Line data Source code
1 : /* Copyright (C) 2014 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 : #include "pari.h"
16 : #include "paripriv.h"
17 :
18 : #define DEBUGLEVEL DEBUGLEVEL_polmodular
19 :
20 : #define dbg_printf(lvl) if (DEBUGLEVEL >= (lvl) + 3) err_printf
21 :
22 : /**
23 : * START Code from AVSs "class_inv.h"
24 : */
25 :
26 : /* actually just returns the square-free part of the level, which is
27 : * all we care about */
28 : long
29 41288 : modinv_level(long inv)
30 : {
31 41288 : switch (inv) {
32 32102 : case INV_J: return 1;
33 917 : case INV_G2:
34 917 : case INV_W3W3E2:return 3;
35 1112 : case INV_F:
36 : case INV_F2:
37 : case INV_F4:
38 1112 : case INV_F8: return 6;
39 70 : case INV_F3: return 2;
40 567 : case INV_W3W3: return 6;
41 1603 : case INV_W2W7E2:
42 1603 : case INV_W2W7: return 14;
43 269 : case INV_W3W5: return 15;
44 301 : case INV_W2W3E2:
45 301 : case INV_W2W3: return 6;
46 546 : case INV_W2W5E2:
47 546 : case INV_W2W5: return 30;
48 357 : case INV_W2W13: return 26;
49 1809 : case INV_W3W7: return 42;
50 578 : case INV_W5W7: return 35;
51 56 : case INV_W3W13: return 39;
52 1001 : case INV_ATKIN3:
53 : case INV_ATKIN5:
54 : case INV_ATKIN7:
55 : case INV_ATKIN11:
56 : case INV_ATKIN13:
57 : case INV_ATKIN17:
58 1001 : case INV_ATKIN19: return inv-100;
59 : }
60 : pari_err_BUG("modinv_level"); return 0;/*LCOV_EXCL_LINE*/
61 : }
62 :
63 : /* Where applicable, returns N=p1*p2 (possibly p2=1) s.t. two j's
64 : * related to the same f are N-isogenous, and 0 otherwise. This is
65 : * often (but not necessarily) equal to the level. */
66 : long
67 7432398 : modinv_degree(long *p1, long *p2, long inv)
68 : {
69 7432398 : switch (inv) {
70 297342 : case INV_W3W5: return (*p1 = 3) * (*p2 = 5);
71 427304 : case INV_W2W3E2:
72 427304 : case INV_W2W3: return (*p1 = 2) * (*p2 = 3);
73 1533918 : case INV_W2W5E2:
74 1533918 : case INV_W2W5: return (*p1 = 2) * (*p2 = 5);
75 947812 : case INV_W2W7E2:
76 947812 : case INV_W2W7: return (*p1 = 2) * (*p2 = 7);
77 1458283 : case INV_W2W13: return (*p1 = 2) * (*p2 = 13);
78 523917 : case INV_W3W7: return (*p1 = 3) * (*p2 = 7);
79 789559 : case INV_W3W3E2:
80 789559 : case INV_W3W3: return (*p1 = 3) * (*p2 = 3);
81 556148 : case INV_W5W7: return (*p1 = 5) * (*p2 = 7);
82 195062 : case INV_W3W13: return (*p1 = 3) * (*p2 = 13);
83 289770 : case INV_ATKIN3:
84 : case INV_ATKIN5:
85 : case INV_ATKIN7:
86 : case INV_ATKIN11:
87 : case INV_ATKIN13:
88 : case INV_ATKIN17:
89 289770 : case INV_ATKIN19: return (*p1 = inv-100) * (*p2 = 1);
90 : }
91 413283 : *p1 = *p2 = 1; return 0;
92 : }
93 :
94 : /* Certain invariants require that D not have 2 in it's conductor, but
95 : * this doesn't apply to every invariant with even level so we handle
96 : * it separately */
97 : INLINE int
98 565092 : modinv_odd_conductor(long inv)
99 : {
100 565092 : switch (inv) {
101 78187 : case INV_F:
102 : case INV_W3W3:
103 78187 : case INV_W3W7: return 1;
104 : }
105 486905 : return 0;
106 : }
107 :
108 : long
109 22916562 : modinv_height_factor(long inv)
110 : {
111 22916562 : switch (inv) {
112 5489 : case INV_J: return 1;
113 30429 : case INV_G2: return 3;
114 3109661 : case INV_F: return 72;
115 28 : case INV_F2: return 36;
116 536179 : case INV_F3: return 24;
117 49 : case INV_F4: return 18;
118 49 : case INV_F8: return 9;
119 63 : case INV_W2W3: return 72;
120 2352476 : case INV_W3W3: return 36;
121 3615878 : case INV_W2W5: return 54;
122 1340774 : case INV_W2W7: return 48;
123 1344 : case INV_W3W5: return 36;
124 3902605 : case INV_W2W13: return 42;
125 1119804 : case INV_W3W7: return 32;
126 1166711 : case INV_W2W3E2:return 36;
127 186515 : case INV_W2W5E2:return 27;
128 1064805 : case INV_W2W7E2:return 24;
129 49 : case INV_W3W3E2:return 18;
130 1133573 : case INV_W5W7: return 24;
131 14 : case INV_W3W13: return 28;
132 3350067 : case INV_ATKIN3:
133 : case INV_ATKIN5:
134 : case INV_ATKIN7:
135 : case INV_ATKIN11:
136 : case INV_ATKIN13:
137 : case INV_ATKIN17:
138 3350067 : case INV_ATKIN19: return (inv-99)/2;
139 : default: pari_err_BUG("modinv_height_factor"); return 0;/*LCOV_EXCL_LINE*/
140 : }
141 : }
142 :
143 : long
144 1907423 : disc_best_modinv(long D)
145 : {
146 : long ret;
147 1907423 : ret = INV_F; if (modinv_good_disc(ret, D)) return ret;
148 1534057 : ret = INV_W2W3; if (modinv_good_disc(ret, D)) return ret;
149 1534057 : ret = INV_W2W5; if (modinv_good_disc(ret, D)) return ret;
150 1238755 : ret = INV_W2W7; if (modinv_good_disc(ret, D)) return ret;
151 1139957 : ret = INV_W2W13; if (modinv_good_disc(ret, D)) return ret;
152 838012 : ret = INV_W3W3; if (modinv_good_disc(ret, D)) return ret;
153 651805 : ret = INV_W2W3E2;if (modinv_good_disc(ret, D)) return ret;
154 579453 : ret = INV_W3W5; if (modinv_good_disc(ret, D)) return ret;
155 579299 : ret = INV_W3W7; if (modinv_good_disc(ret, D)) return ret;
156 511091 : ret = INV_W3W13; if (modinv_good_disc(ret, D)) return ret;
157 511091 : ret = INV_W2W5E2;if (modinv_good_disc(ret, D)) return ret;
158 494753 : ret = INV_F3; if (modinv_good_disc(ret, D)) return ret;
159 464485 : ret = INV_W2W7E2;if (modinv_good_disc(ret, D)) return ret;
160 376656 : ret = INV_W5W7; if (modinv_good_disc(ret, D)) return ret;
161 283836 : ret = INV_W3W3E2;if (modinv_good_disc(ret, D)) return ret;
162 283836 : ret = INV_ATKIN19;if (modinv_good_disc(ret, D)) return ret;
163 129787 : ret = INV_ATKIN17;if (modinv_good_disc(ret, D)) return ret;
164 59780 : ret = INV_ATKIN13;if (modinv_good_disc(ret, D)) return ret;
165 35119 : ret = INV_ATKIN11;if (modinv_good_disc(ret, D)) return ret;
166 15743 : ret = INV_ATKIN7;if (modinv_good_disc(ret, D)) return ret;
167 12558 : ret = INV_ATKIN5;if (modinv_good_disc(ret, D)) return ret;
168 6244 : ret = INV_G2; if (modinv_good_disc(ret, D)) return ret;
169 2933 : ret = INV_ATKIN3;if (modinv_good_disc(ret, D)) return ret;
170 77 : return INV_J;
171 : }
172 :
173 : INLINE long
174 46656 : modinv_sparse_factor(long inv)
175 : {
176 46656 : switch (inv) {
177 3643 : case INV_G2:
178 : case INV_F8:
179 : case INV_W3W5:
180 : case INV_W2W5E2:
181 : case INV_W3W3E2:
182 3643 : return 3;
183 604 : case INV_F:
184 604 : return 24;
185 357 : case INV_F2:
186 : case INV_W2W3:
187 357 : return 12;
188 112 : case INV_F3:
189 112 : return 8;
190 1680 : case INV_F4:
191 : case INV_W2W3E2:
192 : case INV_W2W5:
193 : case INV_W3W3:
194 1680 : return 6;
195 1046 : case INV_W2W7:
196 1046 : return 4;
197 2951 : case INV_W2W7E2:
198 : case INV_W2W13:
199 : case INV_W3W7:
200 2951 : return 2;
201 : }
202 36263 : return 1;
203 : }
204 :
205 : #define IQ_FILTER_1MOD3 1
206 : #define IQ_FILTER_2MOD3 2
207 : #define IQ_FILTER_1MOD4 4
208 : #define IQ_FILTER_3MOD4 8
209 :
210 : INLINE long
211 16397 : modinv_pfilter(long inv)
212 : {
213 16397 : switch (inv) {
214 2066 : case INV_G2:
215 : case INV_W3W3:
216 : case INV_W3W3E2:
217 : case INV_W3W5:
218 : case INV_W2W5:
219 : case INV_W2W3E2:
220 : case INV_W2W5E2:
221 : case INV_W3W13:
222 2066 : return IQ_FILTER_1MOD3; /* ensure unique cube roots */
