1 use std::ops::{Add, Sub, Mul};
2 use std::cmp::{Eq, PartialEq,min};
3 use util::{fixed_time_eq};
4 use step_by::RangeExt;
5
6 /*
7 fe means field element.
8 Here the field is \Z/(2^255-19).
9 An element t, entries t[0]...t[9], represents the integer
10 t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
11 Bounds on each t[i] vary depending on context.
12 */
13
14 #[derive(Clone, Copy)]
15 pub struct Fe(pub [i32; 10]);
16
17 impl PartialEq for Fe {
eq(&self, other: &Fe) -> bool18 fn eq(&self, other: &Fe) -> bool {
19 let &Fe(self_elems) = self;
20 let &Fe(other_elems) = other;
21 self_elems.to_vec() == other_elems.to_vec()
22 }
23 }
24 impl Eq for Fe { }
25
26 static FE_ZERO : Fe = Fe([0,0,0,0,0,0,0,0,0,0]);
27 static FE_ONE : Fe = Fe([1,0,0,0,0,0,0,0,0,0]);
28 static FE_SQRTM1 : Fe = Fe([-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482]);
29 static FE_D : Fe = Fe([-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116]);
30 static FE_D2 : Fe = Fe([-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199]);
31
32
load_4u(s: &[u8]) -> u6433 fn load_4u(s: &[u8]) -> u64 {
34 (s[0] as u64)
35 | ((s[1] as u64)<<8)
36 | ((s[2] as u64)<<16)
37 | ((s[3] as u64)<<24)
38 }
load_4i(s: &[u8]) -> i6439 fn load_4i(s: &[u8]) -> i64 {
40 load_4u(s) as i64
41 }
load_3u(s: &[u8]) -> u6442 fn load_3u(s: &[u8]) -> u64 {
43 (s[0] as u64)
44 | ((s[1] as u64)<<8)
45 | ((s[2] as u64)<<16)
46 }
load_3i(s: &[u8]) -> i6447 fn load_3i(s: &[u8]) -> i64 {
48 load_3u(s) as i64
49 }
50
51 impl Add for Fe {
52 type Output = Fe;
53
54 /*
55 h = f + g
56 Can overlap h with f or g.
57
58 Preconditions:
59 |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
60 |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
61
62 Postconditions:
63 |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
64 */
add(self, _rhs: Fe) -> Fe65 fn add(self, _rhs: Fe) -> Fe {
66 let Fe(f) = self;
67 let Fe(g) = _rhs;
68
69 let f0 = f[0];
70 let f1 = f[1];
71 let f2 = f[2];
72 let f3 = f[3];
73 let f4 = f[4];
74 let f5 = f[5];
75 let f6 = f[6];
76 let f7 = f[7];
77 let f8 = f[8];
78 let f9 = f[9];
79 let g0 = g[0];
80 let g1 = g[1];
81 let g2 = g[2];
82 let g3 = g[3];
83 let g4 = g[4];
84 let g5 = g[5];
85 let g6 = g[6];
86 let g7 = g[7];
87 let g8 = g[8];
88 let g9 = g[9];
89 let h0 = f0 + g0;
90 let h1 = f1 + g1;
91 let h2 = f2 + g2;
92 let h3 = f3 + g3;
93 let h4 = f4 + g4;
94 let h5 = f5 + g5;
95 let h6 = f6 + g6;
96 let h7 = f7 + g7;
97 let h8 = f8 + g8;
98 let h9 = f9 + g9;
99 Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
100 }
101 }
102
103 impl Sub for Fe {
104 type Output = Fe;
105
106 /*
107 h = f - g
108 Can overlap h with f or g.
109
110 Preconditions:
111 |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
112 |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
113
114 Postconditions:
115 |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
116 */
sub(self, _rhs: Fe) -> Fe117 fn sub(self, _rhs: Fe) -> Fe {
118 let Fe(f) = self;
119 let Fe(g) = _rhs;
120
121 let f0 = f[0];
122 let f1 = f[1];
123 let f2 = f[2];
124 let f3 = f[3];
125 let f4 = f[4];
126 let f5 = f[5];
127 let f6 = f[6];
128 let f7 = f[7];
129 let f8 = f[8];
130 let f9 = f[9];
131 let g0 = g[0];
132 let g1 = g[1];
133 let g2 = g[2];
134 let g3 = g[3];
135 let g4 = g[4];
136 let g5 = g[5];
137 let g6 = g[6];
138 let g7 = g[7];
139 let g8 = g[8];
140 let g9 = g[9];
141 let h0 = f0 - g0;
142 let h1 = f1 - g1;
143 let h2 = f2 - g2;
144 let h3 = f3 - g3;
145 let h4 = f4 - g4;
146 let h5 = f5 - g5;
147 let h6 = f6 - g6;
148 let h7 = f7 - g7;
149 let h8 = f8 - g8;
150 let h9 = f9 - g9;
151 Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
152 }
153 }
154
155 impl Mul for Fe {
156 type Output = Fe;
157
158 /*
159 h = f * g
160 Can overlap h with f or g.
161
162 Preconditions:
163 |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
164 |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
165
166 Postconditions:
167 |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
168 */
169
170 /*
171 Notes on implementation strategy:
172
173 Using schoolbook multiplication.
174 Karatsuba would save a little in some cost models.
175
176 Most multiplications by 2 and 19 are 32-bit precomputations;
177 cheaper than 64-bit postcomputations.
178
179 There is one remaining multiplication by 19 in the carry chain;
180 one *19 precomputation can be merged into this,
181 but the resulting data flow is considerably less clean.
182
183 There are 12 carries below.
184 10 of them are 2-way parallelizable and vectorizable.
185 Can get away with 11 carries, but then data flow is much deeper.
186
187 With tighter constraints on inputs can squeeze carries into int32.
188 */
189
mul(self, _rhs: Fe) -> Fe190 fn mul(self, _rhs: Fe) -> Fe {
191 let Fe(f) = self;
192 let Fe(g) = _rhs;
193 let f0 = f[0];
194 let f1 = f[1];
195 let f2 = f[2];
196 let f3 = f[3];
197 let f4 = f[4];
198 let f5 = f[5];
199 let f6 = f[6];
200 let f7 = f[7];
201 let f8 = f[8];
202 let f9 = f[9];
203 let g0 = g[0];
204 let g1 = g[1];
205 let g2 = g[2];
206 let g3 = g[3];
207 let g4 = g[4];
208 let g5 = g[5];
209 let g6 = g[6];
210 let g7 = g[7];
211 let g8 = g[8];
212 let g9 = g[9];
213 let g1_19 = 19 * g1; /* 1.4*2^29 */
214 let g2_19 = 19 * g2; /* 1.4*2^30; still ok */
215 let g3_19 = 19 * g3;
216 let g4_19 = 19 * g4;
217 let g5_19 = 19 * g5;
218 let g6_19 = 19 * g6;
219 let g7_19 = 19 * g7;
220 let g8_19 = 19 * g8;
221 let g9_19 = 19 * g9;
222 let f1_2 = 2 * f1;
223 let f3_2 = 2 * f3;
224 let f5_2 = 2 * f5;
225 let f7_2 = 2 * f7;
226 let f9_2 = 2 * f9;
227 let f0g0 = (f0 as i64) * (g0 as i64);
228 let f0g1 = (f0 as i64) * (g1 as i64);
229 let f0g2 = (f0 as i64) * (g2 as i64);
230 let f0g3 = (f0 as i64) * (g3 as i64);
231 let f0g4 = (f0 as i64) * (g4 as i64);
232 let f0g5 = (f0 as i64) * (g5 as i64);
233 let f0g6 = (f0 as i64) * (g6 as i64);
234 let f0g7 = (f0 as i64) * (g7 as i64);
235 let f0g8 = (f0 as i64) * (g8 as i64);
236 let f0g9 = (f0 as i64) * (g9 as i64);
237 let f1g0 = (f1 as i64) * (g0 as i64);
238 let f1g1_2 = (f1_2 as i64) * (g1 as i64);
239 let f1g2 = (f1 as i64) * (g2 as i64);
240 let f1g3_2 = (f1_2 as i64) * (g3 as i64);
241 let f1g4 = (f1 as i64) * (g4 as i64);
242 let f1g5_2 = (f1_2 as i64) * (g5 as i64);
243 let f1g6 = (f1 as i64) * (g6 as i64);
244 let f1g7_2 = (f1_2 as i64) * (g7 as i64);
245 let f1g8 = (f1 as i64) * (g8 as i64);
246 let f1g9_38 = (f1_2 as i64) * (g9_19 as i64);
247 let f2g0 = (f2 as i64) * (g0 as i64);
248 let f2g1 = (f2 as i64) * (g1 as i64);
249 let f2g2 = (f2 as i64) * (g2 as i64);
250 let f2g3 = (f2 as i64) * (g3 as i64);
251 let f2g4 = (f2 as i64) * (g4 as i64);
252 let f2g5 = (f2 as i64) * (g5 as i64);
253 let f2g6 = (f2 as i64) * (g6 as i64);
254 let f2g7 = (f2 as i64) * (g7 as i64);
255 let f2g8_19 = (f2 as i64) * (g8_19 as i64);
256 let f2g9_19 = (f2 as i64) * (g9_19 as i64);
257 let f3g0 = (f3 as i64) * (g0 as i64);
258 let f3g1_2 = (f3_2 as i64) * (g1 as i64);
259 let f3g2 = (f3 as i64) * (g2 as i64);
260 let f3g3_2 = (f3_2 as i64) * (g3 as i64);
261 let f3g4 = (f3 as i64) * (g4 as i64);
262 let f3g5_2 = (f3_2 as i64) * (g5 as i64);
263 let f3g6 = (f3 as i64) * (g6 as i64);
264 let f3g7_38 = (f3_2 as i64) * (g7_19 as i64);
265 let f3g8_19 = (f3 as i64) * (g8_19 as i64);
266 let f3g9_38 = (f3_2 as i64) * (g9_19 as i64);
267 let f4g0 = (f4 as i64) * (g0 as i64);
268 let f4g1 = (f4 as i64) * (g1 as i64);
269 let f4g2 = (f4 as i64) * (g2 as i64);
270 let f4g3 = (f4 as i64) * (g3 as i64);
271 let f4g4 = (f4 as i64) * (g4 as i64);
272 let f4g5 = (f4 as i64) * (g5 as i64);
273 let f4g6_19 = (f4 as i64) * (g6_19 as i64);
274 let f4g7_19 = (f4 as i64) * (g7_19 as i64);
275 let f4g8_19 = (f4 as i64) * (g8_19 as i64);
276 let f4g9_19 = (f4 as i64) * (g9_19 as i64);
277 let f5g0 = (f5 as i64) * (g0 as i64);
278 let f5g1_2 = (f5_2 as i64) * (g1 as i64);
279 let f5g2 = (f5 as i64) * (g2 as i64);
280 let f5g3_2 = (f5_2 as i64) * (g3 as i64);
281 let f5g4 = (f5 as i64) * (g4 as i64);
282 let f5g5_38 = (f5_2 as i64) * (g5_19 as i64);
283 let f5g6_19 = (f5 as i64) * (g6_19 as i64);
284 let f5g7_38 = (f5_2 as i64) * (g7_19 as i64);
285 let f5g8_19 = (f5 as i64) * (g8_19 as i64);
286 let f5g9_38 = (f5_2 as i64) * (g9_19 as i64);
287 let f6g0 = (f6 as i64) * (g0 as i64);
288 let f6g1 = (f6 as i64) * (g1 as i64);
289 let f6g2 = (f6 as i64) * (g2 as i64);
290 let f6g3 = (f6 as i64) * (g3 as i64);
291 let f6g4_19 = (f6 as i64) * (g4_19 as i64);
292 let f6g5_19 = (f6 as i64) * (g5_19 as i64);
293 let f6g6_19 = (f6 as i64) * (g6_19 as i64);
294 let f6g7_19 = (f6 as i64) * (g7_19 as i64);
295 let f6g8_19 = (f6 as i64) * (g8_19 as i64);
296 let f6g9_19 = (f6 as i64) * (g9_19 as i64);
297 let f7g0 = (f7 as i64) * (g0 as i64);
298 let f7g1_2 = (f7_2 as i64) * (g1 as i64);
299 let f7g2 = (f7 as i64) * (g2 as i64);
300 let f7g3_38 = (f7_2 as i64) * (g3_19 as i64);
301 let f7g4_19 = (f7 as i64) * (g4_19 as i64);
302 let f7g5_38 = (f7_2 as i64) * (g5_19 as i64);
303 let f7g6_19 = (f7 as i64) * (g6_19 as i64);
304 let f7g7_38 = (f7_2 as i64) * (g7_19 as i64);
305 let f7g8_19 = (f7 as i64) * (g8_19 as i64);
306 let f7g9_38 = (f7_2 as i64) * (g9_19 as i64);
307 let f8g0 = (f8 as i64) * (g0 as i64);
308 let f8g1 = (f8 as i64) * (g1 as i64);
309 let f8g2_19 = (f8 as i64) * (g2_19 as i64);
310 let f8g3_19 = (f8 as i64) * (g3_19 as i64);
311 let f8g4_19 = (f8 as i64) * (g4_19 as i64);
312 let f8g5_19 = (f8 as i64) * (g5_19 as i64);
313 let f8g6_19 = (f8 as i64) * (g6_19 as i64);
314 let f8g7_19 = (f8 as i64) * (g7_19 as i64);
315 let f8g8_19 = (f8 as i64) * (g8_19 as i64);
316 let f8g9_19 = (f8 as i64) * (g9_19 as i64);
317 let f9g0 = (f9 as i64) * (g0 as i64);
318 let f9g1_38 = (f9_2 as i64) * (g1_19 as i64);
319 let f9g2_19 = (f9 as i64) * (g2_19 as i64);
320 let f9g3_38 = (f9_2 as i64) * (g3_19 as i64);
321 let f9g4_19 = (f9 as i64) * (g4_19 as i64);
322 let f9g5_38 = (f9_2 as i64) * (g5_19 as i64);
323 let f9g6_19 = (f9 as i64) * (g6_19 as i64);
324 let f9g7_38 = (f9_2 as i64) * (g7_19 as i64);
325 let f9g8_19 = (f9 as i64) * (g8_19 as i64);
326 let f9g9_38 = (f9_2 as i64) * (g9_19 as i64);
327 let mut h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
328 let mut h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
329 let mut h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
330 let mut h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
331 let mut h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
332 let mut h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
333 let mut h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
334 let mut h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
335 let mut h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
336 let mut h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
337 let mut carry0;
338 let carry1;
339 let carry2;
340 let carry3;
341 let mut carry4;
342 let carry5;
343 let carry6;
344 let carry7;
345 let carry8;
346 let carry9;
347
348 /*
349 |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
350 i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
351 |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
352 i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
353 */
354
355 carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
356 carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
357 /* |h0| <= 2^25 */
358 /* |h4| <= 2^25 */
359 /* |h1| <= 1.51*2^58 */
360 /* |h5| <= 1.51*2^58 */
361
362 carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
363 carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
364 /* |h1| <= 2^24; from now on fits into int32 */
365 /* |h5| <= 2^24; from now on fits into int32 */
366 /* |h2| <= 1.21*2^59 */
367 /* |h6| <= 1.21*2^59 */
368
369 carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
370 carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
371 /* |h2| <= 2^25; from now on fits into int32 unchanged */
372 /* |h6| <= 2^25; from now on fits into int32 unchanged */
373 /* |h3| <= 1.51*2^58 */
374 /* |h7| <= 1.51*2^58 */
375
376 carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
377 carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
378 /* |h3| <= 2^24; from now on fits into int32 unchanged */
379 /* |h7| <= 2^24; from now on fits into int32 unchanged */
380 /* |h4| <= 1.52*2^33 */
381 /* |h8| <= 1.52*2^33 */
382
383 carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
384 carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
385 /* |h4| <= 2^25; from now on fits into int32 unchanged */
386 /* |h8| <= 2^25; from now on fits into int32 unchanged */
387 /* |h5| <= 1.01*2^24 */
388 /* |h9| <= 1.51*2^58 */
389
390 carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
391 /* |h9| <= 2^24; from now on fits into int32 unchanged */
392 /* |h0| <= 1.8*2^37 */
393
394 carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
395 /* |h0| <= 2^25; from now on fits into int32 unchanged */
396 /* |h1| <= 1.01*2^24 */
397
398 Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
399 h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
400 }
401 }
402
403 impl Fe {
from_bytes(s: &[u8]) -> Fe404 pub fn from_bytes(s: &[u8]) -> Fe {
405 let mut h0 = load_4i(&s[0..4]);
406 let mut h1 = load_3i(&s[4..7]) << 6;
407 let mut h2 = load_3i(&s[7..10]) << 5;
408 let mut h3 = load_3i(&s[10..13]) << 3;
409 let mut h4 = load_3i(&s[13..16]) << 2;
410 let mut h5 = load_4i(&s[16..20]);
411 let mut h6 = load_3i(&s[20..23]) << 7;
412 let mut h7 = load_3i(&s[23..26]) << 5;
413 let mut h8 = load_3i(&s[26..29]) << 4;
414 let mut h9 = (load_3i(&s[29..32]) & 8388607) << 2;
415
416 let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
417 let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
418 let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
419 let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
420 let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
421
422 let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
423 let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
424 let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
425 let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
426 let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
427
428 Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
429 h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
430 }
431
432 /*
433 Preconditions:
434 |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
435
436 Write p=2^255-19; q=floor(h/p).
437 Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
438
439 Proof:
440 Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
441 Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
442
443 Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
444 Then 0<y<1.
445
446 Write r=h-pq.
447 Have 0<=r<=p-1=2^255-20.
448 Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
449
450 Write x=r+19(2^-255)r+y.
451 Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
452
453 Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
454 so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
455 */
456
to_bytes(&self) -> [u8; 32]457 pub fn to_bytes(&self) -> [u8; 32] {
458 let &Fe(es) = self;
459 let mut h0 = es[0];
460 let mut h1 = es[1];
461 let mut h2 = es[2];
462 let mut h3 = es[3];
463 let mut h4 = es[4];
464 let mut h5 = es[5];
465 let mut h6 = es[6];
466 let mut h7 = es[7];
467 let mut h8 = es[8];
468 let mut h9 = es[9];
469 let mut q;
470
471 q = (19 * h9 + (1 << 24)) >> 25;
472 q = (h0 + q) >> 26;
473 q = (h1 + q) >> 25;
474 q = (h2 + q) >> 26;
475 q = (h3 + q) >> 25;
476 q = (h4 + q) >> 26;
477 q = (h5 + q) >> 25;
478 q = (h6 + q) >> 26;
479 q = (h7 + q) >> 25;
480 q = (h8 + q) >> 26;
481 q = (h9 + q) >> 25;
482
483 /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
484 h0 += 19 * q;
485 /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
486
487 let carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
488 let carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
489 let carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
490 let carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
491 let carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
492 let carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
493 let carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
494 let carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
495 let carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
496 let carry9 = h9 >> 25; h9 -= carry9 << 25;
497 /* h10 = carry9 */
498
499 /*
500 Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
501 Have h0+...+2^230 h9 between 0 and 2^255-1;
502 evidently 2^255 h10-2^255 q = 0.
503 Goal: Output h0+...+2^230 h9.
504 */
505 [
506 (h0 >> 0) as u8,
507 (h0 >> 8) as u8,
508 (h0 >> 16) as u8,
509 ((h0 >> 24) | (h1 << 2)) as u8,
510 (h1 >> 6) as u8,
511 (h1 >> 14) as u8,
512 ((h1 >> 22) | (h2 << 3)) as u8,
513 (h2 >> 5) as u8,
514 (h2 >> 13) as u8,
515 ((h2 >> 21) | (h3 << 5)) as u8,
516 (h3 >> 3) as u8,
517 (h3 >> 11) as u8,
518 ((h3 >> 19) | (h4 << 6)) as u8,
519 (h4 >> 2) as u8,
520 (h4 >> 10) as u8,
521 (h4 >> 18) as u8,
522 (h5 >> 0) as u8,
523 (h5 >> 8) as u8,
524 (h5 >> 16) as u8,
525 ((h5 >> 24) | (h6 << 1)) as u8,
526 (h6 >> 7) as u8,
527 (h6 >> 15) as u8,
528 ((h6 >> 23) | (h7 << 3)) as u8,
529 (h7 >> 5) as u8,
530 (h7 >> 13) as u8,
531 ((h7 >> 21) | (h8 << 4)) as u8,
532 (h8 >> 4) as u8,
533 (h8 >> 12) as u8,
534 ((h8 >> 20) | (h9 << 6)) as u8,
535 (h9 >> 2) as u8,
536 (h9 >> 10) as u8,
537 (h9 >> 18) as u8,
538 ]
539 }
540
maybe_swap_with(&mut self, other: &mut Fe, do_swap: i32)541 pub fn maybe_swap_with(&mut self, other: &mut Fe, do_swap: i32) {
542 let &mut Fe(f) = self;
543 let &mut Fe(g) = other;
544 let f0 = f[0];
545 let f1 = f[1];
546 let f2 = f[2];
547 let f3 = f[3];
548 let f4 = f[4];
549 let f5 = f[5];
550 let f6 = f[6];
551 let f7 = f[7];
552 let f8 = f[8];
553 let f9 = f[9];
554 let g0 = g[0];
555 let g1 = g[1];
556 let g2 = g[2];
557 let g3 = g[3];
558 let g4 = g[4];
559 let g5 = g[5];
560 let g6 = g[6];
561 let g7 = g[7];
562 let g8 = g[8];
563 let g9 = g[9];
564 let mut x0 = f0 ^ g0;
565 let mut x1 = f1 ^ g1;
566 let mut x2 = f2 ^ g2;
567 let mut x3 = f3 ^ g3;
568 let mut x4 = f4 ^ g4;
569 let mut x5 = f5 ^ g5;
570 let mut x6 = f6 ^ g6;
571 let mut x7 = f7 ^ g7;
572 let mut x8 = f8 ^ g8;
573 let mut x9 = f9 ^ g9;
574 let b = -do_swap;
575 x0 &= b;
576 x1 &= b;
577 x2 &= b;
578 x3 &= b;
579 x4 &= b;
580 x5 &= b;
581 x6 &= b;
582 x7 &= b;
583 x8 &= b;
584 x9 &= b;
585 *self = Fe([f0^x0, f1^x1, f2^x2, f3^x3, f4^x4,
586 f5^x5, f6^x6, f7^x7, f8^x8, f9^x9]);
587 *other = Fe([g0^x0, g1^x1, g2^x2, g3^x3, g4^x4,
588 g5^x5, g6^x6, g7^x7, g8^x8, g9^x9]);
589 }
590
maybe_set(&mut self, other: &Fe, do_swap: i32)591 pub fn maybe_set(&mut self, other: &Fe, do_swap: i32) {
592 let &mut Fe(f) = self;
593 let &Fe(g) = other;
594 let f0 = f[0];
595 let f1 = f[1];
596 let f2 = f[2];
597 let f3 = f[3];
598 let f4 = f[4];
599 let f5 = f[5];
600 let f6 = f[6];
601 let f7 = f[7];
602 let f8 = f[8];
603 let f9 = f[9];
604 let g0 = g[0];
605 let g1 = g[1];
606 let g2 = g[2];
607 let g3 = g[3];
608 let g4 = g[4];
609 let g5 = g[5];
610 let g6 = g[6];
611 let g7 = g[7];
612 let g8 = g[8];
613 let g9 = g[9];
614 let mut x0 = f0 ^ g0;
615 let mut x1 = f1 ^ g1;
616 let mut x2 = f2 ^ g2;
617 let mut x3 = f3 ^ g3;
618 let mut x4 = f4 ^ g4;
619 let mut x5 = f5 ^ g5;
620 let mut x6 = f6 ^ g6;
621 let mut x7 = f7 ^ g7;
622 let mut x8 = f8 ^ g8;
623 let mut x9 = f9 ^ g9;
624 let b = -do_swap;
625 x0 &= b;
626 x1 &= b;
627 x2 &= b;
628 x3 &= b;
629 x4 &= b;
630 x5 &= b;
631 x6 &= b;
632 x7 &= b;
633 x8 &= b;
634 x9 &= b;
635 *self = Fe([f0^x0, f1^x1, f2^x2, f3^x3, f4^x4,
636 f5^x5, f6^x6, f7^x7, f8^x8, f9^x9]);
