123 a[0],
124 self.two_q - 1
125 );
126 debug_assert!(
127 b[0] < self.two_q,
128 "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)",
129 b[0],
130 self.two_q - 1
131 );
132 },
133 );
134 } else {
135 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(
136 |(a, psi)| {
137 let (a, b) = a.split_at_mut(size);
138 self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
139 self.prime.barrett.reduce_assign::<BARRETT>(&mut a[0]);
140 self.prime.barrett.reduce_assign::<BARRETT>(&mut b[0]);
141 debug_assert!(
142 a[0] < self.q,
143 "forward_inplace_core::<LAZY=false> output {} > {} (q-1)",
144 a[0],
145 self.q - 1
146 );
147 debug_assert!(
148 b[0] < self.q,
149 "forward_inplace_core::<LAZY=false> output {} > {} (q-1)",
150 b[0],
151 self.q - 1
152 );
153 },
154 );
155 }
156 } else if t >= 16 {
157 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
158 let (a, b) = a.split_at_mut(size);
159 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
160 self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
161 self.dit_inplace::<true>(&mut a[1], &mut b[1], *psi);
162 self.dit_inplace::<true>(&mut a[2], &mut b[2], *psi);
163 self.dit_inplace::<true>(&mut a[3], &mut b[3], *psi);
164 self.dit_inplace::<true>(&mut a[4], &mut b[4], *psi);
165 self.dit_inplace::<true>(&mut a[5], &mut b[5], *psi);
166 self.dit_inplace::<true>(&mut a[6], &mut b[6], *psi);
167 self.dit_inplace::<true>(&mut a[7], &mut b[7], *psi);
168 });
169 });
170 } else {
171 izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
172 let (a, b) = a.split_at_mut(size);
173 izip!(a, b).for_each(|(a, b)| self.dit_inplace::<true>(a, b, *psi));
174 });
175 }
176 }
177 }
178
179 #[inline(always)]
180 fn dit_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
181 debug_assert!(*a < self.four_q, "a:{} q:{}", a, self.four_q);
182 debug_assert!(*b < self.four_q, "b:{} q:{}", b, self.four_q);
183 a.reduce_once_assign(self.two_q);
184 let bt: u64 = self.prime.barrett.mul_external::<NONE>(t, *b);
185 *b = *a + self.two_q - bt;
186 *a += bt;
187 if !LAZY {
188 a.reduce_once_assign(self.two_q);
189 b.reduce_once_assign(self.two_q);
190 }
191 }
192
193 pub fn backward_inplace<const LAZY: bool>(&self, a: &mut [u64]) {
194 self.backward_inplace_core::<LAZY, 0, 0>(a);
195 }
196
197 pub fn backward_inplace_core<const LAZY: bool, const SKIPSTART: u8, const SKIPEND: u8>(
198 &self,
199 a: &mut [u64],
200 ) {
201 let n: usize = a.len();
202 assert!(
203 n & n - 1 == 0,
204 "invalid x.len()= {} must be a power of two",
205 n
206 );
207 let log_n = usize::BITS - ((n as usize) - 1).leading_zeros();
208
209 let start: u32 = SKIPEND as u32;
210 let end: u32 = log_n - (SKIPSTART as u32);
211
212 for layer in (start..end).rev() {
213 let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
214 let t: usize = 2 * size;
215 if layer == 0 {
216 let n_inv: Barrett<u64> = self.prime.barrett.prepare(self.prime.inv(n as u64));
217 let psi: Barrett<u64> = self.prime.barrett.prepare(
218 self.prime
219 .barrett
220 .mul_external::<ONCE>(n_inv, self.psi_backward_rev[1].0),
221 );
222
223 izip!(a.chunks_exact_mut(2 * size)).for_each(|a| {
224 let (a, b) = a.split_at_mut(size);
225 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