223 529 : case INV_W2W7:
224 : case INV_F3:
225 529 : return IQ_FILTER_1MOD4; /* ensure at most two 4th/8th roots */
226 951 : case INV_F:
227 : case INV_F2:
228 : case INV_F4:
229 : case INV_F8:
230 : case INV_W2W3:
231 : /* Ensure unique cube roots and at most two 4th/8th roots */
232 951 : return IQ_FILTER_1MOD3 | IQ_FILTER_1MOD4;
233 : }
234 12851 : return 0;
235 : }
236 :
237 : int
238 11344184 : modinv_good_prime(long inv, long p)
239 : {
240 11344184 : switch (inv) {
241 352996 : case INV_G2:
242 : case INV_W2W3E2:
243 : case INV_W3W3:
244 : case INV_W3W3E2:
245 : case INV_W3W5:
246 : case INV_W2W5E2:
247 : case INV_W2W5:
248 352996 : return (p % 3) == 2;
249 410256 : case INV_W2W7:
250 : case INV_F3:
251 410256 : return (p & 3) != 1;
252 405380 : case INV_F2:
253 : case INV_F4:
254 : case INV_F8:
255 : case INV_F:
256 : case INV_W2W3:
257 405380 : return ((p % 3) == 2) && (p & 3) != 1;
258 : }
259 10175552 : return 1;
260 : }
261 :
262 : /* Returns true if the prime p does not divide the conductor of D */
263 : INLINE int
264 3493271 : prime_to_conductor(long D, long p)
265 : {
266 : long b;
267 3493271 : if (p > 2) return (D % (p * p));
268 1288213 : b = D & 0xF;
269 1288213 : return (b && b != 4); /* 2 divides the conductor of D <=> D=0,4 mod 16 */
270 : }
271 :
272 : INLINE GEN
273 3493271 : red_primeform(long D, long p)
274 : {
275 3493271 : pari_sp av = avma;
276 : GEN P;
277 3493271 : if (!prime_to_conductor(D, p)) return NULL;
278 3493271 : P = primeform_u(stoi(D), p); /* primitive since p \nmid conductor */
279 3493271 : return gc_upto(av, qfi_red(P));
280 : }
281 :
282 : /* Computes product of primeforms over primes appearing in the prime
283 : * factorization of n (including multiplicity) */
284 : GEN
285 144620 : qfb_nform(long D, long n)
286 : {
287 144620 : pari_sp av = avma;
288 144620 : GEN N = NULL, fa = factoru(n), P = gel(fa,1), E = gel(fa,2);
289 144620 : long i, l = lg(P);
290 :
291 433594 : for (i = 1; i < l; ++i)
292 : {
293 : long j, e;
294 288974 : GEN Q = red_primeform(D, P[i]);
295 288974 : if (!Q) return gc_NULL(av);
296 288974 : e = E[i];
297 288974 : if (i == 1) { N = Q; j = 1; } else j = 0;
298 433419 : for (; j < e; ++j) N = qfbcomp_i(Q, N);
299 : }
300 144620 : return gc_upto(av, N);
301 : }
302 :
303 : INLINE int
304 1716120 : qfb_is_two_torsion(GEN x)
305 : {
306 3432240 : return equali1(gel(x,1)) || !signe(gel(x,2))
307 3432240 : || equalii(gel(x,1), gel(x,2)) || equalii(gel(x,1), gel(x,3));
308 : }
309 :
310 : /* Returns true iff the products p1*p2, p1*p2^-1, p1^-1*p2, and
311 : * p1^-1*p2^-1 are all distinct in cl(D) */
312 : INLINE int
313 234312 : qfb_distinct_prods(long D, long p1, long p2)
314 : {
315 : GEN P1, P2;
316 :
317 234312 : P1 = red_primeform(D, p1);
318 234312 : if (!P1) return 0;
319 234312 : P1 = qfbsqr_i(P1);
320 :
321 234312 : P2 = red_primeform(D, p2);
322 234312 : if (!P2) return 0;
323 234312 : P2 = qfbsqr_i(P2);
324 :
325 234312 : return !(equalii(gel(P1,1), gel(P2,1)) && absequalii(gel(P1,2), gel(P2,2)));
326 : }
327 :
328 : /* By Corollary 3.1 of Enge-Schertz Constructing elliptic curves over finite
329 : * fields using double eta-quotients, we need p1 != p2 to both be noninert
330 : * and prime to the conductor, and if p1=p2=p we want p split and prime to the
331 : * conductor. We exclude the case that p1=p2 divides the conductor, even
332 : * though this does yield class invariants */
333 : INLINE int
334 5494837 : modinv_double_eta_good_disc(long D, long inv)
335 : {
336 5494837 : pari_sp av = avma;
337 : GEN P;
338 : long i1, i2, p1, p2, N;
339 :
340 5494837 : N = modinv_degree(&p1, &p2, inv);
341 5494837 : if (! N) return 0;
342 5494837 : i1 = kross(D, p1);
343 5494837 : if (i1 < 0) return 0;
344 : /* Exclude ramified case for w_{p,p} */
345 2515481 : if (p1 == p2 && !i1) return 0;
346 2515481 : i2 = kross(D, p2);
347 2515481 : if (i2 < 0) return 0;
348 : /* this also verifies that p1 is prime to the conductor */
349 1402869 : P = red_primeform(D, p1);
350 1402869 : if (!P || gequal1(gel(P,1)) /* don't allow p1 to be principal */
351 : /* if p1 is unramified, require it to have order > 2 */
352 1402869 : || (i1 && qfb_is_two_torsion(P))) return gc_bool(av,0);
353 1401070 : if (p1 == p2) /* if p1=p2 we need p1*p1 to be distinct from its inverse */
354 224098 : return gc_bool(av, !qfb_is_two_torsion(qfbsqr_i(P)));
355 :
356 : /* this also verifies that p2 is prime to the conductor */
357 1176972 : P = red_primeform(D, p2);
358 1176972 : if (!P || gequal1(gel(P,1)) /* don't allow p2 to be principal */
359 : /* if p2 is unramified, require it to have order > 2 */
360 1176972 : || (i2 && qfb_is_two_torsion(P))) return gc_bool(av,0);
361 1175432 : set_avma(av);
362 :
363 : /* if p1 and p2 are split, we also require p1*p2, p1*p2^-1, p1^-1*p2,
364 : * and p1^-1*p2^-1 to be distinct */
365 1175432 : if (i1>0 && i2>0 && !qfb_distinct_prods(D, p1, p2)) return gc_bool(av,0);
366 1172372 : if (!i1 && !i2) {
367 : /* if both p1 and p2 are ramified, make sure their product is not
368 : * principal */
369 144060 : P = qfb_nform(D, N);
370 144060 : if (equali1(gel(P,1))) return gc_bool(av,0);
371 143829 : set_avma(av);
372 : }
373 1172141 : return 1;
374 : }
375 :
376 : /* Assumes D is a good discriminant for inv, which implies that the
377 : * level is prime to the conductor */
378 : long
379 798 : modinv_ramified(long D, long inv, long *pN)
380 : {
381 798 : long p1, p2; *pN = modinv_degree(&p1, &p2, inv);
382 798 : if (*pN <= 1) return 0;
383 798 : return !(D % p1) && !(D % p2);
384 : }
385 :
386 : static int
387 661521 : modinv_good_atkin(long L, long D)
388 : {
389 661521 : long L2 = L*L;
390 : GEN q;
391 661521 : if (kross(D,L) < 0 || -D%L2==0) return 0;
392 348866 : if (-D > 4*L2) return 1;
393 18921 : q = red_primeform(D,L);
394 18921 : if (equali1(gel(q,1))) return 0;
395 16555 : if (D%L==0) return 1;
396 14287 : q = qfbsqr(q);
397 14287 : if (equali1(gel(q,1))) return 0;
398 10409 : return 1;
399 : }
400 :
401 : int
402 15152433 : modinv_good_disc(long inv, long D)
403 : {
404 15152433 : switch (inv) {
405 909454 : case INV_J:
406 909454 : return 1;
407 102781 : case INV_G2:
408 102781 : return !!(D % 3);
409 502845 : case INV_F3:
410 502845 : return (-D & 7) == 7;
411 2058390 : case INV_F:
412 : case INV_F2:
413 : case INV_F4:
414 : case INV_F8:
415 2058390 : return ((-D & 7) == 7) && (D % 3);
416 622069 : case INV_W3W5:
417 622069 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
418 310919 : case INV_W3W3E2:
419 310919 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
420 905674 : case INV_W3W3:
421 905674 : return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
422 667688 : case INV_W2W3E2:
423 667688 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
424 1554721 : case INV_W2W3:
425 1554721 : return ((-D & 7) == 7) && (D % 3) && modinv_double_eta_good_disc(D, inv);
426 1577387 : case INV_W2W5:
427 1577387 : return ((-D % 80) != 20) && (D % 3) && modinv_double_eta_good_disc(D, inv);