637 }
638
639 /*
640 h = f * 121666
641 Can overlap h with f.
642
643 Preconditions:
644 |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
645
646 Postconditions:
647 |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
648 */
649
mul_121666(&self) -> Fe650 fn mul_121666(&self) -> Fe {
651 let &Fe(f) = self;
652
653 let mut h0 = (f[0] as i64) * 121666;
654 let mut h1 = (f[1] as i64) * 121666;
655 let mut h2 = (f[2] as i64) * 121666;
656 let mut h3 = (f[3] as i64) * 121666;
657 let mut h4 = (f[4] as i64) * 121666;
658 let mut h5 = (f[5] as i64) * 121666;
659 let mut h6 = (f[6] as i64) * 121666;
660 let mut h7 = (f[7] as i64) * 121666;
661 let mut h8 = (f[8] as i64) * 121666;
662 let mut h9 = (f[9] as i64) * 121666;
663
664 let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
665 let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
666 let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
667 let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
668 let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
669
670 let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
671 let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
672 let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
673 let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
674 let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
675
676 Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
677 h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
678 }
679
680
681 /*
682 h = f * f
683 Can overlap h with f.
684
685 Preconditions:
686 |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
687
688 Postconditions:
689 |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
690 */
691
692 /*
693 See fe_mul.c for discussion of implementation strategy.
694 */
square(&self) -> Fe695 fn square(&self) -> Fe {
696 let &Fe(f) = self;
697
698 let f0 = f[0];
699 let f1 = f[1];
700 let f2 = f[2];
701 let f3 = f[3];
702 let f4 = f[4];
703 let f5 = f[5];
704 let f6 = f[6];
705 let f7 = f[7];
706 let f8 = f[8];
707 let f9 = f[9];
708 let f0_2 = 2 * f0;
709 let f1_2 = 2 * f1;
710 let f2_2 = 2 * f2;
711 let f3_2 = 2 * f3;
712 let f4_2 = 2 * f4;
713 let f5_2 = 2 * f5;
714 let f6_2 = 2 * f6;
715 let f7_2 = 2 * f7;
716 let f5_38 = 38 * f5; /* 1.31*2^30 */
717 let f6_19 = 19 * f6; /* 1.31*2^30 */
718 let f7_38 = 38 * f7; /* 1.31*2^30 */
719 let f8_19 = 19 * f8; /* 1.31*2^30 */
720 let f9_38 = 38 * f9; /* 1.31*2^30 */
721 let f0f0 = (f0 as i64) * (f0 as i64);
722 let f0f1_2 = (f0_2 as i64) * (f1 as i64);
723 let f0f2_2 = (f0_2 as i64) * (f2 as i64);
724 let f0f3_2 = (f0_2 as i64) * (f3 as i64);
725 let f0f4_2 = (f0_2 as i64) * (f4 as i64);
726 let f0f5_2 = (f0_2 as i64) * (f5 as i64);
727 let f0f6_2 = (f0_2 as i64) * (f6 as i64);
728 let f0f7_2 = (f0_2 as i64) * (f7 as i64);
729 let f0f8_2 = (f0_2 as i64) * (f8 as i64);
730 let f0f9_2 = (f0_2 as i64) * (f9 as i64);
731 let f1f1_2 = (f1_2 as i64) * (f1 as i64);
732 let f1f2_2 = (f1_2 as i64) * (f2 as i64);
733 let f1f3_4 = (f1_2 as i64) * (f3_2 as i64);
734 let f1f4_2 = (f1_2 as i64) * (f4 as i64);
735 let f1f5_4 = (f1_2 as i64) * (f5_2 as i64);
736 let f1f6_2 = (f1_2 as i64) * (f6 as i64);
737 let f1f7_4 = (f1_2 as i64) * (f7_2 as i64);
738 let f1f8_2 = (f1_2 as i64) * (f8 as i64);
739 let f1f9_76 = (f1_2 as i64) * (f9_38 as i64);
740 let f2f2 = (f2 as i64) * (f2 as i64);
741 let f2f3_2 = (f2_2 as i64) * (f3 as i64);
742 let f2f4_2 = (f2_2 as i64) * (f4 as i64);
743 let f2f5_2 = (f2_2 as i64) * (f5 as i64);
744 let f2f6_2 = (f2_2 as i64) * (f6 as i64);
745 let f2f7_2 = (f2_2 as i64) * (f7 as i64);
746 let f2f8_38 = (f2_2 as i64) * (f8_19 as i64);
747 let f2f9_38 = (f2 as i64) * (f9_38 as i64);
748 let f3f3_2 = (f3_2 as i64) * (f3 as i64);
749 let f3f4_2 = (f3_2 as i64) * (f4 as i64);
750 let f3f5_4 = (f3_2 as i64) * (f5_2 as i64);
751 let f3f6_2 = (f3_2 as i64) * (f6 as i64);
752 let f3f7_76 = (f3_2 as i64) * (f7_38 as i64);
753 let f3f8_38 = (f3_2 as i64) * (f8_19 as i64);
754 let f3f9_76 = (f3_2 as i64) * (f9_38 as i64);
755 let f4f4 = (f4 as i64) * (f4 as i64);
756 let f4f5_2 = (f4_2 as i64) * (f5 as i64);
757 let f4f6_38 = (f4_2 as i64) * (f6_19 as i64);
758 let f4f7_38 = (f4 as i64) * (f7_38 as i64);
759 let f4f8_38 = (f4_2 as i64) * (f8_19 as i64);
760 let f4f9_38 = (f4 as i64) * (f9_38 as i64);
761 let f5f5_38 = (f5 as i64) * (f5_38 as i64);
762 let f5f6_38 = (f5_2 as i64) * (f6_19 as i64);
763 let f5f7_76 = (f5_2 as i64) * (f7_38 as i64);
764 let f5f8_38 = (f5_2 as i64) * (f8_19 as i64);
765 let f5f9_76 = (f5_2 as i64) * (f9_38 as i64);
766 let f6f6_19 = (f6 as i64) * (f6_19 as i64);
767 let f6f7_38 = (f6 as i64) * (f7_38 as i64);
768 let f6f8_38 = (f6_2 as i64) * (f8_19 as i64);
769 let f6f9_38 = (f6 as i64) * (f9_38 as i64);
770 let f7f7_38 = (f7 as i64) * (f7_38 as i64);
771 let f7f8_38 = (f7_2 as i64) * (f8_19 as i64);
772 let f7f9_76 = (f7_2 as i64) * (f9_38 as i64);
773 let f8f8_19 = (f8 as i64) * (f8_19 as i64);
774 let f8f9_38 = (f8 as i64) * (f9_38 as i64);
775 let f9f9_38 = (f9 as i64) * (f9_38 as i64);
776 let mut h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
777 let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
778 let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
779 let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
780 let mut h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
781 let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
782 let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
783 let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
784 let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
785 let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
786
787 let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
788 let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
789
790 let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
791 let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
792
793 let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
794 let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
795
796 let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
797 let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
798
799 let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
800 let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
801
802 let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
803
804 let carrya = (h0 + (1<<25)) >> 26; h1 += carrya; h0 -= carrya << 26;
805
806 Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
807 h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
808 }
809
square_and_double(&self) -> Fe810 fn square_and_double(&self) -> Fe {
811 let &Fe(f) = self;
812
813 let f0 = f[0];
814 let f1 = f[1];
815 let f2 = f[2];
816 let f3 = f[3];
817 let f4 = f[4];
818 let f5 = f[5];
819 let f6 = f[6];
820 let f7 = f[7];
821 let f8 = f[8];
822 let f9 = f[9];
823 let f0_2 = 2 * f0;
824 let f1_2 = 2 * f1;
825 let f2_2 = 2 * f2;
826 let f3_2 = 2 * f3;
827 let f4_2 = 2 * f4;
828 let f5_2 = 2 * f5;
829 let f6_2 = 2 * f6;
830 let f7_2 = 2 * f7;
831 let f5_38 = 38 * f5; /* 1.959375*2^30 */
832 let f6_19 = 19 * f6; /* 1.959375*2^30 */
833 let f7_38 = 38 * f7; /* 1.959375*2^30 */
834 let f8_19 = 19 * f8; /* 1.959375*2^30 */
835 let f9_38 = 38 * f9; /* 1.959375*2^30 */
836 let f0f0 = (f0 as i64) * (f0 as i64);
837 let f0f1_2 = (f0_2 as i64) * (f1 as i64);
838 let f0f2_2 = (f0_2 as i64) * (f2 as i64);
839 let f0f3_2 = (f0_2 as i64) * (f3 as i64);
840 let f0f4_2 = (f0_2 as i64) * (f4 as i64);
841 let f0f5_2 = (f0_2 as i64) * (f5 as i64);
842 let f0f6_2 = (f0_2 as i64) * (f6 as i64);
843 let f0f7_2 = (f0_2 as i64) * (f7 as i64);
844 let f0f8_2 = (f0_2 as i64) * (f8 as i64);
845 let f0f9_2 = (f0_2 as i64) * (f9 as i64);
846 let f1f1_2 = (f1_2 as i64) * (f1 as i64);
847 let f1f2_2 = (f1_2 as i64) * (f2 as i64);
848 let f1f3_4 = (f1_2 as i64) * (f3_2 as i64);
849 let f1f4_2 = (f1_2 as i64) * (f4 as i64);
850 let f1f5_4 = (f1_2 as i64) * (f5_2 as i64);
851 let f1f6_2 = (f1_2 as i64) * (f6 as i64);
852 let f1f7_4 = (f1_2 as i64) * (f7_2 as i64);
853 let f1f8_2 = (f1_2 as i64) * (f8 as i64);
854 let f1f9_76 = (f1_2 as i64) * (f9_38 as i64);
855 let f2f2 = (f2 as i64) * (f2 as i64);
856 let f2f3_2 = (f2_2 as i64) * (f3 as i64);
857 let f2f4_2 = (f2_2 as i64) * (f4 as i64);
858 let f2f5_2 = (f2_2 as i64) * (f5 as i64);
859 let f2f6_2 = (f2_2 as i64) * (f6 as i64);
860 let f2f7_2 = (f2_2 as i64) * (f7 as i64);
861 let f2f8_38 = (f2_2 as i64) * (f8_19 as i64);
862 let f2f9_38 = (f2 as i64) * (f9_38 as i64);
863 let f3f3_2 = (f3_2 as i64) * (f3 as i64);
864 let f3f4_2 = (f3_2 as i64) * (f4 as i64);
865 let f3f5_4 = (f3_2 as i64) * (f5_2 as i64);
866 let f3f6_2 = (f3_2 as i64) * (f6 as i64);
867 let f3f7_76 = (f3_2 as i64) * (f7_38 as i64);
868 let f3f8_38 = (f3_2 as i64) * (f8_19 as i64);
869 let f3f9_76 = (f3_2 as i64) * (f9_38 as i64);
870 let f4f4 = (f4 as i64) * (f4 as i64);
871 let f4f5_2 = (f4_2 as i64) * (f5 as i64);
872 let f4f6_38 = (f4_2 as i64) * (f6_19 as i64);
873 let f4f7_38 = (f4 as i64) * (f7_38 as i64);
874 let f4f8_38 = (f4_2 as i64) * (f8_19 as i64);
875 let f4f9_38 = (f4 as i64) * (f9_38 as i64);
876 let f5f5_38 = (f5 as i64) * (f5_38 as i64);
877 let f5f6_38 = (f5_2 as i64) * (f6_19 as i64);
878 let f5f7_76 = (f5_2 as i64) * (f7_38 as i64);
879 let f5f8_38 = (f5_2 as i64) * (f8_19 as i64);
880 let f5f9_76 = (f5_2 as i64) * (f9_38 as i64);
881 let f6f6_19 = (f6 as i64) * (f6_19 as i64);
882 let f6f7_38 = (f6 as i64) * (f7_38 as i64);
883 let f6f8_38 = (f6_2 as i64) * (f8_19 as i64);
884 let f6f9_38 = (f6 as i64) * (f9_38 as i64);
885 let f7f7_38 = (f7 as i64) * (f7_38 as i64);
886 let f7f8_38 = (f7_2 as i64) * (f8_19 as i64);
887 let f7f9_76 = (f7_2 as i64) * (f9_38 as i64);
888 let f8f8_19 = (f8 as i64) * (f8_19 as i64);
889 let f8f9_38 = (f8 as i64) * (f9_38 as i64);
890 let f9f9_38 = (f9 as i64) * (f9_38 as i64);
891 let mut h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
892 let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
893 let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
894 let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
895 let mut h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
896 let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
897 let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
898 let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
899 let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
900 let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
901 let mut carry0: i64;
902 let carry1: i64;
903 let carry2: i64;
904 let carry3: i64;
905 let mut carry4: i64;
906 let carry5: i64;
907 let carry6: i64;
908 let carry7: i64;
909 let carry8: i64;
910 let carry9: i64;
911
912 h0 += h0;
913 h1 += h1;
914 h2 += h2;
915 h3 += h3;
916 h4 += h4;
917 h5 += h5;
918 h6 += h6;
919 h7 += h7;
920 h8 += h8;
921 h9 += h9;
922
923 carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
924 carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
925
926 carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
927 carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
928
929 carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
930 carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
931
932 carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
933 carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
934
935 carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
936 carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
937
938 carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
939
940 carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
941
942 Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
943 h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
944 }
945
invert(&self) -> Fe946 pub fn invert(&self) -> Fe {
947 let z1 = *self;
948
949 /* qhasm: z2 = z1^2^1 */
950 let z2 = z1.square();
951 /* qhasm: z8 = z2^2^2 */
952 let z8 = z2.square().square();
953 /* qhasm: z9 = z1*z8 */
954 let z9 = z1*z8;
955
956 /* qhasm: z11 = z2*z9 */
957 let z11 = z2*z9;
958
959 /* qhasm: z22 = z11^2^1 */
960 let z22 = z11.square();
961
962 /* qhasm: z_5_0 = z9*z22 */
963 let z_5_0 = z9*z22;
964
965 /* qhasm: z_10_5 = z_5_0^2^5 */
966 let z_10_5 = (0..5).fold(z_5_0, |z_5_n, _| z_5_n.square());
967
968 /* qhasm: z_10_0 = z_10_5*z_5_0 */
969 let z_10_0 = z_10_5*z_5_0;
970
971 /* qhasm: z_20_10 = z_10_0^2^10 */
972 let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square());
973
974 /* qhasm: z_20_0 = z_20_10*z_10_0 */
975 let z_20_0 = z_20_10*z_10_0;
976
977 /* qhasm: z_40_20 = z_20_0^2^20 */
978 let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square());
979
980 /* qhasm: z_40_0 = z_40_20*z_20_0 */
981 let z_40_0 = z_40_20*z_20_0;
982
983 /* qhasm: z_50_10 = z_40_0^2^10 */
984 let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());
985
986 /* qhasm: z_50_0 = z_50_10*z_10_0 */
987 let z_50_0 = z_50_10*z_10_0;
988
989 /* qhasm: z_100_50 = z_50_0^2^50 */
990 let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square());
991
992 /* qhasm: z_100_0 = z_100_50*z_50_0 */
993 let z_100_0 = z_100_50*z_50_0;
994
995 /* qhasm: z_200_100 = z_100_0^2^100 */
996 let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square());
997
998 /* qhasm: z_200_0 = z_200_100*z_100_0 */
999 /* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
1000 /* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
1001 let z_200_0 = z_200_100*z_100_0;
1002
1003 /* qhasm: z_250_50 = z_200_0^2^50 */
1004 let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());
1005
1006 /* qhasm: z_250_0 = z_250_50*z_50_0 */
1007 let z_250_0 = z_250_50*z_50_0;
1008
1009 /* qhasm: z_255_5 = z_250_0^2^5 */
1010 let z_255_5 = (0..5).fold(z_250_0, |x, _| x.square());
1011
1012 /* qhasm: z_255_21 = z_255_5*z11 */
1013 /* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
1014 /* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
1015 let z_255_21 = z_255_5*z11;
1016
1017 z_255_21
1018 }
1019
1020
is_nonzero(&self) -> bool1021 fn is_nonzero(&self) -> bool {
1022 let bs = self.to_bytes();
1023 let zero = [0; 32];
1024 !fixed_time_eq(bs.as_ref(), zero.as_ref())
1025 }
1026
is_negative(&self) -> bool1027 fn is_negative(&self) -> bool {
1028 (self.to_bytes()[0] & 1) != 0
1029 }
1030
neg(&self) -> Fe1031 fn neg(&self) -> Fe {
1032 let &Fe(f) = self;
1033 Fe([-f[0], -f[1], -f[2], -f[3], -f[4],
1034 -f[5], -f[6], -f[7], -f[8], -f[9]])
1035 }
1036
pow25523(&self) -> Fe1037 fn pow25523(&self) -> Fe {
1038 let z2 = self.square();
1039 let z8 = (0..2).fold(z2, |x, _| x.square());
1040 let z9 = *self * z8;
1041 let z11 = z2 * z9;
1042 let z22 = z11.square();
1043 let z_5_0 = z9 * z22;
1044 let z_10_5 = (0..5).fold(z_5_0, |x, _| x.square());
1045 let z_10_0 = z_10_5 * z_5_0;
1046 let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square());
1047 let z_20_0 = z_20_10 * z_10_0;
1048 let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square());
1049 let z_40_0 = z_40_20 * z_20_0;
1050 let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());
1051 let z_50_0 = z_50_10 * z_10_0;
1052 let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square());
1053 let z_100_0 = z_100_50 * z_50_0;
1054 let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square());
1055 let z_200_0 = z_200_100 * z_100_0;
1056 let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());
1057 let z_250_0 = z_250_50 * z_50_0;
1058 let z_252_2 = (0..2).fold(z_250_0, |x, _| x.square());
1059 let z_252_3 = z_252_2 * *self;
1060
1061 z_252_3
1062 }
1063 }
1064
1065 #[derive(Clone, Copy)]
1066 pub struct GeP2 {
1067 x: Fe,
1068 y: Fe,
1069 z: Fe,
1070 }
1071
1072 #[derive(Clone, Copy)]
1073 pub struct GeP3 {
1074 x: Fe,
1075 y: Fe,
1076 z: Fe,
1077 t: Fe,
1078 }
1079
1080 #[derive(Clone, Copy)]
1081 pub struct GeP1P1 {
1082 x: Fe,
1083 y: Fe,
1084 z: Fe,
1085 t: Fe,
1086 }
1087
1088 #[derive(Clone, Copy)]
1089 pub struct GePrecomp {
1090 y_plus_x: Fe,
1091 y_minus_x: Fe,
1092 xy2d: Fe,
1093 }
1094
1095 #[derive(Clone, Copy)]
1096 pub struct GeCached {
1097 y_plus_x: Fe,
1098 y_minus_x: Fe,
1099 z: Fe,
1100 t2d: Fe,
1101 }
1102
1103 impl GeP1P1 {
to_p2(&self) -> GeP21104 fn to_p2(&self) -> GeP2 {
1105 GeP2 {
1106 x: self.x * self.t,
1107 y: self.y * self.z,
1108 z: self.z * self.t,
1109 }
1110 }
1111
1112
to_p3(&self) -> GeP31113 fn to_p3(&self) -> GeP3 {
1114 GeP3 {
1115 x: self.x * self.t,
1116 y: self.y * self.z,
1117 z: self.z * self.t,
1118 t: self.x * self.y,
1119 }
1120 }
1121
1122 }
1123
1124 impl GeP2 {
zero() -> GeP21125 fn zero() -> GeP2 {
1126 GeP2 {
1127 x: FE_ZERO,
1128 y: FE_ONE,
1129 z: FE_ONE,
1130 }
1131 }
1132
to_bytes(&self) -> [u8; 32]1133 pub fn to_bytes(&self) -> [u8; 32] {
1134 let recip = self.z.invert();
1135 let x = self.x * recip;
1136 let y = self.y * recip;
1137 let mut bs = y.to_bytes();
1138 bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
1139 bs
1140 }
1141
dbl(&self) -> GeP1P11142 fn dbl(&self) -> GeP1P1 {
1143 let xx = self.x.square();
1144 let yy = self.y.square();
1145 let b = self.z.square_and_double();
1146 let a = self.x + self.y;
1147 let aa = a.square();
1148 let y3 = yy + xx;
1149 let z3 = yy - xx;
1150 let x3 = aa - y3;
1151 let t3 = b - z3;
1152
1153 GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
1154 }
1155
slide(a: &[u8]) -> [i8; 256]1156 fn slide(a: &[u8]) -> [i8; 256] {
1157 let mut r = [0i8; 256];
1158 for i in 0..256 {
1159 r[i] = (1 & (a[i >> 3] >> (i & 7))) as i8;
1160 }
1161 for i in 0..256 {
1162 if r[i]!=0 {
1163 for b in 1..min(7, 256-i) {
1164 if r[i + b] != 0 {
1165 if r[i] + (r[i + b] << b) <= 15 {
1166 r[i] += r[i + b] << b; r[i + b] = 0;
1167 } else if r[i] - (r[i + b] << b) >= -15 {
1168 r[i] -= r[i + b] << b;
1169 for k in i+b..256 {
1170 if r[k]==0 {
1171 r[k] = 1;
1172 break;
1173 }
1174 r[k] = 0;
1175 }
1176 } else {
1177 break;
1178 }
1179 }
1180 }
1181 }
1182 }
1183
1184 r
1185 }
1186
1187 /*
1188 r = a * A + b * B
1189 where a = a[0]+256*a[1]+...+256^31 a[31].
1190 and b = b[0]+256*b[1]+...+256^31 b[31].
1191 B is the Ed25519 base point (x,4/5) with x positive.
1192 */
double_scalarmult_vartime(a_scalar: &[u8], a_point: GeP3, b_scalar: &[u8]) -> GeP21193 pub fn double_scalarmult_vartime(a_scalar: &[u8], a_point: GeP3, b_scalar: &[u8]) -> GeP2 {
1194 let aslide = GeP2::slide(a_scalar);
1195 let bslide = GeP2::slide(b_scalar);
1196
1197 let mut ai = [GeCached{y_plus_x:FE_ZERO, y_minus_x: FE_ZERO, z: FE_ZERO, t2d: FE_ZERO}; 8]; /* A,3A,5A,7A,9A,11A,13A,15A */
1198 ai[0] = a_point.to_cached();
1199 let a2 = a_point.dbl().to_p3();
1200 ai[1] = (a2 + ai[0]).to_p3().to_cached();
1201 ai[2] = (a2 + ai[1]).to_p3().to_cached();
1202 ai[3] = (a2 + ai[2]).to_p3().to_cached();
1203 ai[4] = (a2 + ai[3]).to_p3().to_cached();
1204 ai[5] = (a2 + ai[4]).to_p3().to_cached();
1205 ai[6] = (a2 + ai[5]).to_p3().to_cached();
1206 ai[7] = (a2 + ai[6]).to_p3().to_cached();
1207
1208 let mut r = GeP2::zero();
1209
1210 let mut i: usize = 255;
1211 loop {
1212 if aslide[i]!=0 || bslide[i]!=0 {
1213 break;
1214 }
1215 if i==0 {
1216 return r;
1217 }
1218 i -= 1;
1219 }
1220
1221 loop {
1222 let mut t = r.dbl();
1223 if aslide[i] > 0 {
1224 t = t.to_p3() + ai[(aslide[i]/2) as usize];
1225 } else if aslide[i] < 0 {
1226 t = t.to_p3() - ai[(-aslide[i]/2) as usize];
1227 }
1228
1229 if bslide[i] > 0 {
1230 t = t.to_p3() + BI[(bslide[i]/2) as usize];
1231 } else if bslide[i] < 0 {
1232 t = t.to_p3() - BI[(-bslide[i]/2) as usize];
1233 }
1234
1235 r = t.to_p2();
1236
1237 if i==0 {
1238 return r;
1239 }
1240 i -= 1;
1241 }
1242 }
1243
1244 }
1245
1246 impl GeP3 {
from_bytes_negate_vartime(s: &[u8]) -> Option<GeP3>1247 pub fn from_bytes_negate_vartime(s: &[u8]) -> Option<GeP3> {
1248 let y = Fe::from_bytes(s);
1249 let z = FE_ONE;
1250 let y_squared = y.square();
1251 let u = y_squared - FE_ONE;
1252 let v = (y_squared * FE_D) + FE_ONE;
1253 let v_raise_3 = v.square() * v;
1254 let v_raise_7 = v_raise_3.square() * v;
1255 let uv7 = v_raise_7 * u;// Is this commutative? u comes second in the code, but not in the notation...