226 self.dif_last_inplace::<LAZY>(&mut a[0], &mut b[0], psi, n_inv);
227 self.dif_last_inplace::<LAZY>(&mut a[1], &mut b[1], psi, n_inv);
228 self.dif_last_inplace::<LAZY>(&mut a[2], &mut b[2], psi, n_inv);
229 self.dif_last_inplace::<LAZY>(&mut a[3], &mut b[3], psi, n_inv);
230 self.dif_last_inplace::<LAZY>(&mut a[4], &mut b[4], psi, n_inv);
231 self.dif_last_inplace::<LAZY>(&mut a[5], &mut b[5], psi, n_inv);
232 self.dif_last_inplace::<LAZY>(&mut a[6], &mut b[6], psi, n_inv);
233 self.dif_last_inplace::<LAZY>(&mut a[7], &mut b[7], psi, n_inv);
234 });
235 });
236 } else if t >= 16 {
237 izip!(a.chunks_exact_mut(t), &self.psi_backward_rev[m..]).for_each(|(a, psi)| {
238 let (a, b) = a.split_at_mut(size);
239 izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
240 self.dif_inplace::<true>(&mut a[0], &mut b[0], *psi);
241 self.dif_inplace::<true>(&mut a[1], &mut b[1], *psi);
242 self.dif_inplace::<true>(&mut a[2], &mut b[2], *psi);
243 self.dif_inplace::<true>(&mut a[3], &mut b[3], *psi);
244 self.dif_inplace::<true>(&mut a[4], &mut b[4], *psi);
245 self.dif_inplace::<true>(&mut a[5], &mut b[5], *psi);
246 self.dif_inplace::<true>(&mut a[6], &mut b[6], *psi);
247 self.dif_inplace::<true>(&mut a[7], &mut b[7], *psi);
248 });
249 });
250 } else {
251 izip!(a.chunks_exact_mut(2 * size), &self.psi_backward_rev[m..]).for_each(
252 |(a, psi)| {
253 let (a, b) = a.split_at_mut(size);
254 izip!(a, b).for_each(|(a, b)| self.dif_inplace::<true>(a, b, *psi));
255 },
256 );
257 }
258 }
259 }
260
261 #[inline(always)]
262 fn dif_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
263 debug_assert!(*a < self.two_q, "a:{} q:{}", a, self.two_q);
264 debug_assert!(*b < self.two_q, "b:{} q:{}", b, self.two_q);
265 let d: u64 = self
266 .prime
267 .barrett
268 .mul_external::<NONE>(t, *a + self.two_q - *b);
269 *a = *a + *b;
270 a.reduce_once_assign(self.two_q);
271 *b = d;
272 if !LAZY {
273 a.reduce_once_assign(self.q);
274 b.reduce_once_assign(self.q);
275 }
276 }
277
278 fn dif_last_inplace<const LAZY: bool>(
279 &self,
280 a: &mut u64,
281 b: &mut u64,
282 psi: Barrett<u64>,
283 n_inv: Barrett<u64>,
284 ) {
285 debug_assert!(*a < self.two_q);
286 debug_assert!(*b < self.two_q);
287 if LAZY {
288 let d: u64 = self
289 .prime
290 .barrett
291 .mul_external::<NONE>(psi, *a + self.two_q - *b);
292 *a = self.prime.barrett.mul_external::<NONE>(n_inv, *a + *b);
293 *b = d;
294 } else {
295 let d: u64 = self
296 .prime
297 .barrett
298 .mul_external::<ONCE>(psi, *a + self.two_q - *b);
299 *a = self.prime.barrett.mul_external::<ONCE>(n_inv, *a + *b);
300 *b = d;
301 }
302 }
303}
304
305#[cfg(test)]
306mod tests {
307 use super::*;
308
309 #[test]
310 fn test_ntt() {
311 let q_base: u64 = 0x800000000004001;
312 let q_power: usize = 1;
313 let prime_instance: Prime<u64> = Prime::<u64>::new(q_base, q_power);
314 let n: u64 = 32;
315 let two_nth_root: u64 = n << 1;
316 let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, two_nth_root);
317 let mut a: Vec<u64> = vec![0; n as usize];
318 for i in 0..a.len() {
319 a[i] = i as u64;
320 }
321
322 let b: Vec<u64> = a.clone();
323 ntt_table.forward_inplace::<false>(&mut a);
324 ntt_table.backward_inplace::<false>(&mut a);
325 assert!(a == b);
326 }
327}