428 540722 : case INV_W2W5E2:
429 540722 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
430 566027 : case INV_W2W7E2:
431 566027 : return ((-D % 112) != 84) && modinv_double_eta_good_disc(D, inv);
432 1324607 : case INV_W2W7:
433 1324607 : return ((-D & 7) == 7) && modinv_double_eta_good_disc(D, inv);
434 1185429 : case INV_W2W13:
435 1185429 : return ((-D % 208) != 52) && modinv_double_eta_good_disc(D, inv);
436 679735 : case INV_W3W7:
437 679735 : return (D & 1) && (-D % 21) && modinv_double_eta_good_disc(D, inv);
438 461776 : case INV_W5W7: /* NB: This is a guess; avs doesn't have an entry */
439 461776 : return modinv_double_eta_good_disc(D, inv);
440 520688 : case INV_W3W13: /* NB: This is a guess; avs doesn't have an entry */
441 520688 : return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
442 661521 : case INV_ATKIN3:
443 : case INV_ATKIN5:
444 : case INV_ATKIN7:
445 : case INV_ATKIN11:
446 : case INV_ATKIN13:
447 : case INV_ATKIN17:
448 : case INV_ATKIN19:
449 661521 : return modinv_good_atkin(inv-100, D);
450 : }
451 0 : pari_err_BUG("modinv_good_disc");
452 : return 0;/*LCOV_EXCL_LINE*/
453 : }
454 :
455 : int
456 1008 : modinv_is_Weber(long inv)
457 : {
458 0 : return inv == INV_F || inv == INV_F2 || inv == INV_F3 || inv == INV_F4
459 1008 : || inv == INV_F8;
460 : }
461 :
462 : int
463 254598 : modinv_is_double_eta(long inv)
464 : {
465 254598 : switch (inv) {
466 43116 : case INV_W2W3:
467 : case INV_W2W3E2:
468 : case INV_W2W5:
469 : case INV_W2W5E2:
470 : case INV_W2W7:
471 : case INV_W2W7E2:
472 : case INV_W2W13:
473 : case INV_W3W3:
474 : case INV_W3W3E2:
475 : case INV_W3W5:
476 : case INV_W3W7:
477 : case INV_W5W7:
478 : case INV_W3W13:
479 : case INV_ATKIN3: /* as far as we are concerned */
480 : case INV_ATKIN5: /* as far as we are concerned */
481 : case INV_ATKIN7: /* as far as we are concerned */
482 : case INV_ATKIN11: /* as far as we are concerned */
483 : case INV_ATKIN13: /* as far as we are concerned */
484 : case INV_ATKIN17: /* as far as we are concerned */
485 : case INV_ATKIN19: /* as far as we are concerned */
486 43116 : return 1;
487 : }
488 211482 : return 0;
489 : }
490 :
491 : /* END Code from "class_inv.h" */
492 :
493 : INLINE int
494 10317 : safe_abs_sqrt(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
495 : {
496 10317 : if (krouu(x, p) == -1)
497 : {
498 4782 : if (p%4 == 1) return 0;
499 4782 : x = Fl_neg(x, p);
500 : }
501 10317 : *r = Fl_sqrt_pre_i(x, s2, p, pi);
502 10317 : return 1;
503 : }
504 :
505 : INLINE int
506 5368 : eighth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
507 : {
508 : ulong s;
509 5368 : if (krouu(x, p) == -1) return 0;
510 2937 : s = Fl_sqrt_pre_i(x, s2, p, pi);
511 2938 : return safe_abs_sqrt(&s, s, p, pi, s2) && safe_abs_sqrt(r, s, p, pi, s2);
512 : }
513 :
514 : INLINE ulong
515 3196 : modinv_f_from_j(ulong j, ulong p, ulong pi, ulong s2, long only_residue)
516 : {
517 3196 : pari_sp av = avma;
518 : GEN pol, r;
519 : long i;
520 3196 : ulong g2, f = ULONG_MAX;
521 :
522 : /* f^8 must be a root of X^3 - \gamma_2 X - 16 */
523 3196 : g2 = Fl_sqrtl_pre(j, 3, p, pi);
524 :
525 3196 : pol = mkvecsmall5(0UL, Fl_neg(16 % p, p), Fl_neg(g2, p), 0UL, 1UL);
526 3196 : r = Flx_roots_pre(pol, p, pi);
527 5794 : for (i = 1; i < lg(r); ++i)
528 5794 : if (only_residue)
529 1175 : { if (krouu(r[i], p) != -1) return gc_ulong(av,r[i]); }
530 4619 : else if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
531 0 : pari_err_BUG("modinv_f_from_j");
532 : return 0;/*LCOV_EXCL_LINE*/
533 : }
534 :
535 : INLINE ulong
536 358 : modinv_f3_from_j(ulong j, ulong p, ulong pi, ulong s2)
537 : {
538 358 : pari_sp av = avma;
539 : GEN pol, r;
540 : long i;
541 358 : ulong f = ULONG_MAX;
542 :
543 358 : pol = mkvecsmall5(0UL,
544 358 : Fl_neg(4096 % p, p), Fl_sub(768 % p, j, p), Fl_neg(48 % p, p), 1UL);
545 358 : r = Flx_roots_pre(pol, p, pi);
546 749 : for (i = 1; i < lg(r); ++i)
547 749 : if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
548 0 : pari_err_BUG("modinv_f3_from_j");
549 : return 0;/*LCOV_EXCL_LINE*/
550 : }
551 :
552 : /* Return the exponent e for the double-eta "invariant" w such that
553 : * w^e is a class invariant. For example w2w3^12 is a class
554 : * invariant, so double_eta_exponent(INV_W2W3) is 12 and
555 : * double_eta_exponent(INV_W2W3E2) is 6. */
556 : INLINE ulong
557 69118 : double_eta_exponent(long inv)
558 : {
559 69118 : switch (inv) {
560 2446 : case INV_W2W3: return 12;
561 13588 : case INV_W2W3E2:
562 : case INV_W2W5:
563 13588 : case INV_W3W3: return 6;
564 9730 : case INV_W2W7: return 4;
565 5419 : case INV_W3W5:
566 : case INV_W2W5E2:
567 5419 : case INV_W3W3E2: return 3;
568 15648 : case INV_W2W7E2:
569 : case INV_W2W13:
570 15648 : case INV_W3W7: return 2;
571 22287 : default: return 1;
572 : }
573 : }
574 :
575 : INLINE ulong
576 77 : weber_exponent(long inv)
577 : {
578 77 : switch (inv)
579 : {
580 70 : case INV_F: return 24;
581 0 : case INV_F2: return 12;
582 7 : case INV_F3: return 8;
583 0 : case INV_F4: return 6;
584 0 : case INV_F8: return 3;
585 0 : default: return 1;
586 : }
587 : }
588 :
589 : INLINE ulong
590 33127 : double_eta_power(long inv, ulong w, ulong p, ulong pi)
591 : {
592 33127 : return Fl_powu_pre(w, double_eta_exponent(inv), p, pi);
593 : }
594 :
595 : static GEN
596 455 : double_eta_raw_to_Fp(GEN f, GEN p)
597 : {
598 455 : GEN u = FpX_red(RgV_to_RgX(gel(f,1), 0), p);
599 455 : GEN v = FpX_red(RgV_to_RgX(gel(f,2), 0), p);
600 455 : return mkvec3(u, v, gel(f,3));
601 : }
602 :
603 : /* Given a root x of polclass(D, inv) modulo N, returns a root of polclass(D,0)
604 : * modulo N by plugging x to a modular polynomial. For double-eta quotients,
605 : * this is done by plugging x into the modular polynomial Phi(INV_WpWq, j)
606 : * Enge, Morain 2013: Generalised Weber Functions. */
607 : GEN
608 1162 : Fp_modinv_to_j(GEN x, long inv, GEN p)
609 : {
610 1162 : switch(inv)
611 : {
612 322 : case INV_J: return Fp_red(x, p);
613 308 : case INV_G2: return Fp_powu(x, 3, p);
614 77 : case INV_F: case INV_F2: case INV_F3: case INV_F4: case INV_F8:
615 : {
616 77 : GEN xe = Fp_powu(x, weber_exponent(inv), p);
617 77 : return Fp_div(Fp_powu(subiu(xe, 16), 3, p), xe, p);
618 : }
619 455 : default:
620 455 : if (modinv_is_double_eta(inv))
621 : {
622 455 : GEN xe = Fp_powu(x, double_eta_exponent(inv), p);
623 455 : GEN uvk = double_eta_raw_to_Fp(double_eta_raw(inv), p);
624 455 : GEN J0 = FpX_eval(gel(uvk,1), xe, p);
625 455 : GEN J1 = FpX_eval(gel(uvk,2), xe, p);
626 455 : GEN J2 = Fp_pow(xe, gel(uvk,3), p);
627 455 : GEN phi = mkvec3(J0, J1, J2);
628 455 : return FpX_oneroot(RgX_to_FpX(RgV_to_RgX(phi,1), p),p);
629 : }
630 : pari_err_BUG("Fp_modinv_to_j"); return NULL;/* LCOV_EXCL_LINE */
631 : }
632 : }
633 :
634 : /* Assuming p = 2 (mod 3) and p = 3 (mod 4): if the two 12th roots of
635 : * x (mod p) exist, set *r to one of them and return 1, otherwise
636 : * return 0 (without touching *r). */
637 : INLINE int
638 893 : twelth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