1256
1257 let mut x = uv7.pow25523() * v_raise_3 * u;
1258
1259 let vxx = x.square() * v;
1260 let check = vxx - u;
1261 if check.is_nonzero() {
1262 let check2 = vxx + u;
1263 if check2.is_nonzero() {
1264 return None;
1265 }
1266 x = x * FE_SQRTM1;
1267 }
1268
1269 if x.is_negative() == ((s[31]>>7)!=0) {
1270 x = x.neg();
1271 }
1272
1273 let t = x * y;
1274
1275 Some(GeP3{x: x, y: y, z: z, t: t})
1276 }
1277
to_p2(&self) -> GeP21278 fn to_p2(&self) -> GeP2 {
1279 GeP2 {
1280 x: self.x,
1281 y: self.y,
1282 z: self.z,
1283 }
1284 }
1285
to_cached(&self) -> GeCached1286 fn to_cached(&self) -> GeCached {
1287 GeCached {
1288 y_plus_x: self.y + self.x,
1289 y_minus_x: self.y - self.x,
1290 z: self.z,
1291 t2d: self.t * FE_D2
1292 }
1293 }
1294
zero() -> GeP31295 fn zero() -> GeP3 {
1296 GeP3 {
1297 x: FE_ZERO,
1298 y: FE_ONE,
1299 z: FE_ONE,
1300 t: FE_ZERO,
1301 }
1302 }
1303
dbl(&self) -> GeP1P11304 fn dbl(&self) -> GeP1P1 {
1305 self.to_p2().dbl()
1306 }
1307
to_bytes(&self) -> [u8; 32]1308 pub fn to_bytes(&self) -> [u8; 32] {
1309 let recip = self.z.invert();
1310 let x = self.x * recip;
1311 let y = self.y * recip;
1312 let mut bs = y.to_bytes();
1313 bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
1314 bs
1315 }
1316
1317
1318 }
1319
1320 impl Add<GeCached> for GeP3 {
1321 type Output = GeP1P1;
1322
add(self, _rhs: GeCached) -> GeP1P11323 fn add(self, _rhs: GeCached) -> GeP1P1 {
1324 let y1_plus_x1 = self.y + self.x;
1325 let y1_minus_x1 = self.y - self.x;
1326 let a = y1_plus_x1 * _rhs.y_plus_x;
1327 let b = y1_minus_x1 * _rhs.y_minus_x;
1328 let c = _rhs.t2d * self.t;
1329 let zz = self.z * _rhs.z;
1330 let d = zz + zz;
1331 let x3 = a - b;
1332 let y3 = a + b;
1333 let z3 = d + c;
1334 let t3 = d - c;
1335
1336 GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
1337 }
1338 }
1339
1340 impl Add<GePrecomp> for GeP3 {
1341 type Output = GeP1P1;
1342
add(self, _rhs: GePrecomp) -> GeP1P11343 fn add(self, _rhs: GePrecomp) -> GeP1P1 {
1344 let y1_plus_x1 = self.y + self.x;
1345 let y1_minus_x1 = self.y - self.x;
1346 let a = y1_plus_x1 * _rhs.y_plus_x;
1347 let b = y1_minus_x1 * _rhs.y_minus_x;
1348 let c = _rhs.xy2d * self.t;
1349 let d = self.z + self.z;
1350 let x3 = a - b;
1351 let y3 = a + b;
1352 let z3 = d + c;
1353 let t3 = d - c;
1354
1355 GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
1356 }
1357 }
1358
1359 impl Sub<GeCached> for GeP3 {
1360 type Output = GeP1P1;
1361
sub(self, _rhs: GeCached) -> GeP1P11362 fn sub(self, _rhs: GeCached) -> GeP1P1 {
1363 let y1_plus_x1 = self.y + self.x;
1364 let y1_minus_x1 = self.y - self.x;
1365 let a = y1_plus_x1 * _rhs.y_minus_x;
1366 let b = y1_minus_x1 * _rhs.y_plus_x;
1367 let c = _rhs.t2d * self.t;
1368 let zz = self.z * _rhs.z;
1369 let d = zz + zz;
1370 let x3 = a - b;
1371 let y3 = a + b;
1372 let z3 = d - c;
1373 let t3 = d + c;
1374
1375 GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
1376 }
1377 }
1378
1379 impl Sub<GePrecomp> for GeP3 {
1380 type Output = GeP1P1;
1381
sub(self, _rhs: GePrecomp) -> GeP1P11382 fn sub(self, _rhs: GePrecomp) -> GeP1P1 {
1383 let y1_plus_x1 = self.y + self.x;
1384 let y1_minus_x1 = self.y - self.x;
1385 let a = y1_plus_x1 * _rhs.y_minus_x;
1386 let b = y1_minus_x1 * _rhs.y_plus_x;
1387 let c = _rhs.xy2d * self.t;
1388 let d = self.z + self.z;
1389 let x3 = a - b;
1390 let y3 = a + b;
1391 let z3 = d - c;
1392 let t3 = d + c;
1393
1394 GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
1395 }
1396 }
1397
equal(b: u8, c: u8) -> i321398 fn equal(b: u8, c: u8) -> i32 {
1399 let x = b ^ c; /* 0: yes; 1..255: no */
1400 let mut y = x as u32; /* 0: yes; 1..255: no */
1401 y = y.wrapping_sub(1); /* 4294967295: yes; 0..254: no */
1402 y >>= 31; /* 1: yes; 0: no */
1403 y as i32
1404 }
1405
1406
1407
1408 impl GePrecomp {
zero() -> GePrecomp1409 fn zero() -> GePrecomp {
1410 GePrecomp {
1411 y_plus_x: FE_ONE,
1412 y_minus_x: FE_ONE,
1413 xy2d: FE_ZERO,
1414 }
1415 }
1416
maybe_set(&mut self, other: &GePrecomp, do_swap: i32)1417 pub fn maybe_set(&mut self, other: &GePrecomp, do_swap: i32) {
1418 self.y_plus_x.maybe_set(&other.y_plus_x, do_swap);
1419 self.y_minus_x.maybe_set(&other.y_minus_x, do_swap);
1420 self.xy2d.maybe_set(&other.xy2d, do_swap);
1421 }
1422
select(pos: usize, b: i8) -> GePrecomp1423 pub fn select(pos: usize, b: i8) -> GePrecomp {
1424 let bnegative = (b as u8) >> 7;
1425 let babs: u8 = (b - (((-(bnegative as i8)) & b) << 1)) as u8;
1426 let mut t = GePrecomp::zero();
1427 t.maybe_set(&GE_PRECOMP_BASE[pos][0], equal(babs, 1));
1428 t.maybe_set(&GE_PRECOMP_BASE[pos][1], equal(babs, 2));
1429 t.maybe_set(&GE_PRECOMP_BASE[pos][2], equal(babs, 3));
1430 t.maybe_set(&GE_PRECOMP_BASE[pos][3], equal(babs, 4));
1431 t.maybe_set(&GE_PRECOMP_BASE[pos][4], equal(babs, 5));
1432 t.maybe_set(&GE_PRECOMP_BASE[pos][5], equal(babs, 6));
1433 t.maybe_set(&GE_PRECOMP_BASE[pos][6], equal(babs, 7));
1434 t.maybe_set(&GE_PRECOMP_BASE[pos][7], equal(babs, 8));
1435 let minus_t = GePrecomp {
1436 y_plus_x: t.y_minus_x,
1437 y_minus_x: t.y_plus_x,
1438 xy2d: t.xy2d.neg(),
1439 };
1440 t.maybe_set(&minus_t, bnegative as i32);
1441 t
1442 }
1443 }
1444
1445 /*
1446 h = a * B
1447 where a = a[0]+256*a[1]+...+256^31 a[31]
1448 B is the Ed25519 base point (x,4/5) with x positive.
1449
1450 Preconditions:
1451 a[31] <= 127
1452 */
ge_scalarmult_base(a: &[u8]) -> GeP31453 pub fn ge_scalarmult_base(a: &[u8]) -> GeP3 {
1454 let mut es: [i8; 64] = [0; 64];
1455 let mut r: GeP1P1;
1456 let mut s: GeP2;
1457 let mut t: GePrecomp;
1458
1459 for i in 0..32 {
1460 es[2 * i + 0] = ((a[i] >> 0) & 15) as i8;
1461 es[2 * i + 1] = ((a[i] >> 4) & 15) as i8;
1462 }
1463 /* each es[i] is between 0 and 15 */
1464 /* es[63] is between 0 and 7 */
1465
1466 let mut carry: i8 = 0;
1467 for i in 0..63 {
1468 es[i] += carry;
1469 carry = es[i] + 8;
1470 carry >>= 4;
1471 es[i] -= carry << 4;
1472 }
1473 es[63] += carry;
1474 /* each es[i] is between -8 and 8 */
1475
1476 let mut h = GeP3::zero();
1477 for i in (1..64).step_up(2) {
1478 t = GePrecomp::select(i/2, es[i]);
1479 r = h + t;
1480 h = r.to_p3();
1481 }
1482
1483 r = h.dbl(); s = r.to_p2();
1484 r = s.dbl(); s = r.to_p2();
1485 r = s.dbl(); s = r.to_p2();
1486 r = s.dbl(); h = r.to_p3();
1487
1488 for i in (0..64).step_up(2) {
1489 t = GePrecomp::select(i/2, es[i]);
1490 r = h + t;
1491 h = r.to_p3();
1492 }
1493
1494 h
1495 }
1496 /*
1497 Input:
1498 s[0]+256*s[1]+...+256^63*s[63] = s
1499
1500 Output:
1501 s[0]+256*s[1]+...+256^31*s[31] = s mod l
1502 where l = 2^252 + 27742317777372353535851937790883648493.
1503 Overwrites s in place.
1504 */
sc_reduce(s: &mut [u8])1505 pub fn sc_reduce(s: &mut [u8]) {
1506 let mut s0: i64 = 2097151 & load_3i(s);
1507 let mut s1: i64 = 2097151 & (load_4i(&s[2..6]) >> 5);
1508 let mut s2: i64 = 2097151 & (load_3i(&s[5..8]) >> 2);
1509 let mut s3: i64 = 2097151 & (load_4i(&s[7..11]) >> 7);
1510 let mut s4: i64 = 2097151 & (load_4i(&s[10..14]) >> 4);
1511 let mut s5: i64 = 2097151 & (load_3i(&s[13..16]) >> 1);
1512 let mut s6: i64 = 2097151 & (load_4i(&s[15..19]) >> 6);
1513 let mut s7: i64 = 2097151 & (load_3i(&s[18..21]) >> 3);
1514 let mut s8: i64 = 2097151 & load_3i(&s[21..24]);
1515 let mut s9: i64 = 2097151 & (load_4i(&s[23..27]) >> 5);
1516 let mut s10: i64 = 2097151 & (load_3i(&s[26..29]) >> 2);
1517 let mut s11: i64 = 2097151 & (load_4i(&s[28..32]) >> 7);
1518 let mut s12: i64 = 2097151 & (load_4i(&s[31..35]) >> 4);
1519 let mut s13: i64 = 2097151 & (load_3i(&s[34..37]) >> 1);
1520 let mut s14: i64 = 2097151 & (load_4i(&s[36..40]) >> 6);
1521 let mut s15: i64 = 2097151 & (load_3i(&s[39..42]) >> 3);
1522 let mut s16: i64 = 2097151 & load_3i(&s[42..45]);
1523 let mut s17: i64 = 2097151 & (load_4i(&s[44..48]) >> 5);
1524 let s18: i64 = 2097151 & (load_3i(&s[47..50]) >> 2);
1525 let s19: i64 = 2097151 & (load_4i(&s[49..53]) >> 7);
1526 let s20: i64 = 2097151 & (load_4i(&s[52..56]) >> 4);
1527 let s21: i64 = 2097151 & (load_3i(&s[55..58]) >> 1);
1528 let s22: i64 = 2097151 & (load_4i(&s[57..61]) >> 6);
1529 let s23: i64 = load_4i(&s[60..64]) >> 3;
1530 let mut carry0: i64;
1531 let mut carry1: i64;
1532 let mut carry2: i64;
1533 let mut carry3: i64;
1534 let mut carry4: i64;
1535 let mut carry5: i64;
1536 let mut carry6: i64;
1537 let mut carry7: i64;
1538 let mut carry8: i64;
1539 let mut carry9: i64;
1540 let mut carry10: i64;
1541 let mut carry11: i64;
1542 let carry12: i64;
1543 let carry13: i64;
1544 let carry14: i64;
1545 let carry15: i64;
1546 let carry16: i64;
1547
1548 s11 += s23 * 666643;
1549 s12 += s23 * 470296;
1550 s13 += s23 * 654183;
1551 s14 -= s23 * 997805;
1552 s15 += s23 * 136657;
1553 s16 -= s23 * 683901;
1554
1555
1556 s10 += s22 * 666643;
1557 s11 += s22 * 470296;
1558 s12 += s22 * 654183;
1559 s13 -= s22 * 997805;
1560 s14 += s22 * 136657;
1561 s15 -= s22 * 683901;
1562
1563
1564 s9 += s21 * 666643;
1565 s10 += s21 * 470296;
1566 s11 += s21 * 654183;
1567 s12 -= s21 * 997805;
1568 s13 += s21 * 136657;
1569 s14 -= s21 * 683901;
1570
1571
1572 s8 += s20 * 666643;
1573 s9 += s20 * 470296;
1574 s10 += s20 * 654183;
1575 s11 -= s20 * 997805;
1576 s12 += s20 * 136657;
1577 s13 -= s20 * 683901;
1578
1579
1580 s7 += s19 * 666643;
1581 s8 += s19 * 470296;
1582 s9 += s19 * 654183;
1583 s10 -= s19 * 997805;
1584 s11 += s19 * 136657;
1585 s12 -= s19 * 683901;
1586
1587
1588 s6 += s18 * 666643;
1589 s7 += s18 * 470296;
1590 s8 += s18 * 654183;
1591 s9 -= s18 * 997805;
1592 s10 += s18 * 136657;
1593 s11 -= s18 * 683901;
1594
1595
1596 carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
1597 carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
1598 carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
1599 carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
1600 carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
1601 carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
1602
1603 carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
1604 carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
1605 carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
1606 carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
1607 carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
1608
1609 s5 += s17 * 666643;
1610 s6 += s17 * 470296;
1611 s7 += s17 * 654183;
1612 s8 -= s17 * 997805;
1613 s9 += s17 * 136657;
1614 s10 -= s17 * 683901;
1615
1616
1617 s4 += s16 * 666643;
1618 s5 += s16 * 470296;
1619 s6 += s16 * 654183;
1620 s7 -= s16 * 997805;
1621 s8 += s16 * 136657;
1622 s9 -= s16 * 683901;
1623
1624
1625 s3 += s15 * 666643;
1626 s4 += s15 * 470296;
1627 s5 += s15 * 654183;
1628 s6 -= s15 * 997805;
1629 s7 += s15 * 136657;
1630 s8 -= s15 * 683901;
1631
1632
1633 s2 += s14 * 666643;
1634 s3 += s14 * 470296;
1635 s4 += s14 * 654183;
1636 s5 -= s14 * 997805;
1637 s6 += s14 * 136657;
1638 s7 -= s14 * 683901;
1639
1640
1641 s1 += s13 * 666643;
1642 s2 += s13 * 470296;
1643 s3 += s13 * 654183;
1644 s4 -= s13 * 997805;
1645 s5 += s13 * 136657;
1646 s6 -= s13 * 683901;
1647
1648
1649 s0 += s12 * 666643;
1650 s1 += s12 * 470296;
1651 s2 += s12 * 654183;
1652 s3 -= s12 * 997805;
1653 s4 += s12 * 136657;
1654 s5 -= s12 * 683901;
1655 s12 = 0;
1656
1657 carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
1658 carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
1659 carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
1660 carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
1661 carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
1662 carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
1663
1664 carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
1665 carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
1666 carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
1667 carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
1668 carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
1669 carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
1670
1671 s0 += s12 * 666643;
1672 s1 += s12 * 470296;
1673 s2 += s12 * 654183;
1674 s3 -= s12 * 997805;
1675 s4 += s12 * 136657;
1676 s5 -= s12 * 683901;
1677 s12 = 0;
1678
1679 carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
1680 carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
1681 carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
1682 carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
1683 carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
1684 carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
1685 carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
1686 carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
1687 carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
1688 carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
1689 carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
1690 carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
1691
1692 s0 += s12 * 666643;
1693 s1 += s12 * 470296;
1694 s2 += s12 * 654183;
1695 s3 -= s12 * 997805;
1696 s4 += s12 * 136657;
1697 s5 -= s12 * 683901;
1698
1699
1700 carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
1701 carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
1702 carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
1703 carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
1704 carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
1705 carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
1706 carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
1707 carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
1708 carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
1709 carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
1710 carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
1711
1712 s[0] = (s0 >> 0) as u8;
1713 s[1] = (s0 >> 8) as u8;
1714 s[2] = ((s0 >> 16) | (s1 << 5)) as u8;
1715 s[3] = (s1 >> 3) as u8;
1716 s[4] = (s1 >> 11) as u8;
1717 s[5] = ((s1 >> 19) | (s2 << 2)) as u8;
1718 s[6] = (s2 >> 6) as u8;
1719 s[7] = ((s2 >> 14) | (s3 << 7)) as u8;
1720 s[8] = (s3 >> 1) as u8;
1721 s[9] = (s3 >> 9) as u8;
1722 s[10] = ((s3 >> 17) | (s4 << 4)) as u8;
1723 s[11] = (s4 >> 4) as u8;
1724 s[12] = (s4 >> 12) as u8;
1725 s[13] = ((s4 >> 20) | (s5 << 1)) as u8;
1726 s[14] = (s5 >> 7) as u8;
1727 s[15] = ((s5 >> 15) | (s6 << 6)) as u8;
1728 s[16] = (s6 >> 2) as u8;
1729 s[17] = (s6 >> 10) as u8;
1730 s[18] = ((s6 >> 18) | (s7 << 3)) as u8;
1731 s[19] = (s7 >> 5) as u8;
1732 s[20] = (s7 >> 13) as u8;
1733 s[21] = (s8 >> 0) as u8;
1734 s[22] = (s8 >> 8) as u8;
1735 s[23] = ((s8 >> 16) | (s9 << 5)) as u8;
1736 s[24] = (s9 >> 3) as u8;
1737 s[25] = (s9 >> 11) as u8;
1738 s[26] = ((s9 >> 19) | (s10 << 2)) as u8;
1739 s[27] = (s10 >> 6) as u8;
1740 s[28] = ((s10 >> 14) | (s11 << 7)) as u8;
1741 s[29] = (s11 >> 1) as u8;
1742 s[30] = (s11 >> 9) as u8;
1743 s[31] = (s11 >> 17) as u8;
1744 }
1745
1746
1747 /*
1748 Input:
1749 a[0]+256*a[1]+...+256^31*a[31] = a
1750 b[0]+256*b[1]+...+256^31*b[31] = b
1751 c[0]+256*c[1]+...+256^31*c[31] = c
1752
1753 Output:
1754 s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
1755 where l = 2^252 + 27742317777372353535851937790883648493.
1756 */
sc_muladd(s: &mut[u8], a: &[u8], b: &[u8], c: &[u8])1757 pub fn sc_muladd(s: &mut[u8], a: &[u8], b: &[u8], c: &[u8]) {
1758 let a0 = 2097151 & load_3i(&a[0..3]);
1759 let a1 = 2097151 & (load_4i(&a[2..6]) >> 5);
1760 let a2 = 2097151 & (load_3i(&a[5..8]) >> 2);
1761 let a3 = 2097151 & (load_4i(&a[7..11]) >> 7);
1762 let a4 = 2097151 & (load_4i(&a[10..14]) >> 4);
1763 let a5 = 2097151 & (load_3i(&a[13..16]) >> 1);
1764 let a6 = 2097151 & (load_4i(&a[15..19]) >> 6);
1765 let a7 = 2097151 & (load_3i(&a[18..21]) >> 3);
1766 let a8 = 2097151 & load_3i(&a[21..24]);
1767 let a9 = 2097151 & (load_4i(&a[23..27]) >> 5);
1768 let a10 = 2097151 & (load_3i(&a[26..29]) >> 2);
1769 let a11 = load_4i(&a[28..32]) >> 7;
1770 let b0 = 2097151 & load_3i(&b[0..3]);
1771 let b1 = 2097151 & (load_4i(&b[2..6]) >> 5);
1772 let b2 = 2097151 & (load_3i(&b[5..8]) >> 2);
1773 let b3 = 2097151 & (load_4i(&b[7..11]) >> 7);
1774 let b4 = 2097151 & (load_4i(&b[10..14]) >> 4);
1775 let b5 = 2097151 & (load_3i(&b[13..16]) >> 1);
1776 let b6 = 2097151 & (load_4i(&b[15..19]) >> 6);
1777 let b7 = 2097151 & (load_3i(&b[18..21]) >> 3);
1778 let b8 = 2097151 & load_3i(&b[21..24]);
1779 let b9 = 2097151 & (load_4i(&b[23..27]) >> 5);
1780 let b10 = 2097151 & (load_3i(&b[26..29]) >> 2);
1781 let b11 = load_4i(&b[28..32]) >> 7;
1782 let c0 = 2097151 & load_3i(&c[0..3]);
1783 let c1 = 2097151 & (load_4i(&c[2..6]) >> 5);
1784 let c2 = 2097151 & (load_3i(&c[5..8]) >> 2);
1785 let c3 = 2097151 & (load_4i(&c[7..11]) >> 7);
1786 let c4 = 2097151 & (load_4i(&c[10..14]) >> 4);
1787 let c5 = 2097151 & (load_3i(&c[13..16]) >> 1);
1788 let c6 = 2097151 & (load_4i(&c[15..19]) >> 6);
1789 let c7 = 2097151 & (load_3i(&c[18..21]) >> 3);
1790 let c8 = 2097151 & load_3i(&c[21..24]);
1791 let c9 = 2097151 & (load_4i(&c[23..27]) >> 5);
1792 let c10 = 2097151 & (load_3i(&c[26..29]) >> 2);
1793 let c11 = load_4i(&c[28..32]) >> 7;
1794 let mut s0: i64;
1795 let mut s1: i64;
1796 let mut s2: i64;
1797 let mut s3: i64;
1798 let mut s4: i64;
1799 let mut s5: i64;
1800 let mut s6: i64;
1801 let mut s7: i64;
1802 let mut s8: i64;
1803 let mut s9: i64;
1804 let mut s10: i64;
1805 let mut s11: i64;
1806 let mut s12: i64;
1807 let mut s13: i64;
1808 let mut s14: i64;
1809 let mut s15: i64;
1810 let mut s16: i64;
1811 let mut s17: i64;
1812 let mut s18: i64;
1813 let mut s19: i64;
1814 let mut s20: i64;
1815 let mut s21: i64;
1816 let mut s22: i64;
1817 let mut s23: i64;
1818 let mut carry0: i64;
1819 let mut carry1: i64;
1820 let mut carry2: i64;
1821 let mut carry3: i64;
1822 let mut carry4: i64;
1823 let mut carry5: i64;
1824 let mut carry6: i64;
1825 let mut carry7: i64;
1826 let mut carry8: i64;
1827 let mut carry9: i64;
1828 let mut carry10: i64;
1829 let mut carry11: i64;
1830 let mut carry12: i64;
1831 let mut carry13: i64;
1832 let mut carry14: i64;
1833 let mut carry15: i64;
1834 let mut carry16: i64;
1835 let carry17: i64;
1836 let carry18: i64;
1837 let carry19: i64;
1838 let carry20: i64;
1839 let carry21: i64;
1840 let carry22: i64;
1841
1842 s0 = c0 + a0*b0;
1843 s1 = c1 + a0*b1 + a1*b0;
1844 s2 = c2 + a0*b2 + a1*b1 + a2*b0;
1845 s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
1846 s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
1847 s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
1848 s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
1849 s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
1850 s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
1851 s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
1852 s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
1853 s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
1854 s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
1855 s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
1856 s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
1857 s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
1858 s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
1859 s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
1860 s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
1861 s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
1862 s20 = a9*b11 + a10*b10 + a11*b9;
1863 s21 = a10*b11 + a11*b10;
1864 s22 = a11*b11;
1865 s23 = 0;
1866
1867 carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
1868 carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
1869 carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
1870 carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
1871 carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
1872 carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
1873 carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
1874 carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
1875 carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
1876 carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
1877 carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
1878 carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
1879
1880 carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
1881 carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
1882 carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
1883 carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
1884 carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
1885 carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
1886 carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
1887 carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
1888 carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
1889 carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
1890 carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
1891
1892 s11 += s23 * 666643;
1893 s12 += s23 * 470296;
1894 s13 += s23 * 654183;
1895 s14 -= s23 * 997805;
1896 s15 += s23 * 136657;
1897 s16 -= s23 * 683901;
1898
1899
1900 s10 += s22 * 666643;
1901 s11 += s22 * 470296;
1902 s12 += s22 * 654183;
1903 s13 -= s22 * 997805;
1904 s14 += s22 * 136657;
1905 s15 -= s22 * 683901;
1906
1907
1908 s9 += s21 * 666643;
1909 s10 += s21 * 470296;
1910 s11 += s21 * 654183;
1911 s12 -= s21 * 997805;
1912 s13 += s21 * 136657;
1913 s14 -= s21 * 683901;
1914
1915
1916 s8 += s20 * 666643;
1917 s9 += s20 * 470296;
1918 s10 += s20 * 654183;
1919 s11 -= s20 * 997805;
1920 s12 += s20 * 136657;
1921 s13 -= s20 * 683901;
1922
1923
1924 s7 += s19 * 666643;
1925 s8 += s19 * 470296;
1926 s9 += s19 * 654183;
1927 s10 -= s19 * 997805;
1928 s11 += s19 * 136657;
1929 s12 -= s19 * 683901;
1930
1931
1932 s6 += s18 * 666643;
1933 s7 += s18 * 470296;
1934 s8 += s18 * 654183;
1935 s9 -= s18 * 997805;
1936 s10 += s18 * 136657;
1937 s11 -= s18 * 683901;
1938
1939
1940 carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
1941 carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
1942 carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
1943 carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
1944 carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
1945 carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
1946
1947 carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
1948 carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
1949 carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
1950 carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
1951 carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
1952
1953 s5 += s17 * 666643;
1954 s6 += s17 * 470296;
1955 s7 += s17 * 654183;
1956 s8 -= s17 * 997805;
1957 s9 += s17 * 136657;
1958 s10 -= s17 * 683901;
1959
1960
1961 s4 += s16 * 666643;
1962 s5 += s16 * 470296;
1963 s6 += s16 * 654183;
1964 s7 -= s16 * 997805;
1965 s8 += s16 * 136657;
1966 s9 -= s16 * 683901;
1967
1968
1969 s3 += s15 * 666643;
1970 s4 += s15 * 470296;
1971 s5 += s15 * 654183;
1972 s6 -= s15 * 997805;
1973 s7 += s15 * 136657;
1974 s8 -= s15 * 683901;
1975
1976
1977 s2 += s14 * 666643;
1978 s3 += s14 * 470296;
1979 s4 += s14 * 654183;
1980 s5 -= s14 * 997805;
1981 s6 += s14 * 136657;
1982 s7 -= s14 * 683901;
1983
1984
1985 s1 += s13 * 666643;
1986 s2 += s13 * 470296;
1987 s3 += s13 * 654183;
1988 s4 -= s13 * 997805;
1989 s5 += s13 * 136657;
1990 s6 -= s13 * 683901;
1991
1992
1993 s0 += s12 * 666643;
1994 s1 += s12 * 470296;
1995 s2 += s12 * 654183;
1996 s3 -= s12 * 997805;
1997 s4 += s12 * 136657;
1998 s5 -= s12 * 683901;
1999 s12 = 0;
2000
2001 carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
2002 carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
2003 carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
2004 carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
2005 carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
2006 carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
2007
2008 carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
2009 carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
2010 carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
2011 carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
2012 carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
2013 carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
2014
2015 s0 += s12 * 666643;
2016 s1 += s12 * 470296;
2017 s2 += s12 * 654183;
2018 s3 -= s12 * 997805;
2019 s4 += s12 * 136657;
2020 s5 -= s12 * 683901;
2021 s12 = 0;
2022
2023 carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
2024 carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
2025 carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
2026 carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
2027 carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
2028 carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
2029 carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
2030 carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
2031 carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
2032 carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
2033 carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
2034 carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
2035
2036 s0 += s12 * 666643;
2037 s1 += s12 * 470296;
2038 s2 += s12 * 654183;
2039 s3 -= s12 * 997805;
2040 s4 += s12 * 136657;
2041 s5 -= s12 * 683901;
2042
2043
2044 carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
2045 carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
2046 carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
2047 carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
2048 carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
2049 carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
2050 carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
2051 carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
2052 carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
2053 carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
2054 carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
2055
2056 s[0] = (s0 >> 0) as u8;
2057 s[1] = (s0 >> 8) as u8;
2058 s[2] = ((s0 >> 16) | (s1 << 5)) as u8;
2059 s[3] = (s1 >> 3) as u8;
2060 s[4] = (s1 >> 11) as u8;
2061 s[5] = ((s1 >> 19) | (s2 << 2)) as u8;
2062 s[6] = (s2 >> 6) as u8;
2063 s[7] = ((s2 >> 14) | (s3 << 7)) as u8;
2064 s[8] = (s3 >> 1) as u8;
2065 s[9] = (s3 >> 9) as u8;
2066 s[10] = ((s3 >> 17) | (s4 << 4)) as u8;
2067 s[11] = (s4 >> 4) as u8;
2068 s[12] = (s4 >> 12) as u8;
2069 s[13] = ((s4 >> 20) | (s5 << 1)) as u8;
2070 s[14] = (s5 >> 7) as u8;
2071 s[15] = ((s5 >> 15) | (s6 << 6)) as u8;
2072 s[16] = (s6 >> 2) as u8;
2073 s[17] = (s6 >> 10) as u8;
2074 s[18] = ((s6 >> 18) | (s7 << 3)) as u8;
2075 s[19] = (s7 >> 5) as u8;
2076 s[20] = (s7 >> 13) as u8;
2077 s[21] = (s8 >> 0) as u8;
2078 s[22] = (s8 >> 8) as u8;
2079 s[23] = ((s8 >> 16) | (s9 << 5)) as u8;
2080 s[24] = (s9 >> 3) as u8;
2081 s[25] = (s9 >> 11) as u8;
2082 s[26] = ((s9 >> 19) | (s10 << 2)) as u8;
2083 s[27] = (s10 >> 6) as u8;
2084 s[28] = ((s10 >> 14) | (s11 << 7)) as u8;
2085 s[29] = (s11 >> 1) as u8;
2086 s[30] = (s11 >> 9) as u8;
2087 s[31] = (s11 >> 17) as u8;
2088 }
2089
2090
curve25519(n: &[u8], p: &[u8]) -> [u8; 32]2091 pub fn curve25519(n: &[u8], p: &[u8]) -> [u8; 32] {
2092 let mut e = [0u8; 32];
2093 let mut x2;
2094 let mut z2;
2095 let mut x3;
2096 let mut z3;
2097 let mut swap: i32;
2098 let mut b: i32;
2099
2100 for (d,s) in e.iter_mut().zip(n.iter()) {
2101 *d = *s;
2102 }
2103 e[0] &= 248;
2104 e[31] &= 127;
2105 e[31] |= 64;
2106 let x1 = Fe::from_bytes(p);
2107 x2 = FE_ONE;
2108 z2 = FE_ZERO;
2109 x3 = x1;
2110 z3 = FE_ONE;
2111
2112 swap = 0;
2113 // pos starts at 254 and goes down to 0
2114 for pos in (0usize..255).rev() {
2115 b = (e[pos / 8] >> (pos & 7)) as i32;
2116 b &= 1;
2117 swap ^= b;
2118 x2.maybe_swap_with(&mut x3, swap);
2119 z2.maybe_swap_with(&mut z3, swap);
2120 swap = b;
2121
2122 let d = x3 - z3;
2123 let b = x2 - z2;
2124 let a = x2 + z2;
2125 let c = x3 + z3;
2126 let da = d * a;
2127 let cb = c * b;
2128 let bb = b.square();
2129 let aa = a.square();
2130 let t0 = da + cb;
2131 let t1 = da - cb;
2132 let x4 = aa*bb;
2133 let e = aa - bb;
2134 let t2 = t1.square();
2135 let t3 = e.mul_121666();
2136 let x5 = t0.square();
2137 let t4 = bb + t3;
2138 let z5 = x1 * t2;
2139 let z4 = e*t4;
2140
2141 z2 = z4;
2142 z3 = z5;
2143 x2 = x4;
2144 x3 = x5;
2145 }
2146 x2.maybe_swap_with(&mut x3, swap);
2147 z2.maybe_swap_with(&mut z3, swap);
2148
2149 (z2.invert() * x2).to_bytes()
2150 }
2151
curve25519_base(x: &[u8]) -> [u8; 32]2152 pub fn curve25519_base(x: &[u8]) -> [u8; 32] {
2153 let mut base : [u8; 32] = [0; 32];
2154 base[0] = 9;
2155 curve25519(x, base.as_ref())
2156 }
2157
2158 #[cfg(test)]
2159 mod tests {
2160 use curve25519::{Fe, curve25519_base};
2161
2162 #[test]
from_to_bytes_preserves()2163 fn from_to_bytes_preserves() {
2164 for i in 0..50 {
2165 let mut e: Vec<u8> = (0u32..32).map(|idx| (idx*(1289+i*761)) as u8).collect();
2166 e[0] &= 248;
2167 e[31] &= 127;
2168 e[31] |= 64;
2169 let fe = Fe::from_bytes(e.as_ref());
2170 let e_preserved = fe.to_bytes();
2171 assert!(e == e_preserved.to_vec());
2172 }
2173 }
2174
2175 #[test]
swap_test()2176 fn swap_test() {
2177 let mut f = Fe([10,20,30,40,50,60,70,80,90,100]);
2178 let mut g = Fe([11,21,31,41,51,61,71,81,91,101]);
2179 let f_initial = f;
2180 let g_initial = g;
2181 f.maybe_swap_with(&mut g, 0);
2182 assert!(f == f_initial);
2183 assert!(g == g_initial);
2184
2185 f.maybe_swap_with(&mut g, 1);
2186 assert!(f == g_initial);
2187 assert!(g == f_initial);
2188 }
2189
2190 struct CurveGen {
2191 which: u32
2192 }
2193 impl CurveGen {
new(seed: u32) -> CurveGen2194 fn new(seed: u32) -> CurveGen {
2195 CurveGen{which: seed}
2196 }
2197 }
2198 impl Iterator for CurveGen {
2199 type Item = Fe;
2200
next(&mut self) -> Option<Fe>2201 fn next(&mut self) -> Option<Fe> {
2202 let mut e: Vec<u8> = (0..32).map(|idx| (idx*(1289+self.which*761)) as u8).collect();
2203 e[0] &= 248;
2204 e[31] &= 127;
2205 e[31] |= 64;
2206 Some(Fe::from_bytes(e.as_ref()))
2207 }
2208 }
2209
2210 #[test]
mul_commutes()2211 fn mul_commutes() {
2212 for (x,y) in CurveGen::new(1).zip(CurveGen::new(2)).take(40) {
2213 assert!(x*y == y*x);
2214 };
2215 }
2216
2217 #[test]
mul_assoc()2218 fn mul_assoc() {
2219 for (x,(y,z)) in CurveGen::new(1).zip(CurveGen::new(2).zip(CurveGen::new(3))).take(40) {
2220 assert!((x*y)*z == x*(y*z));
2221 };
2222 }
2223
2224 #[test]
invert_inverts()2225 fn invert_inverts() {
2226 for x in CurveGen::new(1).take(40) {
2227 assert!(x.invert().invert() == x);
2228 };
2229 }
2230
2231 #[test]
square_by_mul()2232 fn square_by_mul() {
2233 for x in CurveGen::new(1).take(40) {
2234 assert!(x*x == x.square());
2235 };
2236 }
2237
2238 #[test]
base_example()2239 fn base_example() {
2240 let sk : [u8; 32] = [
2241 0x77, 0x07, 0x6d, 0x0a, 0x73, 0x18, 0xa5, 0x7d, 0x3c, 0x16, 0xc1,
2242 0x72, 0x51, 0xb2, 0x66, 0x45, 0xdf, 0x4c, 0x2f, 0x87, 0xeb, 0xc0,
2243 0x99, 0x2a, 0xb1, 0x77, 0xfb, 0xa5, 0x1d, 0xb9, 0x2c, 0x2a ];
2244 let pk = curve25519_base(sk.as_ref());
2245 let correct : [u8; 32] = [
2246 0x85,0x20,0xf0,0x09,0x89,0x30,0xa7,0x54
2247 ,0x74,0x8b,0x7d,0xdc,0xb4,0x3e,0xf7,0x5a
2248 ,0x0d,0xbf,0x3a,0x0d,0x26,0x38,0x1a,0xf4
2249 ,0xeb,0xa4,0xa9,0x8e,0xaa,0x9b,0x4e,0x6a ];
2250 assert_eq!(pk.to_vec(), correct.to_vec());
2251 }
2252 }
2253
2254 static BI: [GePrecomp; 8] = [
2255 GePrecomp {
2256 y_plus_x: Fe([ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 ]),
2257 y_minus_x: Fe([ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 ]),
2258 xy2d: Fe([ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 ]),
2259 },
2260 GePrecomp {
2261 y_plus_x: Fe([ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 ]),
2262 y_minus_x: Fe([ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 ]),
2263 xy2d: Fe([ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 ]),
2264 },
2265 GePrecomp {
2266 y_plus_x: Fe([ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 ]),
2267 y_minus_x: Fe([ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 ]),
2268 xy2d: Fe([ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 ]),
2269 },
2270 GePrecomp {
2271 y_plus_x: Fe([ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 ]),
2272 y_minus_x: Fe([ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 ]),
2273 xy2d: Fe([ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 ]),
2274 },
2275 GePrecomp {
2276 y_plus_x: Fe([ -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 ]),
2277 y_minus_x: Fe([ -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 ]),
2278 xy2d: Fe([ 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 ]),
2279 },
2280 GePrecomp {
2281 y_plus_x: Fe([ -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 ]),
2282 y_minus_x: Fe([ 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 ]),
2283 xy2d: Fe([ 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 ]),
2284 },
2285 GePrecomp {
2286 y_plus_x: Fe([ -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 ]),
2287 y_minus_x: Fe([ -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 ]),
2288 xy2d: Fe([ -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 ]),
2289 },
2290 GePrecomp {
2291 y_plus_x: Fe([ -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 ]),
2292 y_minus_x: Fe([ -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 ]),
2293 xy2d: Fe([ -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 ]),
2294 },
2295 ];
2296
2297 static GE_PRECOMP_BASE : [[GePrecomp; 8]; 32] = [
2298 [
2299 GePrecomp {
2300 y_plus_x: Fe([25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605]),
2301 y_minus_x: Fe([-12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378]),
2302 xy2d: Fe([-8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546]),
2303 },
2304 GePrecomp {
2305 y_plus_x: Fe([-12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303]),
2306 y_minus_x: Fe([-21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081]),
2307 xy2d: Fe([26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697]),
2308 },
2309 GePrecomp {
2310 y_plus_x: Fe([15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024]),
2311 y_minus_x: Fe([16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574]),
2312 xy2d: Fe([30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357]),
2313 },
2314 GePrecomp {
2315 y_plus_x: Fe([-17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540]),
2316 y_minus_x: Fe([23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397]),
2317 xy2d: Fe([7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325]),
2318 },
2319 GePrecomp {
2320 y_plus_x: Fe([10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380]),
2321 y_minus_x: Fe([4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306]),
2322 xy2d: Fe([19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942]),
2323 },
2324 GePrecomp {
2325 y_plus_x: Fe([-15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777]),
2326 y_minus_x: Fe([-8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737]),
2327 xy2d: Fe([-18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652]),
2328 },
2329 GePrecomp {
2330 y_plus_x: Fe([5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766]),
2331 y_minus_x: Fe([-30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701]),
2332 xy2d: Fe([28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300]),
2333 },
2334 GePrecomp {
2335 y_plus_x: Fe([14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726]),
2336 y_minus_x: Fe([-7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955]),
2337 xy2d: Fe([27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425]),
2338 },
2339 ],
2340 [
2341 GePrecomp {
2342 y_plus_x: Fe([-13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171]),
2343 y_minus_x: Fe([27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510]),
2344 xy2d: Fe([17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660]),
2345 },
2346 GePrecomp {
2347 y_plus_x: Fe([-10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639]),
2348 y_minus_x: Fe([29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963]),
2349 xy2d: Fe([5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950]),
2350 },
2351 GePrecomp {
2352 y_plus_x: Fe([-27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568]),