639 : {
640 893 : ulong t = Fl_sqrtl_pre(x, 3, p, pi);
641 893 : if (krouu(t, p) == -1) return 0;
642 850 : t = Fl_sqrt_pre_i(t, s2, p, pi);
643 850 : return safe_abs_sqrt(r, t, p, pi, s2);
644 : }
645 :
646 : INLINE int
647 5721 : sixth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
648 : {
649 5721 : ulong t = Fl_sqrtl_pre(x, 3, p, pi);
650 5721 : if (krouu(t, p) == -1) return 0;
651 5555 : *r = Fl_sqrt_pre_i(t, s2, p, pi);
652 5555 : return 1;
653 : }
654 :
655 : INLINE int
656 3926 : fourth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
657 : {
658 : ulong s;
659 3926 : if (krouu(x, p) == -1) return 0;
660 3592 : s = Fl_sqrt_pre_i(x, s2, p, pi);
661 3592 : return safe_abs_sqrt(r, s, p, pi, s2);
662 : }
663 :
664 : INLINE int
665 35536 : double_eta_root(long inv, ulong *r, ulong w, ulong p, ulong pi, ulong s2)
666 : {
667 35536 : switch (double_eta_exponent(inv)) {
668 893 : case 12: return twelth_root(r, w, p, pi, s2);
669 5721 : case 6: return sixth_root(r, w, p, pi, s2);
670 3926 : case 4: return fourth_root(r, w, p, pi, s2);
671 2343 : case 3: *r = Fl_sqrtl_pre(w, 3, p, pi); return 1;
672 8537 : case 2: return krouu(w, p) != -1 && !!(*r = Fl_sqrt_pre_i(w, s2, p, pi));
673 14115 : default: *r = w; return 1; /* case 1 */
674 : }
675 : }
676 :
677 : /* F = double_eta_Fl(inv, p) */
678 : static GEN
679 62435 : Flx_double_eta_xpoly(GEN F, ulong j, ulong p, ulong pi)
680 : {
681 62435 : GEN u = gel(F,1), v = gel(F,2), w;
682 62435 : long i, k = itos(gel(F,3)), lu = lg(u), lv = lg(v), lw = lu + 1;
683 :
684 62435 : w = cgetg(lw, t_VECSMALL); /* lu >= max(lv,k) */
685 62435 : w[1] = 0; /* variable number */
686 1476528 : for (i = 1; i < lv; i++) uel(w, i+1) = Fl_add(uel(u,i), Fl_mul_pre(j, uel(v,i), p, pi), p);
687 124882 : for ( ; i < lu; i++) uel(w, i+1) = uel(u,i);
688 62441 : uel(w, k+2) = Fl_add(uel(w, k+2), Fl_sqr_pre(j, p, pi), p);
689 62440 : return Flx_renormalize(w, lw);
690 : }
691 :
692 : /* F = double_eta_Fl(inv, p) */
693 : static GEN
694 33127 : Flx_double_eta_jpoly(GEN F, ulong x, ulong p, ulong pi)
695 : {
696 33127 : pari_sp av = avma;
697 33127 : GEN u = gel(F,1), v = gel(F,2), xs;
698 33127 : long k = itos(gel(F,3));
699 : ulong a, b, c;
700 :
701 : /* u is always longest and the length is bigger than k */
702 33127 : xs = Fl_powers_pre(x, lg(u) - 1, p, pi);
703 33126 : c = Flv_dotproduct_pre(u, xs, p, pi);
704 33128 : b = Flv_dotproduct_pre(v, xs, p, pi);
705 33128 : a = uel(xs, k + 1);
706 33128 : set_avma(av);
707 33128 : return mkvecsmall4(0, c, b, a);
708 : }
709 :
710 : /* reduce F = double_eta_raw(inv) mod p */
711 : static GEN
712 40857 : double_eta_raw_to_Fl(GEN f, ulong p)
713 : {
714 40857 : GEN u = ZV_to_Flv(gel(f,1), p);
715 40856 : GEN v = ZV_to_Flv(gel(f,2), p);
716 40856 : return mkvec3(u, v, gel(f,3));
717 : }
718 : /* double_eta_raw(inv) mod p */
719 : static GEN
720 34684 : double_eta_Fl(long inv, ulong p)
721 34684 : { return double_eta_raw_to_Fl(double_eta_raw(inv), p); }
722 :
723 : /* Go through roots of Psi(X,j) until one has an double_eta_exponent(inv)-th
724 : * root, and return that root. F = double_eta_Fl(inv,p) */
725 : INLINE ulong
726 6928 : modinv_double_eta_from_j(GEN F, long inv, ulong j, ulong p, ulong pi, ulong s2)
727 : {
728 6928 : pari_sp av = avma;
729 : long i;
730 6928 : ulong f = ULONG_MAX;
731 6928 : GEN a = Flx_double_eta_xpoly(F, j, p, pi);
732 6928 : a = Flx_roots_pre(a, p, pi);
733 7780 : for (i = 1; i < lg(a); ++i)
734 7780 : if (double_eta_root(inv, &f, uel(a, i), p, pi, s2)) break;
735 6928 : if (i == lg(a)) pari_err_BUG("modinv_double_eta_from_j");
736 6928 : return gc_ulong(av,f);
737 : }
738 :
739 : /* assume j1 != j2 */
740 : static long
741 20828 : modinv_double_eta_from_2j(
742 : ulong *r, long inv, ulong j1, ulong j2, ulong p, ulong pi, ulong s2)
743 : {
744 20828 : GEN f, g, d, F = double_eta_Fl(inv, p);
745 20828 : f = Flx_double_eta_xpoly(F, j1, p, pi);
746 20826 : g = Flx_double_eta_xpoly(F, j2, p, pi);
747 20828 : d = Flx_gcd(f, g, p);
748 : /* we should have deg(d) = 1, but because j1 or j2 may not have the correct
749 : * endomorphism ring, we use the less strict conditional underneath */
750 41654 : return (degpol(d) > 2 || (*r = Flx_oneroot_pre(d, p, pi)) == p
751 41655 : || ! double_eta_root(inv, r, *r, p, pi, s2));
752 : }
753 :
754 : long
755 20906 : modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb)
756 : {
757 20906 : pari_sp av = avma;
758 20906 : long p1, p2, v = ne->v, p1_depth;
759 20906 : ulong j1, p = ne->p, pi = ne->pi, s2 = ne->s2;
760 : GEN phi;
761 :
762 20906 : (void) modinv_degree(&p1, &p2, inv);
763 20906 : p1_depth = u_lval(v, p1);
764 :
765 20906 : phi = polmodular_db_getp(jdb, p1, p);
766 20908 : if (!next_surface_nbr(&j1, phi, p1, p1_depth, j0, NULL, p, pi))
767 0 : pari_err_BUG("modfn_unambiguous_root");
768 20907 : if (p2 == p1) {
769 2150 : if (!next_surface_nbr(&j1, phi, p1, p1_depth, j1, &j0, p, pi))
770 0 : pari_err_BUG("modfn_unambiguous_root");
771 18757 : } else if (p2 > 1)
772 : {
773 10220 : long p2_depth = u_lval(v, p2);
774 10220 : phi = polmodular_db_getp(jdb, p2, p);
775 10220 : if (!next_surface_nbr(&j1, phi, p2, p2_depth, j1, NULL, p, pi))
776 0 : pari_err_BUG("modfn_unambiguous_root");
777 : }
778 23903 : return gc_long(av, j1 != j0
779 20899 : && !modinv_double_eta_from_2j(r, inv, j0, j1, p, pi, s2));
780 : }
781 :
782 : ulong
783 200997 : modfn_root(ulong j, norm_eqn_t ne, long inv)
784 : {
785 200997 : ulong f, p = ne->p, pi = ne->pi, s2 = ne->s2;
786 200997 : switch (inv) {
787 192719 : case INV_J: return j;
788 4724 : case INV_G2: return Fl_sqrtl_pre(j, 3, p, pi);
789 1831 : case INV_F: return modinv_f_from_j(j, p, pi, s2, 0);
790 196 : case INV_F2:
791 196 : f = modinv_f_from_j(j, p, pi, s2, 0);
792 196 : return Fl_sqr_pre(f, p, pi);
793 358 : case INV_F3: return modinv_f3_from_j(j, p, pi, s2);
794 553 : case INV_F4:
795 553 : f = modinv_f_from_j(j, p, pi, s2, 0);
796 553 : return Fl_sqr_pre(Fl_sqr_pre(f, p, pi), p, pi);
797 616 : case INV_F8: return modinv_f_from_j(j, p, pi, s2, 1);
798 : }
799 0 : if (modinv_is_double_eta(inv))
800 : {
801 0 : pari_sp av = avma;
802 0 : ulong f = modinv_double_eta_from_j(double_eta_Fl(inv,p), inv, j, p, pi, s2);
803 0 : return gc_ulong(av,f);
804 : }
805 : pari_err_BUG("modfn_root"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
806 : }
807 :
808 : /* F = double_eta_raw(inv) */
809 : long
810 6172 : modinv_j_from_2double_eta(
811 : GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi)
812 : {
813 : GEN f, g, d;
814 :
815 6172 : x0 = double_eta_power(inv, x0, p, pi);
816 6172 : x1 = double_eta_power(inv, x1, p, pi);
817 6172 : F = double_eta_raw_to_Fl(F, p);
818 6172 : f = Flx_double_eta_jpoly(F, x0, p, pi);
819 6172 : g = Flx_double_eta_jpoly(F, x1, p, pi);
820 6172 : d = Flx_gcd(f, g, p); /* >= 1 */
821 6172 : return degpol(d) == 1;
822 : }
823 :
824 : /* x root of (X^24 - 16)^3 - X^24 * j = 0 => j = (x^24 - 16)^3 / x^24 */
825 : INLINE ulong
826 1844 : modinv_j_from_f(ulong x, ulong n, ulong p, ulong pi)
827 : {
828 1844 : ulong x24 = Fl_powu_pre(x, 24 / n, p, pi);
829 1844 : return Fl_div(Fl_powu_pre(Fl_sub(x24, 16 % p, p), 3, p, pi), x24, p);
830 : }
831 : /* should never be called if modinv_double_eta(inv) is true */
832 : INLINE ulong
833 66943 : modfn_preimage(ulong x, ulong p, ulong pi, long inv)
834 : {
835 66943 : switch (inv) {
836 61173 : case INV_J: return x;
837 3926 : case INV_G2: return Fl_powu_pre(x, 3, p, pi);
838 : /* NB: could replace these with a single call modinv_j_from_f(x,inv,p,pi)
839 : * but avoid the dependence on the actual value of inv */
840 640 : case INV_F: return modinv_j_from_f(x, 1, p, pi);
841 196 : case INV_F2: return modinv_j_from_f(x, 2, p, pi);
842 168 : case INV_F3: return modinv_j_from_f(x, 3, p, pi);
843 392 : case INV_F4: return modinv_j_from_f(x, 4, p, pi);
844 448 : case INV_F8: return modinv_j_from_f(x, 8, p, pi);
845 : }
846 : pari_err_BUG("modfn_preimage"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
847 : }
848 :
849 : /* SECTION: class group bb_group. */
850 :
851 : INLINE GEN
852 144717 : mkqfis(GEN a, ulong b, ulong c, GEN D) { retmkqfb(a, utoi(b), utoi(c), D); }
853 :
854 : /* SECTION: dot-product-like functions on Fl's with precomputed inverse. */
855 :
856 : /* Computes x0y1 + y0x1 (mod p); assumes p < 2^63. */
857 : INLINE ulong
858 60043825 : Fl_addmul2(
859 : ulong x0, ulong x1, ulong y0, ulong y1,
860 : ulong p, ulong pi)
861 : {
862 60043825 : return Fl_addmulmul_pre(x0,y1,y0,x1,p,pi);
863 : }
864 :
865 : /* Computes x0y2 + x1y1 + x2y0 (mod p); assumes p < 2^62. */
866 : INLINE ulong
867 11155332 : Fl_addmul3(
868 : ulong x0, ulong x1, ulong x2, ulong y0, ulong y1, ulong y2,
869 : ulong p, ulong pi)
870 : {
871 : ulong l0, l1, h0, h1;
872 : LOCAL_OVERFLOW;
873 : LOCAL_HIREMAINDER;
874 11155332 : l0 = mulll(x0, y2); h0 = hiremainder;
875 11155332 : l1 = mulll(x1, y1); h1 = hiremainder;
876 11155332 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
877 11155332 : l0 = mulll(x2, y0); h0 = hiremainder;
878 11155332 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
879 11155332 : return remll_pre(h1, l1, p, pi);
880 : }
881 :
882 : /* Computes x0y3 + x1y2 + x2y1 + x3y0 (mod p); assumes p < 2^62. */
883 : INLINE ulong
884 5173213 : Fl_addmul4(
885 : ulong x0, ulong x1, ulong x2, ulong x3,
886 : ulong y0, ulong y1, ulong y2, ulong y3,
887 : ulong p, ulong pi)
888 : {
889 : ulong l0, l1, h0, h1;
890 : LOCAL_OVERFLOW;
891 : LOCAL_HIREMAINDER;
892 5173213 : l0 = mulll(x0, y3); h0 = hiremainder;
893 5173213 : l1 = mulll(x1, y2); h1 = hiremainder;
894 5173213 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
895 5173213 : l0 = mulll(x2, y1); h0 = hiremainder;
896 5173213 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
897 5173213 : l0 = mulll(x3, y0); h0 = hiremainder;
898 5173213 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
899 5173213 : return remll_pre(h1, l1, p, pi);
900 : }
901 :
902 : /* Computes x0y4 + x1y3 + x2y2 + x3y1 + x4y0 (mod p); assumes p < 2^62. */
903 : INLINE ulong
904 25720444 : Fl_addmul5(
905 : ulong x0, ulong x1, ulong x2, ulong x3, ulong x4,
906 : ulong y0, ulong y1, ulong y2, ulong y3, ulong y4,
907 : ulong p, ulong pi)
908 : {
909 : ulong l0, l1, h0, h1;
910 : LOCAL_OVERFLOW;
911 : LOCAL_HIREMAINDER;
912 25720444 : l0 = mulll(x0, y4); h0 = hiremainder;
913 25720444 : l1 = mulll(x1, y3); h1 = hiremainder;
914 25720444 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
915 25720444 : l0 = mulll(x2, y2); h0 = hiremainder;
916 25720444 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
917 25720444 : l0 = mulll(x3, y1); h0 = hiremainder;
918 25720444 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
919 25720444 : l0 = mulll(x4, y0); h0 = hiremainder;
920 25720444 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
921 25720444 : return remll_pre(h1, l1, p, pi);
922 : }
923 :
924 : /* A polmodular database for a given class invariant consists of a t_VEC whose
925 : * L-th entry is 0 or a GEN pointing to Phi_L. This function produces a pair
926 : * of databases corresponding to the j-invariant and inv */
927 : GEN
928 21492 : polmodular_db_init(long inv)
929 : {
930 21492 : const long LEN = 32;
931 21492 : GEN res = cgetg_block(3, t_VEC);
932 21492 : gel(res, 1) = zerovec_block(LEN);
933 21492 : gel(res, 2) = (inv == INV_J)? gen_0: zerovec_block(LEN);
934 21492 : return res;
935 : }
936 :
937 : void
938 27080 : polmodular_db_add_level(GEN *DB, long L, long inv)
939 : {
940 27080 : GEN db = gel(*DB, (inv == INV_J)? 1: 2);
941 27080 : long max_L = lg(db) - 1;
942 27080 : if (L > max_L) {
943 : GEN newdb;
944 50 : long i, newlen = 2 * L;
945 :
946 50 : newdb = cgetg_block(newlen + 1, t_VEC);
947 1650 : for (i = 1; i <= max_L; ++i) gel(newdb, i) = gel(db, i);
948 3242 : for ( ; i <= newlen; ++i) gel(newdb, i) = gen_0;
949 50 : killblock(db);
950 50 : gel(*DB, (inv == INV_J)? 1: 2) = db = newdb;
951 : }
952 27080 : if (typ(gel(db, L)) == t_INT) {
953 8571 : pari_sp av = avma;
954 8571 : GEN x = polmodular0_ZM(L, inv, NULL, NULL, 0, DB); /* may set db[L] */
955 8571 : GEN y = gel(db, L);
956 8571 : gel(db, L) = gclone(x);
957 8571 : if (typ(y) != t_INT) gunclone(y);
958 8571 : set_avma(av);
959 : }
960 27080 : }
961 :
962 : void
963 5257 : polmodular_db_add_levels(GEN *db, long *levels, long k, long inv)
964 : {
965 : long i;
966 10860 : for (i = 0; i < k; ++i) polmodular_db_add_level(db, levels[i], inv);
967 5257 : }
968 :
969 : GEN
970 387258 : polmodular_db_for_inv(GEN db, long inv) { return gel(db, (inv==INV_J)? 1: 2); }
971 :
972 : /* TODO: Also cache modpoly mod p for most recent p (avoid repeated
973 : * reductions in, for example, polclass.c:oneroot_of_classpoly(). */
974 : GEN
975 560140 : polmodular_db_getp(GEN db, long L, ulong p)
976 : {
977 560140 : GEN f = gel(db, L);
978 560140 : if (isintzero(f)) pari_err_BUG("polmodular_db_getp");
979 560135 : return ZM_to_Flm(f, p);
980 : }
981 :
982 : /* SECTION: Table of discriminants to use. */
983 : typedef struct {
984 : long GENcode0; /* used when serializing the struct to a t_VECSMALL */
985 : long inv; /* invariant */
986 : long L; /* modpoly level */
987 : long D0; /* fundamental discriminant */
988 : long D1; /* chosen discriminant */
989 : long L0; /* first generator norm */
990 : long L1; /* second generator norm */
991 : long n1; /* order of L0 in cl(D1) */
992 : long n2; /* order of L0 in cl(D2) where D2 = L^2 D1 */
993 : long dl1; /* m such that L0^m = L in cl(D1) */
994 : long dl2_0; /* These two are (m, n) such that L0^m L1^n = form of norm L^2 in D2 */
995 : long dl2_1; /* This n is always 1 or 0. */
996 : /* this part is not serialized */
997 : long nprimes; /* number of primes needed for D1 */
998 : long cost; /* cost to enumerate subgroup of cl(L^2D): subgroup size is n2 if L1=0, 2*n2 o.w. */
999 : long bits;
1000 : ulong *primes;
1001 : ulong *traces;
1002 : } disc_info;
1003 :
1004 : #define MODPOLY_MAX_DCNT 64
1005 :
1006 : /* Flag for last parameter of discriminant_with_classno_at_least.