2353 y_minus_x: Fe([12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335]),
2354 xy2d: Fe([25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628]),
2355 },
2356 GePrecomp {
2357 y_plus_x: Fe([-26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007]),
2358 y_minus_x: Fe([-2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772]),
2359 xy2d: Fe([-22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653]),
2360 },
2361 GePrecomp {
2362 y_plus_x: Fe([2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567]),
2363 y_minus_x: Fe([13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686]),
2364 xy2d: Fe([21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372]),
2365 },
2366 GePrecomp {
2367 y_plus_x: Fe([-13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887]),
2368 y_minus_x: Fe([-23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954]),
2369 xy2d: Fe([-29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953]),
2370 },
2371 GePrecomp {
2372 y_plus_x: Fe([24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833]),
2373 y_minus_x: Fe([-16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532]),
2374 xy2d: Fe([-22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876]),
2375 },
2376 GePrecomp {
2377 y_plus_x: Fe([2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268]),
2378 y_minus_x: Fe([33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214]),
2379 xy2d: Fe([1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038]),
2380 },
2381 ],
2382 [
2383 GePrecomp {
2384 y_plus_x: Fe([6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800]),
2385 y_minus_x: Fe([4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645]),
2386 xy2d: Fe([-4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664]),
2387 },
2388 GePrecomp {
2389 y_plus_x: Fe([1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933]),
2390 y_minus_x: Fe([-25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182]),
2391 xy2d: Fe([-17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222]),
2392 },
2393 GePrecomp {
2394 y_plus_x: Fe([-18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991]),
2395 y_minus_x: Fe([20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880]),
2396 xy2d: Fe([9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092]),
2397 },
2398 GePrecomp {
2399 y_plus_x: Fe([-16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295]),
2400 y_minus_x: Fe([19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788]),
2401 xy2d: Fe([8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553]),
2402 },
2403 GePrecomp {
2404 y_plus_x: Fe([-15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026]),
2405 y_minus_x: Fe([11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347]),
2406 xy2d: Fe([-18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033]),
2407 },
2408 GePrecomp {
2409 y_plus_x: Fe([-23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395]),
2410 y_minus_x: Fe([-27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278]),
2411 xy2d: Fe([1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890]),
2412 },
2413 GePrecomp {
2414 y_plus_x: Fe([32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995]),
2415 y_minus_x: Fe([-30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596]),
2416 xy2d: Fe([-11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891]),
2417 },
2418 GePrecomp {
2419 y_plus_x: Fe([31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060]),
2420 y_minus_x: Fe([11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608]),
2421 xy2d: Fe([-20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606]),
2422 },
2423 ],
2424 [
2425 GePrecomp {
2426 y_plus_x: Fe([7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389]),
2427 y_minus_x: Fe([-19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016]),
2428 xy2d: Fe([-11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341]),
2429 },
2430 GePrecomp {
2431 y_plus_x: Fe([-22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505]),
2432 y_minus_x: Fe([14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553]),
2433 xy2d: Fe([-28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655]),
2434 },
2435 GePrecomp {
2436 y_plus_x: Fe([15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220]),
2437 y_minus_x: Fe([12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631]),
2438 xy2d: Fe([-4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099]),
2439 },
2440 GePrecomp {
2441 y_plus_x: Fe([26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556]),
2442 y_minus_x: Fe([14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749]),
2443 xy2d: Fe([236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930]),
2444 },
2445 GePrecomp {
2446 y_plus_x: Fe([1276410,-9371918,22949635,-16322807,-23493039,-5702186,14711875,4874229,-30663140,-2331391]),
2447 y_minus_x: Fe([5855666,4990204,-13711848,7294284,-7804282,1924647,-1423175,-7912378,-33069337,9234253]),
2448 xy2d: Fe([20590503,-9018988,31529744,-7352666,-2706834,10650548,31559055,-11609587,18979186,13396066]),
2449 },
2450 GePrecomp {
2451 y_plus_x: Fe([24474287,4968103,22267082,4407354,24063882,-8325180,-18816887,13594782,33514650,7021958]),
2452 y_minus_x: Fe([-11566906,-6565505,-21365085,15928892,-26158305,4315421,-25948728,-3916677,-21480480,12868082]),
2453 xy2d: Fe([-28635013,13504661,19988037,-2132761,21078225,6443208,-21446107,2244500,-12455797,-8089383]),
2454 },
2455 GePrecomp {
2456 y_plus_x: Fe([-30595528,13793479,-5852820,319136,-25723172,-6263899,33086546,8957937,-15233648,5540521]),
2457 y_minus_x: Fe([-11630176,-11503902,-8119500,-7643073,2620056,1022908,-23710744,-1568984,-16128528,-14962807]),
2458 xy2d: Fe([23152971,775386,27395463,14006635,-9701118,4649512,1689819,892185,-11513277,-15205948]),
2459 },
2460 GePrecomp {
2461 y_plus_x: Fe([9770129,9586738,26496094,4324120,1556511,-3550024,27453819,4763127,-19179614,5867134]),
2462 y_minus_x: Fe([-32765025,1927590,31726409,-4753295,23962434,-16019500,27846559,5931263,-29749703,-16108455]),
2463 xy2d: Fe([27461885,-2977536,22380810,1815854,-23033753,-3031938,7283490,-15148073,-19526700,7734629]),
2464 },
2465 ],
2466 [
2467 GePrecomp {
2468 y_plus_x: Fe([-8010264,-9590817,-11120403,6196038,29344158,-13430885,7585295,-3176626,18549497,15302069]),
2469 y_minus_x: Fe([-32658337,-6171222,-7672793,-11051681,6258878,13504381,10458790,-6418461,-8872242,8424746]),
2470 xy2d: Fe([24687205,8613276,-30667046,-3233545,1863892,-1830544,19206234,7134917,-11284482,-828919]),
2471 },
2472 GePrecomp {
2473 y_plus_x: Fe([11334899,-9218022,8025293,12707519,17523892,-10476071,10243738,-14685461,-5066034,16498837]),
2474 y_minus_x: Fe([8911542,6887158,-9584260,-6958590,11145641,-9543680,17303925,-14124238,6536641,10543906]),
2475 xy2d: Fe([-28946384,15479763,-17466835,568876,-1497683,11223454,-2669190,-16625574,-27235709,8876771]),
2476 },
2477 GePrecomp {
2478 y_plus_x: Fe([-25742899,-12566864,-15649966,-846607,-33026686,-796288,-33481822,15824474,-604426,-9039817]),
2479 y_minus_x: Fe([10330056,70051,7957388,-9002667,9764902,15609756,27698697,-4890037,1657394,3084098]),
2480 xy2d: Fe([10477963,-7470260,12119566,-13250805,29016247,-5365589,31280319,14396151,-30233575,15272409]),
2481 },
2482 GePrecomp {
2483 y_plus_x: Fe([-12288309,3169463,28813183,16658753,25116432,-5630466,-25173957,-12636138,-25014757,1950504]),
2484 y_minus_x: Fe([-26180358,9489187,11053416,-14746161,-31053720,5825630,-8384306,-8767532,15341279,8373727]),
2485 xy2d: Fe([28685821,7759505,-14378516,-12002860,-31971820,4079242,298136,-10232602,-2878207,15190420]),
2486 },
2487 GePrecomp {
2488 y_plus_x: Fe([-32932876,13806336,-14337485,-15794431,-24004620,10940928,8669718,2742393,-26033313,-6875003]),
2489 y_minus_x: Fe([-1580388,-11729417,-25979658,-11445023,-17411874,-10912854,9291594,-16247779,-12154742,6048605]),
2490 xy2d: Fe([-30305315,14843444,1539301,11864366,20201677,1900163,13934231,5128323,11213262,9168384]),
2491 },
2492 GePrecomp {
2493 y_plus_x: Fe([-26280513,11007847,19408960,-940758,-18592965,-4328580,-5088060,-11105150,20470157,-16398701]),
2494 y_minus_x: Fe([-23136053,9282192,14855179,-15390078,-7362815,-14408560,-22783952,14461608,14042978,5230683]),
2495 xy2d: Fe([29969567,-2741594,-16711867,-8552442,9175486,-2468974,21556951,3506042,-5933891,-12449708]),
2496 },
2497 GePrecomp {
2498 y_plus_x: Fe([-3144746,8744661,19704003,4581278,-20430686,6830683,-21284170,8971513,-28539189,15326563]),
2499 y_minus_x: Fe([-19464629,10110288,-17262528,-3503892,-23500387,1355669,-15523050,15300988,-20514118,9168260]),
2500 xy2d: Fe([-5353335,4488613,-23803248,16314347,7780487,-15638939,-28948358,9601605,33087103,-9011387]),
2501 },
2502 GePrecomp {
2503 y_plus_x: Fe([-19443170,-15512900,-20797467,-12445323,-29824447,10229461,-27444329,-15000531,-5996870,15664672]),
2504 y_minus_x: Fe([23294591,-16632613,-22650781,-8470978,27844204,11461195,13099750,-2460356,18151676,13417686]),
2505 xy2d: Fe([-24722913,-4176517,-31150679,5988919,-26858785,6685065,1661597,-12551441,15271676,-15452665]),
2506 },
2507 ],
2508 [
2509 GePrecomp {
2510 y_plus_x: Fe([11433042,-13228665,8239631,-5279517,-1985436,-725718,-18698764,2167544,-6921301,-13440182]),
2511 y_minus_x: Fe([-31436171,15575146,30436815,12192228,-22463353,9395379,-9917708,-8638997,12215110,12028277]),
2512 xy2d: Fe([14098400,6555944,23007258,5757252,-15427832,-12950502,30123440,4617780,-16900089,-655628]),
2513 },
2514 GePrecomp {
2515 y_plus_x: Fe([-4026201,-15240835,11893168,13718664,-14809462,1847385,-15819999,10154009,23973261,-12684474]),
2516 y_minus_x: Fe([-26531820,-3695990,-1908898,2534301,-31870557,-16550355,18341390,-11419951,32013174,-10103539]),
2517 xy2d: Fe([-25479301,10876443,-11771086,-14625140,-12369567,1838104,21911214,6354752,4425632,-837822]),
2518 },
2519 GePrecomp {
2520 y_plus_x: Fe([-10433389,-14612966,22229858,-3091047,-13191166,776729,-17415375,-12020462,4725005,14044970]),
2521 y_minus_x: Fe([19268650,-7304421,1555349,8692754,-21474059,-9910664,6347390,-1411784,-19522291,-16109756]),
2522 xy2d: Fe([-24864089,12986008,-10898878,-5558584,-11312371,-148526,19541418,8180106,9282262,10282508]),
2523 },
2524 GePrecomp {
2525 y_plus_x: Fe([-26205082,4428547,-8661196,-13194263,4098402,-14165257,15522535,8372215,5542595,-10702683]),
2526 y_minus_x: Fe([-10562541,14895633,26814552,-16673850,-17480754,-2489360,-2781891,6993761,-18093885,10114655]),
2527 xy2d: Fe([-20107055,-929418,31422704,10427861,-7110749,6150669,-29091755,-11529146,25953725,-106158]),
2528 },
2529 GePrecomp {
2530 y_plus_x: Fe([-4234397,-8039292,-9119125,3046000,2101609,-12607294,19390020,6094296,-3315279,12831125]),
2531 y_minus_x: Fe([-15998678,7578152,5310217,14408357,-33548620,-224739,31575954,6326196,7381791,-2421839]),
2532 xy2d: Fe([-20902779,3296811,24736065,-16328389,18374254,7318640,6295303,8082724,-15362489,12339664]),
2533 },
2534 GePrecomp {
2535 y_plus_x: Fe([27724736,2291157,6088201,-14184798,1792727,5857634,13848414,15768922,25091167,14856294]),
2536 y_minus_x: Fe([-18866652,8331043,24373479,8541013,-701998,-9269457,12927300,-12695493,-22182473,-9012899]),
2537 xy2d: Fe([-11423429,-5421590,11632845,3405020,30536730,-11674039,-27260765,13866390,30146206,9142070]),
2538 },
2539 GePrecomp {
2540 y_plus_x: Fe([3924129,-15307516,-13817122,-10054960,12291820,-668366,-27702774,9326384,-8237858,4171294]),
2541 y_minus_x: Fe([-15921940,16037937,6713787,16606682,-21612135,2790944,26396185,3731949,345228,-5462949]),
2542 xy2d: Fe([-21327538,13448259,25284571,1143661,20614966,-8849387,2031539,-12391231,-16253183,-13582083]),
2543 },
2544 GePrecomp {
2545 y_plus_x: Fe([31016211,-16722429,26371392,-14451233,-5027349,14854137,17477601,3842657,28012650,-16405420]),
2546 y_minus_x: Fe([-5075835,9368966,-8562079,-4600902,-15249953,6970560,-9189873,16292057,-8867157,3507940]),
2547 xy2d: Fe([29439664,3537914,23333589,6997794,-17555561,-11018068,-15209202,-15051267,-9164929,6580396]),
2548 },
2549 ],
2550 [
2551 GePrecomp {
2552 y_plus_x: Fe([-12185861,-7679788,16438269,10826160,-8696817,-6235611,17860444,-9273846,-2095802,9304567]),
2553 y_minus_x: Fe([20714564,-4336911,29088195,7406487,11426967,-5095705,14792667,-14608617,5289421,-477127]),
2554 xy2d: Fe([-16665533,-10650790,-6160345,-13305760,9192020,-1802462,17271490,12349094,26939669,-3752294]),
2555 },
2556 GePrecomp {
2557 y_plus_x: Fe([-12889898,9373458,31595848,16374215,21471720,13221525,-27283495,-12348559,-3698806,117887]),
2558 y_minus_x: Fe([22263325,-6560050,3984570,-11174646,-15114008,-566785,28311253,5358056,-23319780,541964]),
2559 xy2d: Fe([16259219,3261970,2309254,-15534474,-16885711,-4581916,24134070,-16705829,-13337066,-13552195]),
2560 },
2561 GePrecomp {
2562 y_plus_x: Fe([9378160,-13140186,-22845982,-12745264,28198281,-7244098,-2399684,-717351,690426,14876244]),
2563 y_minus_x: Fe([24977353,-314384,-8223969,-13465086,28432343,-1176353,-13068804,-12297348,-22380984,6618999]),
2564 xy2d: Fe([-1538174,11685646,12944378,13682314,-24389511,-14413193,8044829,-13817328,32239829,-5652762]),
2565 },
2566 GePrecomp {
2567 y_plus_x: Fe([-18603066,4762990,-926250,8885304,-28412480,-3187315,9781647,-10350059,32779359,5095274]),
2568 y_minus_x: Fe([-33008130,-5214506,-32264887,-3685216,9460461,-9327423,-24601656,14506724,21639561,-2630236]),
2569 xy2d: Fe([-16400943,-13112215,25239338,15531969,3987758,-4499318,-1289502,-6863535,17874574,558605]),
2570 },
2571 GePrecomp {
2572 y_plus_x: Fe([-13600129,10240081,9171883,16131053,-20869254,9599700,33499487,5080151,2085892,5119761]),
2573 y_minus_x: Fe([-22205145,-2519528,-16381601,414691,-25019550,2170430,30634760,-8363614,-31999993,-5759884]),
2574 xy2d: Fe([-6845704,15791202,8550074,-1312654,29928809,-12092256,27534430,-7192145,-22351378,12961482]),
2575 },
2576 GePrecomp {
2577 y_plus_x: Fe([-24492060,-9570771,10368194,11582341,-23397293,-2245287,16533930,8206996,-30194652,-5159638]),
2578 y_minus_x: Fe([-11121496,-3382234,2307366,6362031,-135455,8868177,-16835630,7031275,7589640,8945490]),
2579 xy2d: Fe([-32152748,8917967,6661220,-11677616,-1192060,-15793393,7251489,-11182180,24099109,-14456170]),
2580 },
2581 GePrecomp {
2582 y_plus_x: Fe([5019558,-7907470,4244127,-14714356,-26933272,6453165,-19118182,-13289025,-6231896,-10280736]),
2583 y_minus_x: Fe([10853594,10721687,26480089,5861829,-22995819,1972175,-1866647,-10557898,-3363451,-6441124]),
2584 xy2d: Fe([-17002408,5906790,221599,-6563147,7828208,-13248918,24362661,-2008168,-13866408,7421392]),
2585 },
2586 GePrecomp {
2587 y_plus_x: Fe([8139927,-6546497,32257646,-5890546,30375719,1886181,-21175108,15441252,28826358,-4123029]),
2588 y_minus_x: Fe([6267086,9695052,7709135,-16603597,-32869068,-1886135,14795160,-7840124,13746021,-1742048]),
2589 xy2d: Fe([28584902,7787108,-6732942,-15050729,22846041,-7571236,-3181936,-363524,4771362,-8419958]),
2590 },
2591 ],
2592 [
2593 GePrecomp {
2594 y_plus_x: Fe([24949256,6376279,-27466481,-8174608,-18646154,-9930606,33543569,-12141695,3569627,11342593]),
2595 y_minus_x: Fe([26514989,4740088,27912651,3697550,19331575,-11472339,6809886,4608608,7325975,-14801071]),
2596 xy2d: Fe([-11618399,-14554430,-24321212,7655128,-1369274,5214312,-27400540,10258390,-17646694,-8186692]),
2597 },
2598 GePrecomp {
2599 y_plus_x: Fe([11431204,15823007,26570245,14329124,18029990,4796082,-31446179,15580664,9280358,-3973687]),
2600 y_minus_x: Fe([-160783,-10326257,-22855316,-4304997,-20861367,-13621002,-32810901,-11181622,-15545091,4387441]),
2601 xy2d: Fe([-20799378,12194512,3937617,-5805892,-27154820,9340370,-24513992,8548137,20617071,-7482001]),
2602 },
2603 GePrecomp {
2604 y_plus_x: Fe([-938825,-3930586,-8714311,16124718,24603125,-6225393,-13775352,-11875822,24345683,10325460]),
2605 y_minus_x: Fe([-19855277,-1568885,-22202708,8714034,14007766,6928528,16318175,-1010689,4766743,3552007]),
2606 xy2d: Fe([-21751364,-16730916,1351763,-803421,-4009670,3950935,3217514,14481909,10988822,-3994762]),
2607 },
2608 GePrecomp {
2609 y_plus_x: Fe([15564307,-14311570,3101243,5684148,30446780,-8051356,12677127,-6505343,-8295852,13296005]),
2610 y_minus_x: Fe([-9442290,6624296,-30298964,-11913677,-4670981,-2057379,31521204,9614054,-30000824,12074674]),
2611 xy2d: Fe([4771191,-135239,14290749,-13089852,27992298,14998318,-1413936,-1556716,29832613,-16391035]),
2612 },
2613 GePrecomp {
2614 y_plus_x: Fe([7064884,-7541174,-19161962,-5067537,-18891269,-2912736,25825242,5293297,-27122660,13101590]),
2615 y_minus_x: Fe([-2298563,2439670,-7466610,1719965,-27267541,-16328445,32512469,-5317593,-30356070,-4190957]),
2616 xy2d: Fe([-30006540,10162316,-33180176,3981723,-16482138,-13070044,14413974,9515896,19568978,9628812]),
2617 },
2618 GePrecomp {
2619 y_plus_x: Fe([33053803,199357,15894591,1583059,27380243,-4580435,-17838894,-6106839,-6291786,3437740]),
2620 y_minus_x: Fe([-18978877,3884493,19469877,12726490,15913552,13614290,-22961733,70104,7463304,4176122]),
2621 xy2d: Fe([-27124001,10659917,11482427,-16070381,12771467,-6635117,-32719404,-5322751,24216882,5944158]),
2622 },
2623 GePrecomp {
2624 y_plus_x: Fe([8894125,7450974,-2664149,-9765752,-28080517,-12389115,19345746,14680796,11632993,5847885]),
2625 y_minus_x: Fe([26942781,-2315317,9129564,-4906607,26024105,11769399,-11518837,6367194,-9727230,4782140]),
2626 xy2d: Fe([19916461,-4828410,-22910704,-11414391,25606324,-5972441,33253853,8220911,6358847,-1873857]),
2627 },
2628 GePrecomp {
2629 y_plus_x: Fe([801428,-2081702,16569428,11065167,29875704,96627,7908388,-4480480,-13538503,1387155]),
2630 y_minus_x: Fe([19646058,5720633,-11416706,12814209,11607948,12749789,14147075,15156355,-21866831,11835260]),
2631 xy2d: Fe([19299512,1155910,28703737,14890794,2925026,7269399,26121523,15467869,-26560550,5052483]),
2632 },
2633 ],
2634 [
2635 GePrecomp {
2636 y_plus_x: Fe([-3017432,10058206,1980837,3964243,22160966,12322533,-6431123,-12618185,12228557,-7003677]),
2637 y_minus_x: Fe([32944382,14922211,-22844894,5188528,21913450,-8719943,4001465,13238564,-6114803,8653815]),
2638 xy2d: Fe([22865569,-4652735,27603668,-12545395,14348958,8234005,24808405,5719875,28483275,2841751]),
2639 },
2640 GePrecomp {
2641 y_plus_x: Fe([-16420968,-1113305,-327719,-12107856,21886282,-15552774,-1887966,-315658,19932058,-12739203]),
2642 y_minus_x: Fe([-11656086,10087521,-8864888,-5536143,-19278573,-3055912,3999228,13239134,-4777469,-13910208]),
2643 xy2d: Fe([1382174,-11694719,17266790,9194690,-13324356,9720081,20403944,11284705,-14013818,3093230]),
2644 },
2645 GePrecomp {
2646 y_plus_x: Fe([16650921,-11037932,-1064178,1570629,-8329746,7352753,-302424,16271225,-24049421,-6691850]),
2647 y_minus_x: Fe([-21911077,-5927941,-4611316,-5560156,-31744103,-10785293,24123614,15193618,-21652117,-16739389]),
2648 xy2d: Fe([-9935934,-4289447,-25279823,4372842,2087473,10399484,31870908,14690798,17361620,11864968]),
2649 },
2650 GePrecomp {
2651 y_plus_x: Fe([-11307610,6210372,13206574,5806320,-29017692,-13967200,-12331205,-7486601,-25578460,-16240689]),
2652 y_minus_x: Fe([14668462,-12270235,26039039,15305210,25515617,4542480,10453892,6577524,9145645,-6443880]),
2653 xy2d: Fe([5974874,3053895,-9433049,-10385191,-31865124,3225009,-7972642,3936128,-5652273,-3050304]),
2654 },
2655 GePrecomp {
2656 y_plus_x: Fe([30625386,-4729400,-25555961,-12792866,-20484575,7695099,17097188,-16303496,-27999779,1803632]),
2657 y_minus_x: Fe([-3553091,9865099,-5228566,4272701,-5673832,-16689700,14911344,12196514,-21405489,7047412]),
2658 xy2d: Fe([20093277,9920966,-11138194,-5343857,13161587,12044805,-32856851,4124601,-32343828,-10257566]),
2659 },
2660 GePrecomp {
2661 y_plus_x: Fe([-20788824,14084654,-13531713,7842147,19119038,-13822605,4752377,-8714640,-21679658,2288038]),
2662 y_minus_x: Fe([-26819236,-3283715,29965059,3039786,-14473765,2540457,29457502,14625692,-24819617,12570232]),
2663 xy2d: Fe([-1063558,-11551823,16920318,12494842,1278292,-5869109,-21159943,-3498680,-11974704,4724943]),
2664 },
2665 GePrecomp {
2666 y_plus_x: Fe([17960970,-11775534,-4140968,-9702530,-8876562,-1410617,-12907383,-8659932,-29576300,1903856]),
2667 y_minus_x: Fe([23134274,-14279132,-10681997,-1611936,20684485,15770816,-12989750,3190296,26955097,14109738]),
2668 xy2d: Fe([15308788,5320727,-30113809,-14318877,22902008,7767164,29425325,-11277562,31960942,11934971]),
2669 },
2670 GePrecomp {
2671 y_plus_x: Fe([-27395711,8435796,4109644,12222639,-24627868,14818669,20638173,4875028,10491392,1379718]),
2672 y_minus_x: Fe([-13159415,9197841,3875503,-8936108,-1383712,-5879801,33518459,16176658,21432314,12180697]),
2673 xy2d: Fe([-11787308,11500838,13787581,-13832590,-22430679,10140205,1465425,12689540,-10301319,-13872883]),
2674 },
2675 ],
2676 [
2677 GePrecomp {
2678 y_plus_x: Fe([5414091,-15386041,-21007664,9643570,12834970,1186149,-2622916,-1342231,26128231,6032912]),
2679 y_minus_x: Fe([-26337395,-13766162,32496025,-13653919,17847801,-12669156,3604025,8316894,-25875034,-10437358]),
2680 xy2d: Fe([3296484,6223048,24680646,-12246460,-23052020,5903205,-8862297,-4639164,12376617,3188849]),
2681 },
2682 GePrecomp {
2683 y_plus_x: Fe([29190488,-14659046,27549113,-1183516,3520066,-10697301,32049515,-7309113,-16109234,-9852307]),
2684 y_minus_x: Fe([-14744486,-9309156,735818,-598978,-20407687,-5057904,25246078,-15795669,18640741,-960977]),
2685 xy2d: Fe([-6928835,-16430795,10361374,5642961,4910474,12345252,-31638386,-494430,10530747,1053335]),
2686 },
2687 GePrecomp {
2688 y_plus_x: Fe([-29265967,-14186805,-13538216,-12117373,-19457059,-10655384,-31462369,-2948985,24018831,15026644]),
2689 y_minus_x: Fe([-22592535,-3145277,-2289276,5953843,-13440189,9425631,25310643,13003497,-2314791,-15145616]),
2690 xy2d: Fe([-27419985,-603321,-8043984,-1669117,-26092265,13987819,-27297622,187899,-23166419,-2531735]),
2691 },
2692 GePrecomp {
2693 y_plus_x: Fe([-21744398,-13810475,1844840,5021428,-10434399,-15911473,9716667,16266922,-5070217,726099]),
2694 y_minus_x: Fe([29370922,-6053998,7334071,-15342259,9385287,2247707,-13661962,-4839461,30007388,-15823341]),
2695 xy2d: Fe([-936379,16086691,23751945,-543318,-1167538,-5189036,9137109,730663,9835848,4555336]),
2696 },
2697 GePrecomp {
2698 y_plus_x: Fe([-23376435,1410446,-22253753,-12899614,30867635,15826977,17693930,544696,-11985298,12422646]),
2699 y_minus_x: Fe([31117226,-12215734,-13502838,6561947,-9876867,-12757670,-5118685,-4096706,29120153,13924425]),
2700 xy2d: Fe([-17400879,-14233209,19675799,-2734756,-11006962,-5858820,-9383939,-11317700,7240931,-237388]),
2701 },
2702 GePrecomp {
2703 y_plus_x: Fe([-31361739,-11346780,-15007447,-5856218,-22453340,-12152771,1222336,4389483,3293637,-15551743]),
2704 y_minus_x: Fe([-16684801,-14444245,11038544,11054958,-13801175,-3338533,-24319580,7733547,12796905,-6335822]),
2705 xy2d: Fe([-8759414,-10817836,-25418864,10783769,-30615557,-9746811,-28253339,3647836,3222231,-11160462]),
2706 },
2707 GePrecomp {
2708 y_plus_x: Fe([18606113,1693100,-25448386,-15170272,4112353,10045021,23603893,-2048234,-7550776,2484985]),
2709 y_minus_x: Fe([9255317,-3131197,-12156162,-1004256,13098013,-9214866,16377220,-2102812,-19802075,-3034702]),
2710 xy2d: Fe([-22729289,7496160,-5742199,11329249,19991973,-3347502,-31718148,9936966,-30097688,-10618797]),
2711 },
2712 GePrecomp {
2713 y_plus_x: Fe([21878590,-5001297,4338336,13643897,-3036865,13160960,19708896,5415497,-7360503,-4109293]),
2714 y_minus_x: Fe([27736861,10103576,12500508,8502413,-3413016,-9633558,10436918,-1550276,-23659143,-8132100]),
2715 xy2d: Fe([19492550,-12104365,-29681976,-852630,-3208171,12403437,30066266,8367329,13243957,8709688]),
2716 },
2717 ],
2718 [
2719 GePrecomp {
2720 y_plus_x: Fe([12015105,2801261,28198131,10151021,24818120,-4743133,-11194191,-5645734,5150968,7274186]),
2721 y_minus_x: Fe([2831366,-12492146,1478975,6122054,23825128,-12733586,31097299,6083058,31021603,-9793610]),
2722 xy2d: Fe([-2529932,-2229646,445613,10720828,-13849527,-11505937,-23507731,16354465,15067285,-14147707]),
2723 },
2724 GePrecomp {
2725 y_plus_x: Fe([7840942,14037873,-33364863,15934016,-728213,-3642706,21403988,1057586,-19379462,-12403220]),
2726 y_minus_x: Fe([915865,-16469274,15608285,-8789130,-24357026,6060030,-17371319,8410997,-7220461,16527025]),
2727 xy2d: Fe([32922597,-556987,20336074,-16184568,10903705,-5384487,16957574,52992,23834301,6588044]),
2728 },
2729 GePrecomp {
2730 y_plus_x: Fe([32752030,11232950,3381995,-8714866,22652988,-10744103,17159699,16689107,-20314580,-1305992]),
2731 y_minus_x: Fe([-4689649,9166776,-25710296,-10847306,11576752,12733943,7924251,-2752281,1976123,-7249027]),
2732 xy2d: Fe([21251222,16309901,-2983015,-6783122,30810597,12967303,156041,-3371252,12331345,-8237197]),
2733 },
2734 GePrecomp {
2735 y_plus_x: Fe([8651614,-4477032,-16085636,-4996994,13002507,2950805,29054427,-5106970,10008136,-4667901]),
2736 y_minus_x: Fe([31486080,15114593,-14261250,12951354,14369431,-7387845,16347321,-13662089,8684155,-10532952]),
2737 xy2d: Fe([19443825,11385320,24468943,-9659068,-23919258,2187569,-26263207,-6086921,31316348,14219878]),
2738 },
2739 GePrecomp {
2740 y_plus_x: Fe([-28594490,1193785,32245219,11392485,31092169,15722801,27146014,6992409,29126555,9207390]),
2741 y_minus_x: Fe([32382935,1110093,18477781,11028262,-27411763,-7548111,-4980517,10843782,-7957600,-14435730]),
2742 xy2d: Fe([2814918,7836403,27519878,-7868156,-20894015,-11553689,-21494559,8550130,28346258,1994730]),
2743 },
2744 GePrecomp {
2745 y_plus_x: Fe([-19578299,8085545,-14000519,-3948622,2785838,-16231307,-19516951,7174894,22628102,8115180]),
2746 y_minus_x: Fe([-30405132,955511,-11133838,-15078069,-32447087,-13278079,-25651578,3317160,-9943017,930272]),
2747 xy2d: Fe([-15303681,-6833769,28856490,1357446,23421993,1057177,24091212,-1388970,-22765376,-10650715]),
2748 },
2749 GePrecomp {
2750 y_plus_x: Fe([-22751231,-5303997,-12907607,-12768866,-15811511,-7797053,-14839018,-16554220,-1867018,8398970]),
2751 y_minus_x: Fe([-31969310,2106403,-4736360,1362501,12813763,16200670,22981545,-6291273,18009408,-15772772]),
2752 xy2d: Fe([-17220923,-9545221,-27784654,14166835,29815394,7444469,29551787,-3727419,19288549,1325865]),
2753 },
2754 GePrecomp {
2755 y_plus_x: Fe([15100157,-15835752,-23923978,-1005098,-26450192,15509408,12376730,-3479146,33166107,-8042750]),
2756 y_minus_x: Fe([20909231,13023121,-9209752,16251778,-5778415,-8094914,12412151,10018715,2213263,-13878373]),
2757 xy2d: Fe([32529814,-11074689,30361439,-16689753,-9135940,1513226,22922121,6382134,-5766928,8371348]),
2758 },
2759 ],
2760 [
2761 GePrecomp {
2762 y_plus_x: Fe([9923462,11271500,12616794,3544722,-29998368,-1721626,12891687,-8193132,-26442943,10486144]),
2763 y_minus_x: Fe([-22597207,-7012665,8587003,-8257861,4084309,-12970062,361726,2610596,-23921530,-11455195]),
2764 xy2d: Fe([5408411,-1136691,-4969122,10561668,24145918,14240566,31319731,-4235541,19985175,-3436086]),
2765 },
2766 GePrecomp {
2767 y_plus_x: Fe([-13994457,16616821,14549246,3341099,32155958,13648976,-17577068,8849297,65030,8370684]),
2768 y_minus_x: Fe([-8320926,-12049626,31204563,5839400,-20627288,-1057277,-19442942,6922164,12743482,-9800518]),
2769 xy2d: Fe([-2361371,12678785,28815050,4759974,-23893047,4884717,23783145,11038569,18800704,255233]),
2770 },
2771 GePrecomp {
2772 y_plus_x: Fe([-5269658,-1773886,13957886,7990715,23132995,728773,13393847,9066957,19258688,-14753793]),
2773 y_minus_x: Fe([-2936654,-10827535,-10432089,14516793,-3640786,4372541,-31934921,2209390,-1524053,2055794]),
2774 xy2d: Fe([580882,16705327,5468415,-2683018,-30926419,-14696000,-7203346,-8994389,-30021019,7394435]),
2775 },
2776 GePrecomp {
2777 y_plus_x: Fe([23838809,1822728,-15738443,15242727,8318092,-3733104,-21672180,-3492205,-4821741,14799921]),
2778 y_minus_x: Fe([13345610,9759151,3371034,-16137791,16353039,8577942,31129804,13496856,-9056018,7402518]),
2779 xy2d: Fe([2286874,-4435931,-20042458,-2008336,-13696227,5038122,11006906,-15760352,8205061,1607563]),
2780 },
2781 GePrecomp {
2782 y_plus_x: Fe([14414086,-8002132,3331830,-3208217,22249151,-5594188,18364661,-2906958,30019587,-9029278]),
2783 y_minus_x: Fe([-27688051,1585953,-10775053,931069,-29120221,-11002319,-14410829,12029093,9944378,8024]),
2784 xy2d: Fe([4368715,-3709630,29874200,-15022983,-20230386,-11410704,-16114594,-999085,-8142388,5640030]),
2785 },
2786 GePrecomp {
2787 y_plus_x: Fe([10299610,13746483,11661824,16234854,7630238,5998374,9809887,-16694564,15219798,-14327783]),
2788 y_minus_x: Fe([27425505,-5719081,3055006,10660664,23458024,595578,-15398605,-1173195,-18342183,9742717]),
2789 xy2d: Fe([6744077,2427284,26042789,2720740,-847906,1118974,32324614,7406442,12420155,1994844]),
2790 },
2791 GePrecomp {
2792 y_plus_x: Fe([14012521,-5024720,-18384453,-9578469,-26485342,-3936439,-13033478,-10909803,24319929,-6446333]),
2793 y_minus_x: Fe([16412690,-4507367,10772641,15929391,-17068788,-4658621,10555945,-10484049,-30102368,-4739048]),
2794 xy2d: Fe([22397382,-7767684,-9293161,-12792868,17166287,-9755136,-27333065,6199366,21880021,-12250760]),
2795 },
2796 GePrecomp {
2797 y_plus_x: Fe([-4283307,5368523,-31117018,8163389,-30323063,3209128,16557151,8890729,8840445,4957760]),
2798 y_minus_x: Fe([-15447727,709327,-6919446,-10870178,-29777922,6522332,-21720181,12130072,-14796503,5005757]),
2799 xy2d: Fe([-2114751,-14308128,23019042,15765735,-25269683,6002752,10183197,-13239326,-16395286,-2176112]),
2800 },
2801 ],
2802 [
2803 GePrecomp {
2804 y_plus_x: Fe([-19025756,1632005,13466291,-7995100,-23640451,16573537,-32013908,-3057104,22208662,2000468]),
2805 y_minus_x: Fe([3065073,-1412761,-25598674,-361432,-17683065,-5703415,-8164212,11248527,-3691214,-7414184]),
2806 xy2d: Fe([10379208,-6045554,8877319,1473647,-29291284,-12507580,16690915,2553332,-3132688,16400289]),
2807 },
2808 GePrecomp {
2809 y_plus_x: Fe([15716668,1254266,-18472690,7446274,-8448918,6344164,-22097271,-7285580,26894937,9132066]),
2810 y_minus_x: Fe([24158887,12938817,11085297,-8177598,-28063478,-4457083,-30576463,64452,-6817084,-2692882]),
2811 xy2d: Fe([13488534,7794716,22236231,5989356,25426474,-12578208,2350710,-3418511,-4688006,2364226]),
2812 },
2813 GePrecomp {
2814 y_plus_x: Fe([16335052,9132434,25640582,6678888,1725628,8517937,-11807024,-11697457,15445875,-7798101]),
2815 y_minus_x: Fe([29004207,-7867081,28661402,-640412,-12794003,-7943086,31863255,-4135540,-278050,-15759279]),
2816 xy2d: Fe([-6122061,-14866665,-28614905,14569919,-10857999,-3591829,10343412,-6976290,-29828287,-10815811]),
2817 },
2818 GePrecomp {
2819 y_plus_x: Fe([27081650,3463984,14099042,-4517604,1616303,-6205604,29542636,15372179,17293797,960709]),
2820 y_minus_x: Fe([20263915,11434237,-5765435,11236810,13505955,-10857102,-16111345,6493122,-19384511,7639714]),
2821 xy2d: Fe([-2830798,-14839232,25403038,-8215196,-8317012,-16173699,18006287,-16043750,29994677,-15808121]),
2822 },
2823 GePrecomp {
2824 y_plus_x: Fe([9769828,5202651,-24157398,-13631392,-28051003,-11561624,-24613141,-13860782,-31184575,709464]),
2825 y_minus_x: Fe([12286395,13076066,-21775189,-1176622,-25003198,4057652,-32018128,-8890874,16102007,13205847]),
2826 xy2d: Fe([13733362,5599946,10557076,3195751,-5557991,8536970,-25540170,8525972,10151379,10394400]),
2827 },
2828 GePrecomp {
2829 y_plus_x: Fe([4024660,-16137551,22436262,12276534,-9099015,-2686099,19698229,11743039,-33302334,8934414]),
2830 y_minus_x: Fe([-15879800,-4525240,-8580747,-2934061,14634845,-698278,-9449077,3137094,-11536886,11721158]),
2831 xy2d: Fe([17555939,-5013938,8268606,2331751,-22738815,9761013,9319229,8835153,-9205489,-1280045]),
2832 },
2833 GePrecomp {
2834 y_plus_x: Fe([-461409,-7830014,20614118,16688288,-7514766,-4807119,22300304,505429,6108462,-6183415]),
2835 y_minus_x: Fe([-5070281,12367917,-30663534,3234473,32617080,-8422642,29880583,-13483331,-26898490,-7867459]),
2836 xy2d: Fe([-31975283,5726539,26934134,10237677,-3173717,-605053,24199304,3795095,7592688,-14992079]),
2837 },
2838 GePrecomp {
2839 y_plus_x: Fe([21594432,-14964228,17466408,-4077222,32537084,2739898,6407723,12018833,-28256052,4298412]),
2840 y_minus_x: Fe([-20650503,-11961496,-27236275,570498,3767144,-1717540,13891942,-1569194,13717174,10805743]),
2841 xy2d: Fe([-14676630,-15644296,15287174,11927123,24177847,-8175568,-796431,14860609,-26938930,-5863836]),
2842 },
2843 ],
2844 [
2845 GePrecomp {
2846 y_plus_x: Fe([12962541,5311799,-10060768,11658280,18855286,-7954201,13286263,-12808704,-4381056,9882022]),
2847 y_minus_x: Fe([18512079,11319350,-20123124,15090309,18818594,5271736,-22727904,3666879,-23967430,-3299429]),
2848 xy2d: Fe([-6789020,-3146043,16192429,13241070,15898607,-14206114,-10084880,-6661110,-2403099,5276065]),
2849 },
2850 GePrecomp {
2851 y_plus_x: Fe([30169808,-5317648,26306206,-11750859,27814964,7069267,7152851,3684982,1449224,13082861]),
2852 y_minus_x: Fe([10342826,3098505,2119311,193222,25702612,12233820,23697382,15056736,-21016438,-8202000]),
2853 xy2d: Fe([-33150110,3261608,22745853,7948688,19370557,-15177665,-26171976,6482814,-10300080,-11060101]),
2854 },
2855 GePrecomp {
2856 y_plus_x: Fe([32869458,-5408545,25609743,15678670,-10687769,-15471071,26112421,2521008,-22664288,6904815]),
2857 y_minus_x: Fe([29506923,4457497,3377935,-9796444,-30510046,12935080,1561737,3841096,-29003639,-6657642]),
2858 xy2d: Fe([10340844,-6630377,-18656632,-2278430,12621151,-13339055,30878497,-11824370,-25584551,5181966]),
2859 },
2860 GePrecomp {
2861 y_plus_x: Fe([25940115,-12658025,17324188,-10307374,-8671468,15029094,24396252,-16450922,-2322852,-12388574]),
2862 y_minus_x: Fe([-21765684,9916823,-1300409,4079498,-1028346,11909559,1782390,12641087,20603771,-6561742]),
2863 xy2d: Fe([-18882287,-11673380,24849422,11501709,13161720,-4768874,1925523,11914390,4662781,7820689]),
2864 },
2865 GePrecomp {
2866 y_plus_x: Fe([12241050,-425982,8132691,9393934,32846760,-1599620,29749456,12172924,16136752,15264020]),
2867 y_minus_x: Fe([-10349955,-14680563,-8211979,2330220,-17662549,-14545780,10658213,6671822,19012087,3772772]),
2868 xy2d: Fe([3753511,-3421066,10617074,2028709,14841030,-6721664,28718732,-15762884,20527771,12988982]),
2869 },
2870 GePrecomp {
2871 y_plus_x: Fe([-14822485,-5797269,-3707987,12689773,-898983,-10914866,-24183046,-10564943,3299665,-12424953]),
2872 y_minus_x: Fe([-16777703,-15253301,-9642417,4978983,3308785,8755439,6943197,6461331,-25583147,8991218]),
2873 xy2d: Fe([-17226263,1816362,-1673288,-6086439,31783888,-8175991,-32948145,7417950,-30242287,1507265]),
2874 },
2875 GePrecomp {
2876 y_plus_x: Fe([29692663,6829891,-10498800,4334896,20945975,-11906496,-28887608,8209391,14606362,-10647073]),
2877 y_minus_x: Fe([-3481570,8707081,32188102,5672294,22096700,1711240,-33020695,9761487,4170404,-2085325]),
2878 xy2d: Fe([-11587470,14855945,-4127778,-1531857,-26649089,15084046,22186522,16002000,-14276837,-8400798]),
2879 },
2880 GePrecomp {
2881 y_plus_x: Fe([-4811456,13761029,-31703877,-2483919,-3312471,7869047,-7113572,-9620092,13240845,10965870]),
2882 y_minus_x: Fe([-7742563,-8256762,-14768334,-13656260,-23232383,12387166,4498947,14147411,29514390,4302863]),
2883 xy2d: Fe([-13413405,-12407859,20757302,-13801832,14785143,8976368,-5061276,-2144373,17846988,-13971927]),
2884 },
2885 ],
2886 [
2887 GePrecomp {
2888 y_plus_x: Fe([-2244452,-754728,-4597030,-1066309,-6247172,1455299,-21647728,-9214789,-5222701,12650267]),
2889 y_minus_x: Fe([-9906797,-16070310,21134160,12198166,-27064575,708126,387813,13770293,-19134326,10958663]),
2890 xy2d: Fe([22470984,12369526,23446014,-5441109,-21520802,-9698723,-11772496,-11574455,-25083830,4271862]),
2891 },
2892 GePrecomp {
2893 y_plus_x: Fe([-25169565,-10053642,-19909332,15361595,-5984358,2159192,75375,-4278529,-32526221,8469673]),
2894 y_minus_x: Fe([15854970,4148314,-8893890,7259002,11666551,13824734,-30531198,2697372,24154791,-9460943]),
2895 xy2d: Fe([15446137,-15806644,29759747,14019369,30811221,-9610191,-31582008,12840104,24913809,9815020]),
2896 },
2897 GePrecomp {
2898 y_plus_x: Fe([-4709286,-5614269,-31841498,-12288893,-14443537,10799414,-9103676,13438769,18735128,9466238]),
2899 y_minus_x: Fe([11933045,9281483,5081055,-5183824,-2628162,-4905629,-7727821,-10896103,-22728655,16199064]),
2900 xy2d: Fe([14576810,379472,-26786533,-8317236,-29426508,-10812974,-102766,1876699,30801119,2164795]),
2901 },
2902 GePrecomp {
2903 y_plus_x: Fe([15995086,3199873,13672555,13712240,-19378835,-4647646,-13081610,-15496269,-13492807,1268052]),
2904 y_minus_x: Fe([-10290614,-3659039,-3286592,10948818,23037027,3794475,-3470338,-12600221,-17055369,3565904]),
2905 xy2d: Fe([29210088,-9419337,-5919792,-4952785,10834811,-13327726,-16512102,-10820713,-27162222,-14030531]),
2906 },
2907 GePrecomp {
2908 y_plus_x: Fe([-13161890,15508588,16663704,-8156150,-28349942,9019123,-29183421,-3769423,2244111,-14001979]),
2909 y_minus_x: Fe([-5152875,-3800936,-9306475,-6071583,16243069,14684434,-25673088,-16180800,13491506,4641841]),
2910 xy2d: Fe([10813417,643330,-19188515,-728916,30292062,-16600078,27548447,-7721242,14476989,-12767431]),
2911 },
2912 GePrecomp {
2913 y_plus_x: Fe([10292079,9984945,6481436,8279905,-7251514,7032743,27282937,-1644259,-27912810,12651324]),
2914 y_minus_x: Fe([-31185513,-813383,22271204,11835308,10201545,15351028,17099662,3988035,21721536,-3148940]),
2915 xy2d: Fe([10202177,-6545839,-31373232,-9574638,-32150642,-8119683,-12906320,3852694,13216206,14842320]),
2916 },
2917 GePrecomp {
2918 y_plus_x: Fe([-15815640,-10601066,-6538952,-7258995,-6984659,-6581778,-31500847,13765824,-27434397,9900184]),
2919 y_minus_x: Fe([14465505,-13833331,-32133984,-14738873,-27443187,12990492,33046193,15796406,-7051866,-8040114]),
2920 xy2d: Fe([30924417,-8279620,6359016,-12816335,16508377,9071735,-25488601,15413635,9524356,-7018878]),
2921 },
2922 GePrecomp {
2923 y_plus_x: Fe([12274201,-13175547,32627641,-1785326,6736625,13267305,5237659,-5109483,15663516,4035784]),
2924 y_minus_x: Fe([-2951309,8903985,17349946,601635,-16432815,-4612556,-13732739,-15889334,-22258478,4659091]),
2925 xy2d: Fe([-16916263,-4952973,-30393711,-15158821,20774812,15897498,5736189,15026997,-2178256,-13455585]),
2926 },
2927 ],
2928 [
2929 GePrecomp {
2930 y_plus_x: Fe([-8858980,-2219056,28571666,-10155518,-474467,-10105698,-3801496,278095,23440562,-290208]),
2931 y_minus_x: Fe([10226241,-5928702,15139956,120818,-14867693,5218603,32937275,11551483,-16571960,-7442864]),
2932 xy2d: Fe([17932739,-12437276,-24039557,10749060,11316803,7535897,22503767,5561594,-3646624,3898661]),
2933 },
2934 GePrecomp {
2935 y_plus_x: Fe([7749907,-969567,-16339731,-16464,-25018111,15122143,-1573531,7152530,21831162,1245233]),
2936 y_minus_x: Fe([26958459,-14658026,4314586,8346991,-5677764,11960072,-32589295,-620035,-30402091,-16716212]),
2937 xy2d: Fe([-12165896,9166947,33491384,13673479,29787085,13096535,6280834,14587357,-22338025,13987525]),
2938 },
2939 GePrecomp {
2940 y_plus_x: Fe([-24349909,7778775,21116000,15572597,-4833266,-5357778,-4300898,-5124639,-7469781,-2858068]),
2941 y_minus_x: Fe([9681908,-6737123,-31951644,13591838,-6883821,386950,31622781,6439245,-14581012,4091397]),
2942 xy2d: Fe([-8426427,1470727,-28109679,-1596990,3978627,-5123623,-19622683,12092163,29077877,-14741988]),
2943 },
2944 GePrecomp {
2945 y_plus_x: Fe([5269168,-6859726,-13230211,-8020715,25932563,1763552,-5606110,-5505881,-20017847,2357889]),
2946 y_minus_x: Fe([32264008,-15407652,-5387735,-1160093,-2091322,-3946900,23104804,-12869908,5727338,189038]),
2947 xy2d: Fe([14609123,-8954470,-6000566,-16622781,-14577387,-7743898,-26745169,10942115,-25888931,-14884697]),
2948 },
2949 GePrecomp {
2950 y_plus_x: Fe([20513500,5557931,-15604613,7829531,26413943,-2019404,-21378968,7471781,13913677,-5137875]),
2951 y_minus_x: Fe([-25574376,11967826,29233242,12948236,-6754465,4713227,-8940970,14059180,12878652,8511905]),
2952 xy2d: Fe([-25656801,3393631,-2955415,-7075526,-2250709,9366908,-30223418,6812974,5568676,-3127656]),
2953 },
2954 GePrecomp {
2955 y_plus_x: Fe([11630004,12144454,2116339,13606037,27378885,15676917,-17408753,-13504373,-14395196,8070818]),
2956 y_minus_x: Fe([27117696,-10007378,-31282771,-5570088,1127282,12772488,-29845906,10483306,-11552749,-1028714]),
2957 xy2d: Fe([10637467,-5688064,5674781,1072708,-26343588,-6982302,-1683975,9177853,-27493162,15431203]),
2958 },
2959 GePrecomp {
2960 y_plus_x: Fe([20525145,10892566,-12742472,12779443,-29493034,16150075,-28240519,14943142,-15056790,-7935931]),
2961 y_minus_x: Fe([-30024462,5626926,-551567,-9981087,753598,11981191,25244767,-3239766,-3356550,9594024]),
2962 xy2d: Fe([-23752644,2636870,-5163910,-10103818,585134,7877383,11345683,-6492290,13352335,-10977084]),
2963 },
2964 GePrecomp {
2965 y_plus_x: Fe([-1931799,-5407458,3304649,-12884869,17015806,-4877091,-29783850,-7752482,-13215537,-319204]),
2966 y_minus_x: Fe([20239939,6607058,6203985,3483793,-18386976,-779229,-20723742,15077870,-22750759,14523817]),
2967 xy2d: Fe([27406042,-6041657,27423596,-4497394,4996214,10002360,-28842031,-4545494,-30172742,-4805667]),
2968 },
2969 ],
2970 [
2971 GePrecomp {
2972 y_plus_x: Fe([11374242,12660715,17861383,-12540833,10935568,1099227,-13886076,-9091740,-27727044,11358504]),
2973 y_minus_x: Fe([-12730809,10311867,1510375,10778093,-2119455,-9145702,32676003,11149336,-26123651,4985768]),
2974 xy2d: Fe([-19096303,341147,-6197485,-239033,15756973,-8796662,-983043,13794114,-19414307,-15621255]),
2975 },
2976 GePrecomp {
2977 y_plus_x: Fe([6490081,11940286,25495923,-7726360,8668373,-8751316,3367603,6970005,-1691065,-9004790]),
2978 y_minus_x: Fe([1656497,13457317,15370807,6364910,13605745,8362338,-19174622,-5475723,-16796596,-5031438]),
2979 xy2d: Fe([-22273315,-13524424,-64685,-4334223,-18605636,-10921968,-20571065,-7007978,-99853,-10237333]),
2980 },
2981 GePrecomp {
2982 y_plus_x: Fe([17747465,10039260,19368299,-4050591,-20630635,-16041286,31992683,-15857976,-29260363,-5511971]),
2983 y_minus_x: Fe([31932027,-4986141,-19612382,16366580,22023614,88450,11371999,-3744247,4882242,-10626905]),
2984 xy2d: Fe([29796507,37186,19818052,10115756,-11829032,3352736,18551198,3272828,-5190932,-4162409]),
2985 },
2986 GePrecomp {
2987 y_plus_x: Fe([12501286,4044383,-8612957,-13392385,-32430052,5136599,-19230378,-3529697,330070,-3659409]),
2988 y_minus_x: Fe([6384877,2899513,17807477,7663917,-2358888,12363165,25366522,-8573892,-271295,12071499]),
2989 xy2d: Fe([-8365515,-4042521,25133448,-4517355,-6211027,2265927,-32769618,1936675,-5159697,3829363]),
2990 },
2991 GePrecomp {
2992 y_plus_x: Fe([28425966,-5835433,-577090,-4697198,-14217555,6870930,7921550,-6567787,26333140,14267664]),
2993 y_minus_x: Fe([-11067219,11871231,27385719,-10559544,-4585914,-11189312,10004786,-8709488,-21761224,8930324]),