1007 : * Warning: ignoring the sparse factor makes everything slower by
1008 : * something like (sparse factor)^3. */
1009 : #define USE_SPARSE_FACTOR 0
1010 : #define IGNORE_SPARSE_FACTOR 1
1011 :
1012 : static long
1013 : discriminant_with_classno_at_least(disc_info Ds[MODPOLY_MAX_DCNT], long L,
1014 : long inv, GEN Q, long ignore_sparse);
1015 :
1016 : /* SECTION: evaluation functions for modular polynomials of small level. */
1017 :
1018 : /* Based on phi2_eval_ff() in Sutherland's classpoly programme.
1019 : * Calculates Phi_2(X, j) (mod p) with 6M+7A (4 reductions, not
1020 : * counting those for Phi_2) */
1021 : INLINE GEN
1022 28253339 : Flm_Fl_phi2_evalx(GEN phi2, ulong j, ulong p, ulong pi)
1023 : {
1024 28253339 : GEN res = cgetg(6, t_VECSMALL);
1025 : ulong j2, t1;
1026 :
1027 28210714 : res[1] = 0; /* variable name */
1028 :
1029 28210714 : j2 = Fl_sqr_pre(j, p, pi);
1030 28251828 : t1 = Fl_add(j, coeff(phi2, 3, 1), p);
1031 28243022 : t1 = Fl_addmul2(j, j2, t1, coeff(phi2, 2, 1), p, pi);
1032 28329707 : res[2] = Fl_add(t1, coeff(phi2, 1, 1), p);
1033 :
1034 28297069 : t1 = Fl_addmul2(j, j2, coeff(phi2, 3, 2), coeff(phi2, 2, 2), p, pi);
1035 28347706 : res[3] = Fl_add(t1, coeff(phi2, 2, 1), p);
1036 :
1037 28315619 : t1 = Fl_mul_pre(j, coeff(phi2, 3, 2), p, pi);
1038 28324045 : t1 = Fl_add(t1, coeff(phi2, 3, 1), p);
1039 28298673 : res[4] = Fl_sub(t1, j2, p);
1040 :
1041 28275944 : res[5] = 1;
1042 28275944 : return res;
1043 : }
1044 :
1045 : /* Based on phi3_eval_ff() in Sutherland's classpoly programme.
1046 : * Calculates Phi_3(X, j) (mod p) with 13M+13A (6 reductions, not
1047 : * counting those for Phi_3) */
1048 : INLINE GEN
1049 3724928 : Flm_Fl_phi3_evalx(GEN phi3, ulong j, ulong p, ulong pi)
1050 : {
1051 3724928 : GEN res = cgetg(7, t_VECSMALL);
1052 : ulong j2, j3, t1;
1053 :
1054 3721691 : res[1] = 0; /* variable name */
1055 :
1056 3721691 : j2 = Fl_sqr_pre(j, p, pi);
1057 3725055 : j3 = Fl_mul_pre(j, j2, p, pi);
1058 :
1059 3726488 : t1 = Fl_add(j, coeff(phi3, 4, 1), p);
1060 3726801 : t1 = Fl_addmul3(j, j2, j3, t1, coeff(phi3, 3, 1), coeff(phi3, 2, 1), p, pi);
1061 3733472 : res[2] = Fl_add(t1, coeff(phi3, 1, 1), p);
1062 :
1063 3731229 : t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 2),
1064 3731229 : coeff(phi3, 3, 2), coeff(phi3, 2, 2), p, pi);
1065 3734305 : res[3] = Fl_add(t1, coeff(phi3, 2, 1), p);
1066 :
1067 3732227 : t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 3),
1068 3732227 : coeff(phi3, 3, 3), coeff(phi3, 3, 2), p, pi);
1069 3734665 : res[4] = Fl_add(t1, coeff(phi3, 3, 1), p);
1070 :
1071 3732238 : t1 = Fl_addmul2(j, j2, coeff(phi3, 4, 3), coeff(phi3, 4, 2), p, pi);
1072 3734233 : t1 = Fl_add(t1, coeff(phi3, 4, 1), p);
1073 3731917 : res[5] = Fl_sub(t1, j3, p);
1074 :
1075 3729796 : res[6] = 1;
1076 3729796 : return res;
1077 : }
1078 :
1079 : /* Based on phi5_eval_ff() in Sutherland's classpoly programme.
1080 : * Calculates Phi_5(X, j) (mod p) with 33M+31A (10 reductions, not
1081 : * counting those for Phi_5) */
1082 : INLINE GEN
1083 5164136 : Flm_Fl_phi5_evalx(GEN phi5, ulong j, ulong p, ulong pi)
1084 : {
1085 5164136 : GEN res = cgetg(9, t_VECSMALL);
1086 : ulong j2, j3, j4, j5, t1;
1087 :
1088 5159513 : res[1] = 0; /* variable name */
1089 :
1090 5159513 : j2 = Fl_sqr_pre(j, p, pi);
1091 5163033 : j3 = Fl_mul_pre(j, j2, p, pi);
1092 5164785 : j4 = Fl_sqr_pre(j2, p, pi);
1093 5164821 : j5 = Fl_mul_pre(j, j4, p, pi);
1094 :
1095 5167541 : t1 = Fl_add(j, coeff(phi5, 6, 1), p);
1096 5167585 : t1 = Fl_addmul5(j, j2, j3, j4, j5, t1,
1097 5167585 : coeff(phi5, 5, 1), coeff(phi5, 4, 1),
1098 5167585 : coeff(phi5, 3, 1), coeff(phi5, 2, 1),
1099 : p, pi);
1100 5174472 : res[2] = Fl_add(t1, coeff(phi5, 1, 1), p);
1101 :
1102 5170459 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1103 5170459 : coeff(phi5, 6, 2), coeff(phi5, 5, 2),
1104 5170459 : coeff(phi5, 4, 2), coeff(phi5, 3, 2), coeff(phi5, 2, 2),
1105 : p, pi);
1106 5175560 : res[3] = Fl_add(t1, coeff(phi5, 2, 1), p);
1107 :
1108 5171860 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1109 5171860 : coeff(phi5, 6, 3), coeff(phi5, 5, 3),
1110 5171860 : coeff(phi5, 4, 3), coeff(phi5, 3, 3), coeff(phi5, 3, 2),
1111 : p, pi);
1112 5176491 : res[4] = Fl_add(t1, coeff(phi5, 3, 1), p);
1113 :
1114 5173822 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1115 5173822 : coeff(phi5, 6, 4), coeff(phi5, 5, 4),
1116 5173822 : coeff(phi5, 4, 4), coeff(phi5, 4, 3), coeff(phi5, 4, 2),
1117 : p, pi);
1118 5176341 : res[5] = Fl_add(t1, coeff(phi5, 4, 1), p);
1119 :
1120 5172973 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1121 5172973 : coeff(phi5, 6, 5), coeff(phi5, 5, 5),
1122 5172973 : coeff(phi5, 5, 4), coeff(phi5, 5, 3), coeff(phi5, 5, 2),
1123 : p, pi);
1124 5178061 : res[6] = Fl_add(t1, coeff(phi5, 5, 1), p);
1125 :
1126 5174621 : t1 = Fl_addmul4(j, j2, j3, j4,
1127 5174621 : coeff(phi5, 6, 5), coeff(phi5, 6, 4),
1128 5174621 : coeff(phi5, 6, 3), coeff(phi5, 6, 2),
1129 : p, pi);
1130 5178793 : t1 = Fl_add(t1, coeff(phi5, 6, 1), p);
1131 5175158 : res[7] = Fl_sub(t1, j5, p);