2994 xy2d: Fe([-21197785,-16396035,25654216,-1725397,12282012,11008919,1541940,4757911,-26491501,-16408940]),
2995 },
2996 GePrecomp {
2997 y_plus_x: Fe([13537262,-7759490,-20604840,10961927,-5922820,-13218065,-13156584,6217254,-15943699,13814990]),
2998 y_minus_x: Fe([-17422573,15157790,18705543,29619,24409717,-260476,27361681,9257833,-1956526,-1776914]),
2999 xy2d: Fe([-25045300,-10191966,15366585,15166509,-13105086,8423556,-29171540,12361135,-18685978,4578290]),
3000 },
3001 GePrecomp {
3002 y_plus_x: Fe([24579768,3711570,1342322,-11180126,-27005135,14124956,-22544529,14074919,21964432,8235257]),
3003 y_minus_x: Fe([-6528613,-2411497,9442966,-5925588,12025640,-1487420,-2981514,-1669206,13006806,2355433]),
3004 xy2d: Fe([-16304899,-13605259,-6632427,-5142349,16974359,-10911083,27202044,1719366,1141648,-12796236]),
3005 },
3006 GePrecomp {
3007 y_plus_x: Fe([-12863944,-13219986,-8318266,-11018091,-6810145,-4843894,13475066,-3133972,32674895,13715045]),
3008 y_minus_x: Fe([11423335,-5468059,32344216,8962751,24989809,9241752,-13265253,16086212,-28740881,-15642093]),
3009 xy2d: Fe([-1409668,12530728,-6368726,10847387,19531186,-14132160,-11709148,7791794,-27245943,4383347]),
3010 },
3011 ],
3012 [
3013 GePrecomp {
3014 y_plus_x: Fe([-28970898,5271447,-1266009,-9736989,-12455236,16732599,-4862407,-4906449,27193557,6245191]),
3015 y_minus_x: Fe([-15193956,5362278,-1783893,2695834,4960227,12840725,23061898,3260492,22510453,8577507]),
3016 xy2d: Fe([-12632451,11257346,-32692994,13548177,-721004,10879011,31168030,13952092,-29571492,-3635906]),
3017 },
3018 GePrecomp {
3019 y_plus_x: Fe([3877321,-9572739,32416692,5405324,-11004407,-13656635,3759769,11935320,5611860,8164018]),
3020 y_minus_x: Fe([-16275802,14667797,15906460,12155291,-22111149,-9039718,32003002,-8832289,5773085,-8422109]),
3021 xy2d: Fe([-23788118,-8254300,1950875,8937633,18686727,16459170,-905725,12376320,31632953,190926]),
3022 },
3023 GePrecomp {
3024 y_plus_x: Fe([-24593607,-16138885,-8423991,13378746,14162407,6901328,-8288749,4508564,-25341555,-3627528]),
3025 y_minus_x: Fe([8884438,-5884009,6023974,10104341,-6881569,-4941533,18722941,-14786005,-1672488,827625]),
3026 xy2d: Fe([-32720583,-16289296,-32503547,7101210,13354605,2659080,-1800575,-14108036,-24878478,1541286]),
3027 },
3028 GePrecomp {
3029 y_plus_x: Fe([2901347,-1117687,3880376,-10059388,-17620940,-3612781,-21802117,-3567481,20456845,-1885033]),
3030 y_minus_x: Fe([27019610,12299467,-13658288,-1603234,-12861660,-4861471,-19540150,-5016058,29439641,15138866]),
3031 xy2d: Fe([21536104,-6626420,-32447818,-10690208,-22408077,5175814,-5420040,-16361163,7779328,109896]),
3032 },
3033 GePrecomp {
3034 y_plus_x: Fe([30279744,14648750,-8044871,6425558,13639621,-743509,28698390,12180118,23177719,-554075]),
3035 y_minus_x: Fe([26572847,3405927,-31701700,12890905,-19265668,5335866,-6493768,2378492,4439158,-13279347]),
3036 xy2d: Fe([-22716706,3489070,-9225266,-332753,18875722,-1140095,14819434,-12731527,-17717757,-5461437]),
3037 },
3038 GePrecomp {
3039 y_plus_x: Fe([-5056483,16566551,15953661,3767752,-10436499,15627060,-820954,2177225,8550082,-15114165]),
3040 y_minus_x: Fe([-18473302,16596775,-381660,15663611,22860960,15585581,-27844109,-3582739,-23260460,-8428588]),
3041 xy2d: Fe([-32480551,15707275,-8205912,-5652081,29464558,2713815,-22725137,15860482,-21902570,1494193]),
3042 },
3043 GePrecomp {
3044 y_plus_x: Fe([-19562091,-14087393,-25583872,-9299552,13127842,759709,21923482,16529112,8742704,12967017]),
3045 y_minus_x: Fe([-28464899,1553205,32536856,-10473729,-24691605,-406174,-8914625,-2933896,-29903758,15553883]),
3046 xy2d: Fe([21877909,3230008,9881174,10539357,-4797115,2841332,11543572,14513274,19375923,-12647961]),
3047 },
3048 GePrecomp {
3049 y_plus_x: Fe([8832269,-14495485,13253511,5137575,5037871,4078777,24880818,-6222716,2862653,9455043]),
3050 y_minus_x: Fe([29306751,5123106,20245049,-14149889,9592566,8447059,-2077124,-2990080,15511449,4789663]),
3051 xy2d: Fe([-20679756,7004547,8824831,-9434977,-4045704,-3750736,-5754762,108893,23513200,16652362]),
3052 },
3053 ],
3054 [
3055 GePrecomp {
3056 y_plus_x: Fe([-33256173,4144782,-4476029,-6579123,10770039,-7155542,-6650416,-12936300,-18319198,10212860]),
3057 y_minus_x: Fe([2756081,8598110,7383731,-6859892,22312759,-1105012,21179801,2600940,-9988298,-12506466]),
3058 xy2d: Fe([-24645692,13317462,-30449259,-15653928,21365574,-10869657,11344424,864440,-2499677,-16710063]),
3059 },
3060 GePrecomp {
3061 y_plus_x: Fe([-26432803,6148329,-17184412,-14474154,18782929,-275997,-22561534,211300,2719757,4940997]),
3062 y_minus_x: Fe([-1323882,3911313,-6948744,14759765,-30027150,7851207,21690126,8518463,26699843,5276295]),
3063 xy2d: Fe([-13149873,-6429067,9396249,365013,24703301,-10488939,1321586,149635,-15452774,7159369]),
3064 },
3065 GePrecomp {
3066 y_plus_x: Fe([9987780,-3404759,17507962,9505530,9731535,-2165514,22356009,8312176,22477218,-8403385]),
3067 y_minus_x: Fe([18155857,-16504990,19744716,9006923,15154154,-10538976,24256460,-4864995,-22548173,9334109]),
3068 xy2d: Fe([2986088,-4911893,10776628,-3473844,10620590,-7083203,-21413845,14253545,-22587149,536906]),
3069 },
3070 GePrecomp {
3071 y_plus_x: Fe([4377756,8115836,24567078,15495314,11625074,13064599,7390551,10589625,10838060,-15420424]),
3072 y_minus_x: Fe([-19342404,867880,9277171,-3218459,-14431572,-1986443,19295826,-15796950,6378260,699185]),
3073 xy2d: Fe([7895026,4057113,-7081772,-13077756,-17886831,-323126,-716039,15693155,-5045064,-13373962]),
3074 },
3075 GePrecomp {
3076 y_plus_x: Fe([-7737563,-5869402,-14566319,-7406919,11385654,13201616,31730678,-10962840,-3918636,-9669325]),
3077 y_minus_x: Fe([10188286,-15770834,-7336361,13427543,22223443,14896287,30743455,7116568,-21786507,5427593]),
3078 xy2d: Fe([696102,13206899,27047647,-10632082,15285305,-9853179,10798490,-4578720,19236243,12477404]),
3079 },
3080 GePrecomp {
3081 y_plus_x: Fe([-11229439,11243796,-17054270,-8040865,-788228,-8167967,-3897669,11180504,-23169516,7733644]),
3082 y_minus_x: Fe([17800790,-14036179,-27000429,-11766671,23887827,3149671,23466177,-10538171,10322027,15313801]),
3083 xy2d: Fe([26246234,11968874,32263343,-5468728,6830755,-13323031,-15794704,-101982,-24449242,10890804]),
3084 },
3085 GePrecomp {
3086 y_plus_x: Fe([-31365647,10271363,-12660625,-6267268,16690207,-13062544,-14982212,16484931,25180797,-5334884]),
3087 y_minus_x: Fe([-586574,10376444,-32586414,-11286356,19801893,10997610,2276632,9482883,316878,13820577]),
3088 xy2d: Fe([-9882808,-4510367,-2115506,16457136,-11100081,11674996,30756178,-7515054,30696930,-3712849]),
3089 },
3090 GePrecomp {
3091 y_plus_x: Fe([32988917,-9603412,12499366,7910787,-10617257,-11931514,-7342816,-9985397,-32349517,7392473]),
3092 y_minus_x: Fe([-8855661,15927861,9866406,-3649411,-2396914,-16655781,-30409476,-9134995,25112947,-2926644]),
3093 xy2d: Fe([-2504044,-436966,25621774,-5678772,15085042,-5479877,-24884878,-13526194,5537438,-13914319]),
3094 },
3095 ],
3096 [
3097 GePrecomp {
3098 y_plus_x: Fe([-11225584,2320285,-9584280,10149187,-33444663,5808648,-14876251,-1729667,31234590,6090599]),
3099 y_minus_x: Fe([-9633316,116426,26083934,2897444,-6364437,-2688086,609721,15878753,-6970405,-9034768]),
3100 xy2d: Fe([-27757857,247744,-15194774,-9002551,23288161,-10011936,-23869595,6503646,20650474,1804084]),
3101 },
3102 GePrecomp {
3103 y_plus_x: Fe([-27589786,15456424,8972517,8469608,15640622,4439847,3121995,-10329713,27842616,-202328]),
3104 y_minus_x: Fe([-15306973,2839644,22530074,10026331,4602058,5048462,28248656,5031932,-11375082,12714369]),
3105 xy2d: Fe([20807691,-7270825,29286141,11421711,-27876523,-13868230,-21227475,1035546,-19733229,12796920]),
3106 },
3107 GePrecomp {
3108 y_plus_x: Fe([12076899,-14301286,-8785001,-11848922,-25012791,16400684,-17591495,-12899438,3480665,-15182815]),
3109 y_minus_x: Fe([-32361549,5457597,28548107,7833186,7303070,-11953545,-24363064,-15921875,-33374054,2771025]),
3110 xy2d: Fe([-21389266,421932,26597266,6860826,22486084,-6737172,-17137485,-4210226,-24552282,15673397]),
3111 },
3112 GePrecomp {
3113 y_plus_x: Fe([-20184622,2338216,19788685,-9620956,-4001265,-8740893,-20271184,4733254,3727144,-12934448]),
3114 y_minus_x: Fe([6120119,814863,-11794402,-622716,6812205,-15747771,2019594,7975683,31123697,-10958981]),
3115 xy2d: Fe([30069250,-11435332,30434654,2958439,18399564,-976289,12296869,9204260,-16432438,9648165]),
3116 },
3117 GePrecomp {
3118 y_plus_x: Fe([32705432,-1550977,30705658,7451065,-11805606,9631813,3305266,5248604,-26008332,-11377501]),
3119 y_minus_x: Fe([17219865,2375039,-31570947,-5575615,-19459679,9219903,294711,15298639,2662509,-16297073]),
3120 xy2d: Fe([-1172927,-7558695,-4366770,-4287744,-21346413,-8434326,32087529,-1222777,32247248,-14389861]),
3121 },
3122 GePrecomp {
3123 y_plus_x: Fe([14312628,1221556,17395390,-8700143,-4945741,-8684635,-28197744,-9637817,-16027623,-13378845]),
3124 y_minus_x: Fe([-1428825,-9678990,-9235681,6549687,-7383069,-468664,23046502,9803137,17597934,2346211]),
3125 xy2d: Fe([18510800,15337574,26171504,981392,-22241552,7827556,-23491134,-11323352,3059833,-11782870]),
3126 },
3127 GePrecomp {
3128 y_plus_x: Fe([10141598,6082907,17829293,-1947643,9830092,13613136,-25556636,-5544586,-33502212,3592096]),
3129 y_minus_x: Fe([33114168,-15889352,-26525686,-13343397,33076705,8716171,1151462,1521897,-982665,-6837803]),
3130 xy2d: Fe([-32939165,-4255815,23947181,-324178,-33072974,-12305637,-16637686,3891704,26353178,693168]),
3131 },
3132 GePrecomp {
3133 y_plus_x: Fe([30374239,1595580,-16884039,13186931,4600344,406904,9585294,-400668,31375464,14369965]),
3134 y_minus_x: Fe([-14370654,-7772529,1510301,6434173,-18784789,-6262728,32732230,-13108839,17901441,16011505]),
3135 xy2d: Fe([18171223,-11934626,-12500402,15197122,-11038147,-15230035,-19172240,-16046376,8764035,12309598]),
3136 },
3137 ],
3138 [
3139 GePrecomp {
3140 y_plus_x: Fe([5975908,-5243188,-19459362,-9681747,-11541277,14015782,-23665757,1228319,17544096,-10593782]),
3141 y_minus_x: Fe([5811932,-1715293,3442887,-2269310,-18367348,-8359541,-18044043,-15410127,-5565381,12348900]),
3142 xy2d: Fe([-31399660,11407555,25755363,6891399,-3256938,14872274,-24849353,8141295,-10632534,-585479]),
3143 },
3144 GePrecomp {
3145 y_plus_x: Fe([-12675304,694026,-5076145,13300344,14015258,-14451394,-9698672,-11329050,30944593,1130208]),
3146 y_minus_x: Fe([8247766,-6710942,-26562381,-7709309,-14401939,-14648910,4652152,2488540,23550156,-271232]),
3147 xy2d: Fe([17294316,-3788438,7026748,15626851,22990044,113481,2267737,-5908146,-408818,-137719]),
3148 },
3149 GePrecomp {
3150 y_plus_x: Fe([16091085,-16253926,18599252,7340678,2137637,-1221657,-3364161,14550936,3260525,-7166271]),
3151 y_minus_x: Fe([-4910104,-13332887,18550887,10864893,-16459325,-7291596,-23028869,-13204905,-12748722,2701326]),
3152 xy2d: Fe([-8574695,16099415,4629974,-16340524,-20786213,-6005432,-10018363,9276971,11329923,1862132]),
3153 },
3154 GePrecomp {
3155 y_plus_x: Fe([14763076,-15903608,-30918270,3689867,3511892,10313526,-21951088,12219231,-9037963,-940300]),
3156 y_minus_x: Fe([8894987,-3446094,6150753,3013931,301220,15693451,-31981216,-2909717,-15438168,11595570]),
3157 xy2d: Fe([15214962,3537601,-26238722,-14058872,4418657,-15230761,13947276,10730794,-13489462,-4363670]),
3158 },
3159 GePrecomp {
3160 y_plus_x: Fe([-2538306,7682793,32759013,263109,-29984731,-7955452,-22332124,-10188635,977108,699994]),
3161 y_minus_x: Fe([-12466472,4195084,-9211532,550904,-15565337,12917920,19118110,-439841,-30534533,-14337913]),
3162 xy2d: Fe([31788461,-14507657,4799989,7372237,8808585,-14747943,9408237,-10051775,12493932,-5409317]),
3163 },
3164 GePrecomp {
3165 y_plus_x: Fe([-25680606,5260744,-19235809,-6284470,-3695942,16566087,27218280,2607121,29375955,6024730]),
3166 y_minus_x: Fe([842132,-2794693,-4763381,-8722815,26332018,-12405641,11831880,6985184,-9940361,2854096]),
3167 xy2d: Fe([-4847262,-7969331,2516242,-5847713,9695691,-7221186,16512645,960770,12121869,16648078]),
3168 },
3169 GePrecomp {
3170 y_plus_x: Fe([-15218652,14667096,-13336229,2013717,30598287,-464137,-31504922,-7882064,20237806,2838411]),
3171 y_minus_x: Fe([-19288047,4453152,15298546,-16178388,22115043,-15972604,12544294,-13470457,1068881,-12499905]),
3172 xy2d: Fe([-9558883,-16518835,33238498,13506958,30505848,-1114596,-8486907,-2630053,12521378,4845654]),
3173 },
3174 GePrecomp {
3175 y_plus_x: Fe([-28198521,10744108,-2958380,10199664,7759311,-13088600,3409348,-873400,-6482306,-12885870]),
3176 y_minus_x: Fe([-23561822,6230156,-20382013,10655314,-24040585,-11621172,10477734,-1240216,-3113227,13974498]),
3177 xy2d: Fe([12966261,15550616,-32038948,-1615346,21025980,-629444,5642325,7188737,18895762,12629579]),
3178 },
3179 ],
3180 [
3181 GePrecomp {
3182 y_plus_x: Fe([14741879,-14946887,22177208,-11721237,1279741,8058600,11758140,789443,32195181,3895677]),
3183 y_minus_x: Fe([10758205,15755439,-4509950,9243698,-4879422,6879879,-2204575,-3566119,-8982069,4429647]),
3184 xy2d: Fe([-2453894,15725973,-20436342,-10410672,-5803908,-11040220,-7135870,-11642895,18047436,-15281743]),
3185 },
3186 GePrecomp {
3187 y_plus_x: Fe([-25173001,-11307165,29759956,11776784,-22262383,-15820455,10993114,-12850837,-17620701,-9408468]),
3188 y_minus_x: Fe([21987233,700364,-24505048,14972008,-7774265,-5718395,32155026,2581431,-29958985,8773375]),
3189 xy2d: Fe([-25568350,454463,-13211935,16126715,25240068,8594567,20656846,12017935,-7874389,-13920155]),
3190 },
3191 GePrecomp {
3192 y_plus_x: Fe([6028182,6263078,-31011806,-11301710,-818919,2461772,-31841174,-5468042,-1721788,-2776725]),
3193 y_minus_x: Fe([-12278994,16624277,987579,-5922598,32908203,1248608,7719845,-4166698,28408820,6816612]),
3194 xy2d: Fe([-10358094,-8237829,19549651,-12169222,22082623,16147817,20613181,13982702,-10339570,5067943]),
3195 },
3196 GePrecomp {
3197 y_plus_x: Fe([-30505967,-3821767,12074681,13582412,-19877972,2443951,-19719286,12746132,5331210,-10105944]),
3198 y_minus_x: Fe([30528811,3601899,-1957090,4619785,-27361822,-15436388,24180793,-12570394,27679908,-1648928]),
3199 xy2d: Fe([9402404,-13957065,32834043,10838634,-26580150,-13237195,26653274,-8685565,22611444,-12715406]),
3200 },
3201 GePrecomp {
3202 y_plus_x: Fe([22190590,1118029,22736441,15130463,-30460692,-5991321,19189625,-4648942,4854859,6622139]),
3203 y_minus_x: Fe([-8310738,-2953450,-8262579,-3388049,-10401731,-271929,13424426,-3567227,26404409,13001963]),
3204 xy2d: Fe([-31241838,-15415700,-2994250,8939346,11562230,-12840670,-26064365,-11621720,-15405155,11020693]),
3205 },
3206 GePrecomp {
3207 y_plus_x: Fe([1866042,-7949489,-7898649,-10301010,12483315,13477547,3175636,-12424163,28761762,1406734]),
3208 y_minus_x: Fe([-448555,-1777666,13018551,3194501,-9580420,-11161737,24760585,-4347088,25577411,-13378680]),
3209 xy2d: Fe([-24290378,4759345,-690653,-1852816,2066747,10693769,-29595790,9884936,-9368926,4745410]),
3210 },
3211 GePrecomp {
3212 y_plus_x: Fe([-9141284,6049714,-19531061,-4341411,-31260798,9944276,-15462008,-11311852,10931924,-11931931]),
3213 y_minus_x: Fe([-16561513,14112680,-8012645,4817318,-8040464,-11414606,-22853429,10856641,-20470770,13434654]),
3214 xy2d: Fe([22759489,-10073434,-16766264,-1871422,13637442,-10168091,1765144,-12654326,28445307,-5364710]),
3215 },
3216 GePrecomp {
3217 y_plus_x: Fe([29875063,12493613,2795536,-3786330,1710620,15181182,-10195717,-8788675,9074234,1167180]),
3218 y_minus_x: Fe([-26205683,11014233,-9842651,-2635485,-26908120,7532294,-18716888,-9535498,3843903,9367684]),
3219 xy2d: Fe([-10969595,-6403711,9591134,9582310,11349256,108879,16235123,8601684,-139197,4242895]),
3220 },
3221 ],
3222 [
3223 GePrecomp {
3224 y_plus_x: Fe([22092954,-13191123,-2042793,-11968512,32186753,-11517388,-6574341,2470660,-27417366,16625501]),
3225 y_minus_x: Fe([-11057722,3042016,13770083,-9257922,584236,-544855,-7770857,2602725,-27351616,14247413]),
3226 xy2d: Fe([6314175,-10264892,-32772502,15957557,-10157730,168750,-8618807,14290061,27108877,-1180880]),
3227 },
3228 GePrecomp {
3229 y_plus_x: Fe([-8586597,-7170966,13241782,10960156,-32991015,-13794596,33547976,-11058889,-27148451,981874]),
3230 y_minus_x: Fe([22833440,9293594,-32649448,-13618667,-9136966,14756819,-22928859,-13970780,-10479804,-16197962]),
3231 xy2d: Fe([-7768587,3326786,-28111797,10783824,19178761,14905060,22680049,13906969,-15933690,3797899]),
3232 },
3233 GePrecomp {
3234 y_plus_x: Fe([21721356,-4212746,-12206123,9310182,-3882239,-13653110,23740224,-2709232,20491983,-8042152]),
3235 y_minus_x: Fe([9209270,-15135055,-13256557,-6167798,-731016,15289673,25947805,15286587,30997318,-6703063]),
3236 xy2d: Fe([7392032,16618386,23946583,-8039892,-13265164,-1533858,-14197445,-2321576,17649998,-250080]),
3237 },
3238 GePrecomp {
3239 y_plus_x: Fe([-9301088,-14193827,30609526,-3049543,-25175069,-1283752,-15241566,-9525724,-2233253,7662146]),
3240 y_minus_x: Fe([-17558673,1763594,-33114336,15908610,-30040870,-12174295,7335080,-8472199,-3174674,3440183]),
3241 xy2d: Fe([-19889700,-5977008,-24111293,-9688870,10799743,-16571957,40450,-4431835,4862400,1133]),
3242 },
3243 GePrecomp {
3244 y_plus_x: Fe([-32856209,-7873957,-5422389,14860950,-16319031,7956142,7258061,311861,-30594991,-7379421]),
3245 y_minus_x: Fe([-3773428,-1565936,28985340,7499440,24445838,9325937,29727763,16527196,18278453,15405622]),
3246 xy2d: Fe([-4381906,8508652,-19898366,-3674424,-5984453,15149970,-13313598,843523,-21875062,13626197]),
3247 },
3248 GePrecomp {
3249 y_plus_x: Fe([2281448,-13487055,-10915418,-2609910,1879358,16164207,-10783882,3953792,13340839,15928663]),
3250 y_minus_x: Fe([31727126,-7179855,-18437503,-8283652,2875793,-16390330,-25269894,-7014826,-23452306,5964753]),
3251 xy2d: Fe([4100420,-5959452,-17179337,6017714,-18705837,12227141,-26684835,11344144,2538215,-7570755]),
3252 },
3253 GePrecomp {
3254 y_plus_x: Fe([-9433605,6123113,11159803,-2156608,30016280,14966241,-20474983,1485421,-629256,-15958862]),
3255 y_minus_x: Fe([-26804558,4260919,11851389,9658551,-32017107,16367492,-20205425,-13191288,11659922,-11115118]),
3256 xy2d: Fe([26180396,10015009,-30844224,-8581293,5418197,9480663,2231568,-10170080,33100372,-1306171]),
3257 },
3258 GePrecomp {
3259 y_plus_x: Fe([15121113,-5201871,-10389905,15427821,-27509937,-15992507,21670947,4486675,-5931810,-14466380]),
3260 y_minus_x: Fe([16166486,-9483733,-11104130,6023908,-31926798,-1364923,2340060,-16254968,-10735770,-10039824]),
3261 xy2d: Fe([28042865,-3557089,-12126526,12259706,-3717498,-6945899,6766453,-8689599,18036436,5803270]),
3262 },
3263 ],
3264 [
3265 GePrecomp {
3266 y_plus_x: Fe([-817581,6763912,11803561,1585585,10958447,-2671165,23855391,4598332,-6159431,-14117438]),
3267 y_minus_x: Fe([-31031306,-14256194,17332029,-2383520,31312682,-5967183,696309,50292,-20095739,11763584]),
3268 xy2d: Fe([-594563,-2514283,-32234153,12643980,12650761,14811489,665117,-12613632,-19773211,-10713562]),
3269 },
3270 GePrecomp {
3271 y_plus_x: Fe([30464590,-11262872,-4127476,-12734478,19835327,-7105613,-24396175,2075773,-17020157,992471]),
3272 y_minus_x: Fe([18357185,-6994433,7766382,16342475,-29324918,411174,14578841,8080033,-11574335,-10601610]),
3273 xy2d: Fe([19598397,10334610,12555054,2555664,18821899,-10339780,21873263,16014234,26224780,16452269]),
3274 },
3275 GePrecomp {
3276 y_plus_x: Fe([-30223925,5145196,5944548,16385966,3976735,2009897,-11377804,-7618186,-20533829,3698650]),
3277 y_minus_x: Fe([14187449,3448569,-10636236,-10810935,-22663880,-3433596,7268410,-10890444,27394301,12015369]),
3278 xy2d: Fe([19695761,16087646,28032085,12999827,6817792,11427614,20244189,-1312777,-13259127,-3402461]),
3279 },
3280 GePrecomp {
3281 y_plus_x: Fe([30860103,12735208,-1888245,-4699734,-16974906,2256940,-8166013,12298312,-8550524,-10393462]),
3282 y_minus_x: Fe([-5719826,-11245325,-1910649,15569035,26642876,-7587760,-5789354,-15118654,-4976164,12651793]),
3283 xy2d: Fe([-2848395,9953421,11531313,-5282879,26895123,-12697089,-13118820,-16517902,9768698,-2533218]),
3284 },
3285 GePrecomp {
3286 y_plus_x: Fe([-24719459,1894651,-287698,-4704085,15348719,-8156530,32767513,12765450,4940095,10678226]),
3287 y_minus_x: Fe([18860224,15980149,-18987240,-1562570,-26233012,-11071856,-7843882,13944024,-24372348,16582019]),
3288 xy2d: Fe([-15504260,4970268,-29893044,4175593,-20993212,-2199756,-11704054,15444560,-11003761,7989037]),
3289 },
3290 GePrecomp {
3291 y_plus_x: Fe([31490452,5568061,-2412803,2182383,-32336847,4531686,-32078269,6200206,-19686113,-14800171]),
3292 y_minus_x: Fe([-17308668,-15879940,-31522777,-2831,-32887382,16375549,8680158,-16371713,28550068,-6857132]),
3293 xy2d: Fe([-28126887,-5688091,16837845,-1820458,-6850681,12700016,-30039981,4364038,1155602,5988841]),
3294 },
3295 GePrecomp {
3296 y_plus_x: Fe([21890435,-13272907,-12624011,12154349,-7831873,15300496,23148983,-4470481,24618407,8283181]),
3297 y_minus_x: Fe([-33136107,-10512751,9975416,6841041,-31559793,16356536,3070187,-7025928,1466169,10740210]),
3298 xy2d: Fe([-1509399,-15488185,-13503385,-10655916,32799044,909394,-13938903,-5779719,-32164649,-15327040]),
3299 },
3300 GePrecomp {
3301 y_plus_x: Fe([3960823,-14267803,-28026090,-15918051,-19404858,13146868,15567327,951507,-3260321,-573935]),
3302 y_minus_x: Fe([24740841,5052253,-30094131,8961361,25877428,6165135,-24368180,14397372,-7380369,-6144105]),
3303 xy2d: Fe([-28888365,3510803,-28103278,-1158478,-11238128,-10631454,-15441463,-14453128,-1625486,-6494814]),
3304 },
3305 ],
3306 [
3307 GePrecomp {
3308 y_plus_x: Fe([793299,-9230478,8836302,-6235707,-27360908,-2369593,33152843,-4885251,-9906200,-621852]),
3309 y_minus_x: Fe([5666233,525582,20782575,-8038419,-24538499,14657740,16099374,1468826,-6171428,-15186581]),
3310 xy2d: Fe([-4859255,-3779343,-2917758,-6748019,7778750,11688288,-30404353,-9871238,-1558923,-9863646]),
3311 },
3312 GePrecomp {
3313 y_plus_x: Fe([10896332,-7719704,824275,472601,-19460308,3009587,25248958,14783338,-30581476,-15757844]),
3314 y_minus_x: Fe([10566929,12612572,-31944212,11118703,-12633376,12362879,21752402,8822496,24003793,14264025]),
3315 xy2d: Fe([27713862,-7355973,-11008240,9227530,27050101,2504721,23886875,-13117525,13958495,-5732453]),
3316 },
3317 GePrecomp {
3318 y_plus_x: Fe([-23481610,4867226,-27247128,3900521,29838369,-8212291,-31889399,-10041781,7340521,-15410068]),
3319 y_minus_x: Fe([4646514,-8011124,-22766023,-11532654,23184553,8566613,31366726,-1381061,-15066784,-10375192]),
3320 xy2d: Fe([-17270517,12723032,-16993061,14878794,21619651,-6197576,27584817,3093888,-8843694,3849921]),
3321 },
3322 GePrecomp {
3323 y_plus_x: Fe([-9064912,2103172,25561640,-15125738,-5239824,9582958,32477045,-9017955,5002294,-15550259]),
3324 y_minus_x: Fe([-12057553,-11177906,21115585,-13365155,8808712,-12030708,16489530,13378448,-25845716,12741426]),
3325 xy2d: Fe([-5946367,10645103,-30911586,15390284,-3286982,-7118677,24306472,15852464,28834118,-7646072]),
3326 },
3327 GePrecomp {
3328 y_plus_x: Fe([-17335748,-9107057,-24531279,9434953,-8472084,-583362,-13090771,455841,20461858,5491305]),
3329 y_minus_x: Fe([13669248,-16095482,-12481974,-10203039,-14569770,-11893198,-24995986,11293807,-28588204,-9421832]),
3330 xy2d: Fe([28497928,6272777,-33022994,14470570,8906179,-1225630,18504674,-14165166,29867745,-8795943]),
3331 },
3332 GePrecomp {
3333 y_plus_x: Fe([-16207023,13517196,-27799630,-13697798,24009064,-6373891,-6367600,-13175392,22853429,-4012011]),
3334 y_minus_x: Fe([24191378,16712145,-13931797,15217831,14542237,1646131,18603514,-11037887,12876623,-2112447]),
3335 xy2d: Fe([17902668,4518229,-411702,-2829247,26878217,5258055,-12860753,608397,16031844,3723494]),
3336 },
3337 GePrecomp {
3338 y_plus_x: Fe([-28632773,12763728,-20446446,7577504,33001348,-13017745,17558842,-7872890,23896954,-4314245]),
3339 y_minus_x: Fe([-20005381,-12011952,31520464,605201,2543521,5991821,-2945064,7229064,-9919646,-8826859]),
3340 xy2d: Fe([28816045,298879,-28165016,-15920938,19000928,-1665890,-12680833,-2949325,-18051778,-2082915]),
3341 },
3342 GePrecomp {
3343 y_plus_x: Fe([16000882,-344896,3493092,-11447198,-29504595,-13159789,12577740,16041268,-19715240,7847707]),
3344 y_minus_x: Fe([10151868,10572098,27312476,7922682,14825339,4723128,-32855931,-6519018,-10020567,3852848]),
3345 xy2d: Fe([-11430470,15697596,-21121557,-4420647,5386314,15063598,16514493,-15932110,29330899,-15076224]),
3346 },
3347 ],
3348 [
3349 GePrecomp {
3350 y_plus_x: Fe([-25499735,-4378794,-15222908,-6901211,16615731,2051784,3303702,15490,-27548796,12314391]),
3351 y_minus_x: Fe([15683520,-6003043,18109120,-9980648,15337968,-5997823,-16717435,15921866,16103996,-3731215]),
3352 xy2d: Fe([-23169824,-10781249,13588192,-1628807,-3798557,-1074929,-19273607,5402699,-29815713,-9841101]),
3353 },
3354 GePrecomp {
3355 y_plus_x: Fe([23190676,2384583,-32714340,3462154,-29903655,-1529132,-11266856,8911517,-25205859,2739713]),
3356 y_minus_x: Fe([21374101,-3554250,-33524649,9874411,15377179,11831242,-33529904,6134907,4931255,11987849]),
3357 xy2d: Fe([-7732,-2978858,-16223486,7277597,105524,-322051,-31480539,13861388,-30076310,10117930]),
3358 },
3359 GePrecomp {
3360 y_plus_x: Fe([-29501170,-10744872,-26163768,13051539,-25625564,5089643,-6325503,6704079,12890019,15728940]),
3361 y_minus_x: Fe([-21972360,-11771379,-951059,-4418840,14704840,2695116,903376,-10428139,12885167,8311031]),
3362 xy2d: Fe([-17516482,5352194,10384213,-13811658,7506451,13453191,26423267,4384730,1888765,-5435404]),
3363 },
3364 GePrecomp {
3365 y_plus_x: Fe([-25817338,-3107312,-13494599,-3182506,30896459,-13921729,-32251644,-12707869,-19464434,-3340243]),
3366 y_minus_x: Fe([-23607977,-2665774,-526091,4651136,5765089,4618330,6092245,14845197,17151279,-9854116]),
3367 xy2d: Fe([-24830458,-12733720,-15165978,10367250,-29530908,-265356,22825805,-7087279,-16866484,16176525]),
3368 },
3369 GePrecomp {
3370 y_plus_x: Fe([-23583256,6564961,20063689,3798228,-4740178,7359225,2006182,-10363426,-28746253,-10197509]),
3371 y_minus_x: Fe([-10626600,-4486402,-13320562,-5125317,3432136,-6393229,23632037,-1940610,32808310,1099883]),
3372 xy2d: Fe([15030977,5768825,-27451236,-2887299,-6427378,-15361371,-15277896,-6809350,2051441,-15225865]),
3373 },
3374 GePrecomp {
3375 y_plus_x: Fe([-3362323,-7239372,7517890,9824992,23555850,295369,5148398,-14154188,-22686354,16633660]),
3376 y_minus_x: Fe([4577086,-16752288,13249841,-15304328,19958763,-14537274,18559670,-10759549,8402478,-9864273]),
3377 xy2d: Fe([-28406330,-1051581,-26790155,-907698,-17212414,-11030789,9453451,-14980072,17983010,9967138]),
3378 },
3379 GePrecomp {
3380 y_plus_x: Fe([-25762494,6524722,26585488,9969270,24709298,1220360,-1677990,7806337,17507396,3651560]),
3381 y_minus_x: Fe([-10420457,-4118111,14584639,15971087,-15768321,8861010,26556809,-5574557,-18553322,-11357135]),
3382 xy2d: Fe([2839101,14284142,4029895,3472686,14402957,12689363,-26642121,8459447,-5605463,-7621941]),
3383 },
3384 GePrecomp {
3385 y_plus_x: Fe([-4839289,-3535444,9744961,2871048,25113978,3187018,-25110813,-849066,17258084,-7977739]),
3386 y_minus_x: Fe([18164541,-10595176,-17154882,-1542417,19237078,-9745295,23357533,-15217008,26908270,12150756]),
3387 xy2d: Fe([-30264870,-7647865,5112249,-7036672,-1499807,-6974257,43168,-5537701,-32302074,16215819]),
3388 },
3389 ],
3390 [
3391 GePrecomp {
3392 y_plus_x: Fe([-6898905,9824394,-12304779,-4401089,-31397141,-6276835,32574489,12532905,-7503072,-8675347]),
3393 y_minus_x: Fe([-27343522,-16515468,-27151524,-10722951,946346,16291093,254968,7168080,21676107,-1943028]),
3394 xy2d: Fe([21260961,-8424752,-16831886,-11920822,-23677961,3968121,-3651949,-6215466,-3556191,-7913075]),
3395 },
3396 GePrecomp {
3397 y_plus_x: Fe([16544754,13250366,-16804428,15546242,-4583003,12757258,-2462308,-8680336,-18907032,-9662799]),
3398 y_minus_x: Fe([-2415239,-15577728,18312303,4964443,-15272530,-12653564,26820651,16690659,25459437,-4564609]),
3399 xy2d: Fe([-25144690,11425020,28423002,-11020557,-6144921,-15826224,9142795,-2391602,-6432418,-1644817]),
3400 },
3401 GePrecomp {
3402 y_plus_x: Fe([-23104652,6253476,16964147,-3768872,-25113972,-12296437,-27457225,-16344658,6335692,7249989]),
3403 y_minus_x: Fe([-30333227,13979675,7503222,-12368314,-11956721,-4621693,-30272269,2682242,25993170,-12478523]),
3404 xy2d: Fe([4364628,5930691,32304656,-10044554,-8054781,15091131,22857016,-10598955,31820368,15075278]),
3405 },
3406 GePrecomp {
3407 y_plus_x: Fe([31879134,-8918693,17258761,90626,-8041836,-4917709,24162788,-9650886,-17970238,12833045]),
3408 y_minus_x: Fe([19073683,14851414,-24403169,-11860168,7625278,11091125,-19619190,2074449,-9413939,14905377]),
3409 xy2d: Fe([24483667,-11935567,-2518866,-11547418,-1553130,15355506,-25282080,9253129,27628530,-7555480]),
3410 },
3411 GePrecomp {
3412 y_plus_x: Fe([17597607,8340603,19355617,552187,26198470,-3176583,4593324,-9157582,-14110875,15297016]),
3413 y_minus_x: Fe([510886,14337390,-31785257,16638632,6328095,2713355,-20217417,-11864220,8683221,2921426]),
3414 xy2d: Fe([18606791,11874196,27155355,-5281482,-24031742,6265446,-25178240,-1278924,4674690,13890525]),
3415 },
3416 GePrecomp {
3417 y_plus_x: Fe([13609624,13069022,-27372361,-13055908,24360586,9592974,14977157,9835105,4389687,288396]),
3418 y_minus_x: Fe([9922506,-519394,13613107,5883594,-18758345,-434263,-12304062,8317628,23388070,16052080]),
3419 xy2d: Fe([12720016,11937594,-31970060,-5028689,26900120,8561328,-20155687,-11632979,-14754271,-10812892]),
3420 },
3421 GePrecomp {
3422 y_plus_x: Fe([15961858,14150409,26716931,-665832,-22794328,13603569,11829573,7467844,-28822128,929275]),
3423 y_minus_x: Fe([11038231,-11582396,-27310482,-7316562,-10498527,-16307831,-23479533,-9371869,-21393143,2465074]),
3424 xy2d: Fe([20017163,-4323226,27915242,1529148,12396362,15675764,13817261,-9658066,2463391,-4622140]),
3425 },
3426 GePrecomp {
3427 y_plus_x: Fe([-16358878,-12663911,-12065183,4996454,-1256422,1073572,9583558,12851107,4003896,12673717]),
3428 y_minus_x: Fe([-1731589,-15155870,-3262930,16143082,19294135,13385325,14741514,-9103726,7903886,2348101]),
3429 xy2d: Fe([24536016,-16515207,12715592,-3862155,1511293,10047386,-3842346,-7129159,-28377538,10048127]),
3430 },
3431 ],
3432 [
3433 GePrecomp {
3434 y_plus_x: Fe([-12622226,-6204820,30718825,2591312,-10617028,12192840,18873298,-7297090,-32297756,15221632]),
3435 y_minus_x: Fe([-26478122,-11103864,11546244,-1852483,9180880,7656409,-21343950,2095755,29769758,6593415]),
3436 xy2d: Fe([-31994208,-2907461,4176912,3264766,12538965,-868111,26312345,-6118678,30958054,8292160]),
3437 },
3438 GePrecomp {
3439 y_plus_x: Fe([31429822,-13959116,29173532,15632448,12174511,-2760094,32808831,3977186,26143136,-3148876]),
3440 y_minus_x: Fe([22648901,1402143,-22799984,13746059,7936347,365344,-8668633,-1674433,-3758243,-2304625]),
3441 xy2d: Fe([-15491917,8012313,-2514730,-12702462,-23965846,-10254029,-1612713,-1535569,-16664475,8194478]),
3442 },
3443 GePrecomp {
3444 y_plus_x: Fe([27338066,-7507420,-7414224,10140405,-19026427,-6589889,27277191,8855376,28572286,3005164]),
3445 y_minus_x: Fe([26287124,4821776,25476601,-4145903,-3764513,-15788984,-18008582,1182479,-26094821,-13079595]),
3446 xy2d: Fe([-7171154,3178080,23970071,6201893,-17195577,-4489192,-21876275,-13982627,32208683,-1198248]),
3447 },
3448 GePrecomp {
3449 y_plus_x: Fe([-16657702,2817643,-10286362,14811298,6024667,13349505,-27315504,-10497842,-27672585,-11539858]),
3450 y_minus_x: Fe([15941029,-9405932,-21367050,8062055,31876073,-238629,-15278393,-1444429,15397331,-4130193]),
3451 xy2d: Fe([8934485,-13485467,-23286397,-13423241,-32446090,14047986,31170398,-1441021,-27505566,15087184]),
3452 },
3453 GePrecomp {
3454 y_plus_x: Fe([-18357243,-2156491,24524913,-16677868,15520427,-6360776,-15502406,11461896,16788528,-5868942]),
3455 y_minus_x: Fe([-1947386,16013773,21750665,3714552,-17401782,-16055433,-3770287,-10323320,31322514,-11615635]),
3456 xy2d: Fe([21426655,-5650218,-13648287,-5347537,-28812189,-4920970,-18275391,-14621414,13040862,-12112948]),
3457 },
3458 GePrecomp {
3459 y_plus_x: Fe([11293895,12478086,-27136401,15083750,-29307421,14748872,14555558,-13417103,1613711,4896935]),
3460 y_minus_x: Fe([-25894883,15323294,-8489791,-8057900,25967126,-13425460,2825960,-4897045,-23971776,-11267415]),
3461 xy2d: Fe([-15924766,-5229880,-17443532,6410664,3622847,10243618,20615400,12405433,-23753030,-8436416]),
3462 },
3463 GePrecomp {
3464 y_plus_x: Fe([-7091295,12556208,-20191352,9025187,-17072479,4333801,4378436,2432030,23097949,-566018]),
3465 y_minus_x: Fe([4565804,-16025654,20084412,-7842817,1724999,189254,24767264,10103221,-18512313,2424778]),
3466 xy2d: Fe([366633,-11976806,8173090,-6890119,30788634,5745705,-7168678,1344109,-3642553,12412659]),
3467 },
3468 GePrecomp {
3469 y_plus_x: Fe([-24001791,7690286,14929416,-168257,-32210835,-13412986,24162697,-15326504,-3141501,11179385]),
3470 y_minus_x: Fe([18289522,-14724954,8056945,16430056,-21729724,7842514,-6001441,-1486897,-18684645,-11443503]),
3471 xy2d: Fe([476239,6601091,-6152790,-9723375,17503545,-4863900,27672959,13403813,11052904,5219329]),
3472 },
3473 ],
3474 [
3475 GePrecomp {
3476 y_plus_x: Fe([20678546,-8375738,-32671898,8849123,-5009758,14574752,31186971,-3973730,9014762,-8579056]),
3477 y_minus_x: Fe([-13644050,-10350239,-15962508,5075808,-1514661,-11534600,-33102500,9160280,8473550,-3256838]),
3478 xy2d: Fe([24900749,14435722,17209120,-15292541,-22592275,9878983,-7689309,-16335821,-24568481,11788948]),
3479 },
3480 GePrecomp {
3481 y_plus_x: Fe([-3118155,-11395194,-13802089,14797441,9652448,-6845904,-20037437,10410733,-24568470,-1458691]),
3482 y_minus_x: Fe([-15659161,16736706,-22467150,10215878,-9097177,7563911,11871841,-12505194,-18513325,8464118]),
3483 xy2d: Fe([-23400612,8348507,-14585951,-861714,-3950205,-6373419,14325289,8628612,33313881,-8370517]),
3484 },
3485 GePrecomp {
3486 y_plus_x: Fe([-20186973,-4967935,22367356,5271547,-1097117,-4788838,-24805667,-10236854,-8940735,-5818269]),
3487 y_minus_x: Fe([-6948785,-1795212,-32625683,-16021179,32635414,-7374245,15989197,-12838188,28358192,-4253904]),
3488 xy2d: Fe([-23561781,-2799059,-32351682,-1661963,-9147719,10429267,-16637684,4072016,-5351664,5596589]),
3489 },
3490 GePrecomp {
3491 y_plus_x: Fe([-28236598,-3390048,12312896,6213178,3117142,16078565,29266239,2557221,1768301,15373193]),
3492 y_minus_x: Fe([-7243358,-3246960,-4593467,-7553353,-127927,-912245,-1090902,-4504991,-24660491,3442910]),
3493 xy2d: Fe([-30210571,5124043,14181784,8197961,18964734,-11939093,22597931,7176455,-18585478,13365930]),
3494 },
3495 GePrecomp {
3496 y_plus_x: Fe([-7877390,-1499958,8324673,4690079,6261860,890446,24538107,-8570186,-9689599,-3031667]),
3497 y_minus_x: Fe([25008904,-10771599,-4305031,-9638010,16265036,15721635,683793,-11823784,15723479,-15163481]),
3498 xy2d: Fe([-9660625,12374379,-27006999,-7026148,-7724114,-12314514,11879682,5400171,519526,-1235876]),
3499 },
3500 GePrecomp {
3501 y_plus_x: Fe([22258397,-16332233,-7869817,14613016,-22520255,-2950923,-20353881,7315967,16648397,7605640]),
3502 y_minus_x: Fe([-8081308,-8464597,-8223311,9719710,19259459,-15348212,23994942,-5281555,-9468848,4763278]),
3503 xy2d: Fe([-21699244,9220969,-15730624,1084137,-25476107,-2852390,31088447,-7764523,-11356529,728112]),
3504 },
3505 GePrecomp {
3506 y_plus_x: Fe([26047220,-11751471,-6900323,-16521798,24092068,9158119,-4273545,-12555558,-29365436,-5498272]),
3507 y_minus_x: Fe([17510331,-322857,5854289,8403524,17133918,-3112612,-28111007,12327945,10750447,10014012]),
3508 xy2d: Fe([-10312768,3936952,9156313,-8897683,16498692,-994647,-27481051,-666732,3424691,7540221]),
3509 },
3510 GePrecomp {
3511 y_plus_x: Fe([30322361,-6964110,11361005,-4143317,7433304,4989748,-7071422,-16317219,-9244265,15258046]),
3512 y_minus_x: Fe([13054562,-2779497,19155474,469045,-12482797,4566042,5631406,2711395,1062915,-5136345]),
3513 xy2d: Fe([-19240248,-11254599,-29509029,-7499965,-5835763,13005411,-6066489,12194497,32960380,1459310]),
3514 },
3515 ],
3516 [
3517 GePrecomp {
3518 y_plus_x: Fe([19852034,7027924,23669353,10020366,8586503,-6657907,394197,-6101885,18638003,-11174937]),
3519 y_minus_x: Fe([31395534,15098109,26581030,8030562,-16527914,-5007134,9012486,-7584354,-6643087,-5442636]),
3520 xy2d: Fe([-9192165,-2347377,-1997099,4529534,25766844,607986,-13222,9677543,-32294889,-6456008]),
3521 },
3522 GePrecomp {
3523 y_plus_x: Fe([-2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429]),
3524 y_minus_x: Fe([-15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576]),
3525 xy2d: Fe([31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066]),
3526 },
3527 GePrecomp {
3528 y_plus_x: Fe([-9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490]),
3529 y_minus_x: Fe([-12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104]),
3530 xy2d: Fe([33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053]),
3531 },
3532 GePrecomp {
3533 y_plus_x: Fe([31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275]),
3534 y_minus_x: Fe([-20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511]),
3535 xy2d: Fe([22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095]),
3536 },
3537 GePrecomp {
3538 y_plus_x: Fe([-28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439]),
3539 y_minus_x: Fe([23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939]),
3540 xy2d: Fe([-23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424]),
3541 },
3542 GePrecomp {
3543 y_plus_x: Fe([2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310]),
3544 y_minus_x: Fe([3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608]),
3545 xy2d: Fe([-32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079]),
3546 },
3547 GePrecomp {
3548 y_plus_x: Fe([-23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101]),
3549 y_minus_x: Fe([21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418]),
3550 xy2d: Fe([18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576]),
3551 },
3552 GePrecomp {
3553 y_plus_x: Fe([30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356]),
3554 y_minus_x: Fe([9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996]),
3555 xy2d: Fe([-26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099]),
3556 },
3557 ],
3558 [
3559 GePrecomp {
3560 y_plus_x: Fe([-26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728]),
3561 y_minus_x: Fe([-13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658]),
3562 xy2d: Fe([-10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242]),
3563 },
3564 GePrecomp {
3565 y_plus_x: Fe([-21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001]),
3566 y_minus_x: Fe([-4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766]),
3567 xy2d: Fe([18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373]),
3568 },
3569 GePrecomp {
3570 y_plus_x: Fe([26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458]),
3571 y_minus_x: Fe([-17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628]),
3572 xy2d: Fe([-13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657]),
3573 },
3574 GePrecomp {
3575 y_plus_x: Fe([-23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062]),
3576 y_minus_x: Fe([25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616]),
3577 xy2d: Fe([31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014]),
3578 },
3579 GePrecomp {
3580 y_plus_x: Fe([24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383]),
3581 y_minus_x: Fe([-25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814]),
3582 xy2d: Fe([-20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718]),
3583 },
3584 GePrecomp {
3585 y_plus_x: Fe([30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417]),
3586 y_minus_x: Fe([2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222]),
3587 xy2d: Fe([33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444]),
3588 },
3589 GePrecomp {
3590 y_plus_x: Fe([-20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597]),
3591 y_minus_x: Fe([23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970]),
3592 xy2d: Fe([1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799]),
3593 },
3594 GePrecomp {
3595 y_plus_x: Fe([-5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647]),
3596 y_minus_x: Fe([13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511]),
3597 xy2d: Fe([-29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032]),
3598 },
3599 ],
3600 [
3601 GePrecomp {
3602 y_plus_x: Fe([9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834]),
3603 y_minus_x: Fe([-23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461]),
3604 xy2d: Fe([29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062]),
3605 },
3606 GePrecomp {
3607 y_plus_x: Fe([-25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516]),
3608 y_minus_x: Fe([-20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547]),
3609 xy2d: Fe([-24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240]),
3610 },
3611 GePrecomp {
3612 y_plus_x: Fe([-17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038]),
3613 y_minus_x: Fe([-33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741]),
3614 xy2d: Fe([16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103]),
3615 },
3616 GePrecomp {
3617 y_plus_x: Fe([-19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747]),
3618 y_minus_x: Fe([-1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323]),
3619 xy2d: Fe([31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016]),
3620 },
3621 GePrecomp {
3622 y_plus_x: Fe([-14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373]),
3623 y_minus_x: Fe([15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228]),
3624 xy2d: Fe([-2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141]),
3625 },
3626 GePrecomp {
3627 y_plus_x: Fe([16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399]),
3628 y_minus_x: Fe([11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831]),
3629 xy2d: Fe([-185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376]),
3630 },
3631 GePrecomp {
3632 y_plus_x: Fe([-32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313]),
3633 y_minus_x: Fe([-18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958]),
3634 xy2d: Fe([-6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577]),
3635 },
3636 GePrecomp {
3637 y_plus_x: Fe([-22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743]),
3638 y_minus_x: Fe([29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684]),
3639 xy2d: Fe([-20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476]),
3640 },
3641 ],
3642 ];
3643