1132 :
1133 5172549 : res[8] = 1;
1134 5172549 : return res;
1135 : }
1136 :
1137 : GEN
1138 44164033 : Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi)
1139 : {
1140 44164033 : switch (L) {
1141 28257452 : case 2: return Flm_Fl_phi2_evalx(phi, j, p, pi);
1142 3723803 : case 3: return Flm_Fl_phi3_evalx(phi, j, p, pi);
1143 5162965 : case 5: return Flm_Fl_phi5_evalx(phi, j, p, pi);
1144 7019813 : default: { /* not GC clean, but gc_upto-safe */
1145 7019813 : GEN j_powers = Fl_powers_pre(j, L + 1, p, pi);
1146 7105599 : return Flm_Flc_mul_pre_Flx(phi, j_powers, p, pi, 0);
1147 : }
1148 : }
1149 : }
1150 :
1151 : /* SECTION: Velu's formula for the codmain curve (Fl case). */
1152 :
1153 : INLINE ulong
1154 1769299 : Fl_mul4(ulong x, ulong p)
1155 1769299 : { return Fl_double(Fl_double(x, p), p); }
1156 :
1157 : INLINE ulong
1158 96360 : Fl_mul5(ulong x, ulong p)
1159 96360 : { return Fl_add(x, Fl_mul4(x, p), p); }
1160 :
1161 : INLINE ulong
1162 884763 : Fl_mul8(ulong x, ulong p)
1163 884763 : { return Fl_double(Fl_mul4(x, p), p); }
1164 :
1165 : INLINE ulong
1166 788446 : Fl_mul6(ulong x, ulong p)
1167 788446 : { return Fl_sub(Fl_mul8(x, p), Fl_double(x, p), p); }
1168 :
1169 : INLINE ulong
1170 96359 : Fl_mul7(ulong x, ulong p)
1171 96359 : { return Fl_sub(Fl_mul8(x, p), x, p); }
1172 :
1173 : /* Given an elliptic curve E = [a4, a6] over F_p and a nonzero point
1174 : * pt on E, return the quotient E' = E/<P> = [a4_img, a6_img] */
1175 : static void
1176 96360 : Fle_quotient_from_kernel_generator(
1177 : ulong *a4_img, ulong *a6_img, ulong a4, ulong a6, GEN pt, ulong p, ulong pi)
1178 : {
1179 96360 : pari_sp av = avma;
1180 96360 : ulong t = 0, w = 0;
1181 : GEN Q;
1182 : ulong xQ, yQ, tQ, uQ;
1183 :
1184 96360 : Q = gcopy(pt);
1185 : /* Note that, as L is odd, say L = 2n + 1, we necessarily have
1186 : * [(L - 1)/2]P = [n]P = [n - L]P = -[n + 1]P = -[(L + 1)/2]P. This is
1187 : * what the condition Q[1] != xQ tests, so the loop will execute n times. */
1188 : do {
1189 788381 : xQ = uel(Q, 1);
1190 788381 : yQ = uel(Q, 2);
1191 : /* tQ = 6 xQ^2 + b2 xQ + b4
1192 : * = 6 xQ^2 + 2 a4 (since b2 = 0 and b4 = 2 a4) */
1193 788381 : tQ = Fl_add(Fl_mul6(Fl_sqr_pre(xQ, p, pi), p), Fl_double(a4, p), p);
1194 788337 : uQ = Fl_add(Fl_mul4(Fl_sqr_pre(yQ, p, pi), p),
1195 : Fl_mul_pre(tQ, xQ, p, pi), p);
1196 :
1197 788362 : t = Fl_add(t, tQ, p);
1198 788315 : w = Fl_add(w, uQ, p);
1199 788285 : Q = gc_upto(av, Fle_add(pt, Q, a4, p));
1200 788381 : } while (uel(Q, 1) != xQ);
1201 :
1202 96360 : set_avma(av);
1203 : /* a4_img = a4 - 5 * t */
1204 96360 : *a4_img = Fl_sub(a4, Fl_mul5(t, p), p);
1205 : /* a6_img = a6 - b2 * t - 7 * w = a6 - 7 * w (since a1 = a2 = 0 ==> b2 = 0) */
1206 96359 : *a6_img = Fl_sub(a6, Fl_mul7(w, p), p);
1207 96358 : }
1208 :
1209 : /* SECTION: Calculation of modular polynomials. */
1210 :
1211 : /* Given an elliptic curve [a4, a6] over FF_p, try to find a
1212 : * nontrivial L-torsion point on the curve by considering n times a
1213 : * random point; val controls the maximum L-valuation expected of n
1214 : * times a random point */
1215 : static GEN
1216 140797 : find_L_tors_point(
1217 : ulong *ival,
1218 : ulong a4, ulong a6, ulong p, ulong pi,
1219 : ulong n, ulong L, ulong val)
1220 : {
1221 140797 : pari_sp av = avma;
1222 : ulong i;
1223 : GEN P, Q;
1224 : do {
1225 142213 : Q = random_Flj_pre(a4, a6, p, pi);
1226 142215 : P = Flj_mulu_pre(Q, n, a4, p, pi);
1227 142223 : } while (P[3] == 0);
1228 :
1229 273290 : for (i = 0; i < val; ++i) {
1230 228842 : Q = Flj_mulu_pre(P, L, a4, p, pi);
1231 228843 : if (Q[3] == 0) break;
1232 132483 : P = Q;
1233 : }
1234 140808 : if (ival) *ival = i;
1235 140808 : return gc_GEN(av, P);
1236 : }
1237 :
1238 : static GEN
1239 87721 : select_curve_with_L_tors_point(
1240 : ulong *a4, ulong *a6,
1241 : ulong L, ulong j, ulong n, ulong card, ulong val,
1242 : norm_eqn_t ne)
1243 : {
1244 87721 : pari_sp av = avma;
1245 : ulong A4, A4t, A6, A6t;
1246 87721 : ulong p = ne->p, pi = ne->pi;
1247 : GEN P;
1248 87721 : if (card % L != 0) {
1249 0 : pari_err_BUG("select_curve_with_L_tors_point: "
1250 : "Cardinality not divisible by L");
1251 : }
1252 :
1253 87721 : Fl_ellj_to_a4a6(j, p, &A4, &A6);
1254 87721 : Fl_elltwist_disc(A4, A6, ne->T, p, &A4t, &A6t);
1255 :
1256 : /* Either E = [a4, a6] or its twist has cardinality divisible by L
1257 : * because of the choice of p and t earlier on. We find out which
1258 : * by attempting to find a point of order L on each. See bot p16 of
1259 : * Sutherland 2012. */
1260 44449 : while (1) {
1261 : ulong i;
1262 132165 : P = find_L_tors_point(&i, A4, A6, p, pi, n, L, val);
1263 132175 : if (i < val)
1264 87728 : break;
1265 44447 : set_avma(av);
1266 44449 : lswap(A4, A4t);
1267 44449 : lswap(A6, A6t);
1268 : }
1269 87728 : *a4 = A4;
1270 87728 : *a6 = A6; return gc_GEN(av, P);
1271 : }
1272 :
1273 : /* Return 1 if the L-Sylow subgroup of the curve [a4, a6] (mod p) is
1274 : * cyclic, return 0 if it is not cyclic with "high" probability (I
1275 : * guess around 1/L^3 chance it is still cyclic when we return 0).
1276 : *
1277 : * Based on Sutherland's velu.c:velu_verify_Sylow_cyclic() in classpoly-1.0.1 */
1278 : INLINE long
1279 49032 : verify_L_sylow_is_cyclic(long e, ulong a4, ulong a6, ulong p, ulong pi)
1280 : {
1281 : /* Number of times to try to find a point with maximal order in the
1282 : * L-Sylow subgroup. */
1283 : enum { N_RETRIES = 3 };
1284 49032 : pari_sp av = avma;
1285 49032 : long i, res = 0;
1286 : GEN P;
1287 79511 : for (i = 0; i < N_RETRIES; ++i) {
1288 70879 : P = random_Flj_pre(a4, a6, p, pi);
1289 70873 : P = Flj_mulu_pre(P, e, a4, p, pi);
1290 70880 : if (P[3] != 0) { res = 1; break; }
1291 : }
1292 49033 : return gc_long(av,res);
1293 : }
1294 :
1295 : static ulong
1296 87728 : find_noniso_L_isogenous_curve(
1297 : ulong L, ulong n,
1298 : norm_eqn_t ne, long e, ulong val, ulong a4, ulong a6, GEN init_pt, long verify)
1299 : {
1300 : pari_sp ltop, av;
1301 87728 : ulong p = ne->p, pi = ne->pi, j_res = 0;
1302 87728 : GEN pt = init_pt;
1303 87728 : ltop = av = avma;
1304 8632 : while (1) {
1305 : /* c. Use Velu to calculate L-isogenous curve E' = E/<P> */
1306 : ulong a4_img, a6_img;
1307 96360 : ulong z2 = Fl_sqr_pre(pt[3], p, pi);
1308 96360 : pt = mkvecsmall2(Fl_div(pt[1], z2, p),
1309 96360 : Fl_div(pt[2], Fl_mul_pre(z2, pt[3], p, pi), p));
1310 96360 : Fle_quotient_from_kernel_generator(&a4_img, &a6_img,
1311 : a4, a6, pt, p, pi);
1312 :
1313 : /* d. If j(E') = j_res has a different endo ring to j(E), then
1314 : * return j(E'). Otherwise, go to b. */
1315 96358 : if (!verify || verify_L_sylow_is_cyclic(e, a4_img, a6_img, p, pi)) {
1316 87727 : j_res = Fl_ellj_pre(a4_img, a6_img, p, pi);
1317 87730 : break;
1318 : }
1319 :
1320 : /* b. Generate random point P on E of order L */
1321 8632 : set_avma(av);
1322 8632 : pt = find_L_tors_point(NULL, a4, a6, p, pi, n, L, val);
1323 : }
1324 87730 : return gc_ulong(ltop, j_res);
1325 : }
1326 :
1327 : /* Given a prime L and a j-invariant j (mod p), return the j-invariant
1328 : * of a curve which has a different endomorphism ring to j and is
1329 : * L-isogenous to j */
1330 : INLINE ulong
1331 87720 : compute_L_isogenous_curve(
1332 : ulong L, ulong n, norm_eqn_t ne,
1333 : ulong j, ulong card, ulong val, long verify)
1334 : {
1335 : ulong a4, a6;
1336 : long e;
1337 : GEN pt;
1338 :
1339 87720 : if (ne->p < 5 || j == 0 || j == 1728 % ne->p)
1340 0 : pari_err_BUG("compute_L_isogenous_curve");
1341 87720 : pt = select_curve_with_L_tors_point(&a4, &a6, L, j, n, card, val, ne);
1342 87727 : e = card / L;
1343 87727 : if (e * L != card) pari_err_BUG("compute_L_isogenous_curve");
1344 :
1345 87727 : return find_noniso_L_isogenous_curve(L, n, ne, e, val, a4, a6, pt, verify);
1346 : }
1347 :
1348 : INLINE GEN
1349 40400 : get_Lsqr_cycle(const disc_info *dinfo)
1350 : {
1351 40400 : long i, n1 = dinfo->n1, L = dinfo->L;
1352 40400 : GEN cyc = cgetg(L, t_VECSMALL);
1353 40401 : cyc[1] = 0;
1354 330960 : for (i = 2; i <= L / 2; ++i) cyc[i] = cyc[i - 1] + n1;
1355 40401 : if ( ! dinfo->L1) {
1356 119700 : for ( ; i < L; ++i) cyc[i] = cyc[i - 1] + n1;
1357 : } else {
1358 26082 : cyc[L - 1] = 2 * dinfo->n2 - n1 / 2;
1359 225579 : for (i = L - 2; i > L / 2; --i) cyc[i] = cyc[i + 1] - n1;
1360 : }
1361 40401 : return cyc;
1362 : }
1363 :
1364 : INLINE void
1365 573733 : update_Lsqr_cycle(GEN cyc, const disc_info *dinfo)
1366 : {
1367 573733 : long i, L = dinfo->L;
1368 16378424 : for (i = 1; i < L; ++i) ++cyc[i];
1369 573733 : if (dinfo->L1 && cyc[L - 1] == 2 * dinfo->n2) {
1370 24405 : long n1 = dinfo->n1;
1371 220910 : for (i = L / 2 + 1; i < L; ++i) cyc[i] -= n1;
1372 : }
1373 573733 : }
1374 :
1375 : static ulong
1376 40396 : oneroot_of_classpoly(GEN hilb, GEN factu, norm_eqn_t ne, GEN jdb)
1377 : {
1378 40396 : pari_sp av = avma;
1379 40396 : ulong j0, p = ne->p, pi = ne->pi;
1380 40396 : long i, nfactors = lg(gel(factu, 1)) - 1;
1381 40396 : GEN hilbp = ZX_to_Flx(hilb, p);
1382 :
1383 : /* TODO: Work out how to use hilb with better invariant */
1384 40387 : j0 = Flx_oneroot_split_pre(hilbp, p, pi);
1385 40398 : if (j0 == p) {
1386 0 : pari_err_BUG("oneroot_of_classpoly: "
1387 : "Didn't find a root of the class polynomial");
1388 : }
1389 41959 : for (i = 1; i <= nfactors; ++i) {
1390 1560 : long L = gel(factu, 1)[i];
1391 1560 : long val = gel(factu, 2)[i];
1392 1560 : GEN phi = polmodular_db_getp(jdb, L, p);
1393 1561 : val += z_lval(ne->v, L);
1394 1561 : j0 = descend_volcano(phi, j0, p, pi, 0, L, val, val);
1395 1561 : set_avma(av);
1396 : }
1397 40399 : return gc_ulong(av, j0);
1398 : }
1399 :
1400 : /* TODO: Precompute the GEN structs and link them to dinfo */
1401 : INLINE GEN
1402 3077 : make_pcp_surface(const disc_info *dinfo)
1403 : {
1404 3077 : GEN L = mkvecsmall(dinfo->L0);
1405 3077 : GEN n = mkvecsmall(dinfo->n1);
1406 3077 : GEN o = mkvecsmall(dinfo->n1);
1407 3077 : return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, 1, dinfo->n1));
1408 : }
1409 :
1410 : INLINE GEN
1411 3077 : make_pcp_floor(const disc_info *dinfo)
1412 : {
1413 3077 : long k = dinfo->L1 ? 2 : 1;
1414 : GEN L, n, o;
1415 3077 : if (k==1)
1416 : {
1417 1482 : L = mkvecsmall(dinfo->L0);
1418 1482 : n = mkvecsmall(dinfo->n2);
1419 1482 : o = mkvecsmall(dinfo->n2);
1420 : } else
1421 : {
1422 1595 : L = mkvecsmall2(dinfo->L0, dinfo->L1);
1423 1595 : n = mkvecsmall2(dinfo->n2, 2);
1424 1595 : o = mkvecsmall2(dinfo->n2, 2);
1425 : }
1426 3077 : return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, k, dinfo->n2*k));
1427 : }
1428 :
1429 : INLINE GEN
1430 40401 : enum_volcano_surface(norm_eqn_t ne, ulong j0, GEN fdb, GEN G)
1431 : {
1432 40401 : pari_sp av = avma;
1433 40401 : return gc_upto(av, enum_roots(j0, ne, fdb, G, NULL));
1434 : }
1435 :
1436 : INLINE GEN
1437 40400 : enum_volcano_floor(long L, norm_eqn_t ne, ulong j0_pr, GEN fdb, GEN G)
1438 : {
1439 40400 : pari_sp av = avma;
1440 : /* L^2 D is the discriminant for the order R = Z + L OO. */
1441 40400 : long DR = L * L * ne->D;
1442 40400 : long R_cond = L * ne->u; /* conductor(DR); */
1443 40400 : long w = R_cond * ne->v;
1444 : /* TODO: Calculate these once and for all in polmodular0_ZM(). */
1445 : norm_eqn_t eqn;
1446 40400 : memcpy(eqn, ne, sizeof *ne);
1447 40400 : eqn->D = DR;
1448 40400 : eqn->u = R_cond;
1449 40400 : eqn->v = w;
1450 40400 : return gc_upto(av, enum_roots(j0_pr, eqn, fdb, G, NULL));
1451 : }
1452 :
1453 : INLINE void
1454 19448 : carray_reverse_inplace(long *arr, long n)
1455 : {
1456 19448 : long lim = n>>1, i;
1457 19448 : --n;
1458 197354 : for (i = 0; i < lim; i++) lswap(arr[i], arr[n - i]);
1459 19448 : }
1460 :
1461 : INLINE void
1462 614138 : append_neighbours(GEN rts, GEN surface_js, long njs, long L, long m, long i)
1463 : {
1464 614138 : long r_idx = (((i - 1) + m) % njs) + 1; /* (i + m) % njs */
1465 614138 : long l_idx = umodsu((i - 1) - m, njs) + 1; /* (i - m) % njs */
1466 614136 : rts[L] = surface_js[l_idx];
1467 614136 : rts[L + 1] = surface_js[r_idx];
1468 614136 : }
1469 :
1470 : INLINE GEN
1471 42764 : roots_to_coeffs(GEN rts, ulong p, long L)
1472 : {
1473 42764 : long i, k, lrts= lg(rts);
1474 42764 : GEN M = cgetg(L+2+1, t_MAT);
1475 913793 : for (i = 1; i <= L+2; ++i)
1476 871033 : gel(M, i) = cgetg(lrts, t_VECSMALL);
1477 682447 : for (i = 1; i < lrts; ++i) {
1478 639740 : pari_sp av = avma;
1479 639740 : GEN modpol = Flv_roots_to_pol(gel(rts, i), p, 0);
1480 20410945 : for (k = 1; k <= L + 2; ++k) mael(M, k, i) = modpol[k + 1];
1481 639531 : set_avma(av);
1482 : }
1483 42707 : return M;
1484 : }
1485 :
1486 : /* NB: Assumes indices are offset at 0, not at 1 like in GENs;
1487 : * i.e. indices[i] will pick out v[indices[i] + 1] from v. */
1488 : INLINE void
1489 614133 : vecsmall_pick(GEN res, GEN v, GEN indices)
1490 : {
1491 : long i;
1492 17080959 : for (i = 1; i < lg(indices); ++i) res[i] = v[indices[i] + 1];
1493 614133 : }
1494 :
1495 : /* First element of surface_js must lie above the first element of floor_js.
1496 : * Reverse surface_js if it is not oriented in the same direction as floor_js */
1497 : INLINE GEN
1498 40400 : root_matrix(long L, const disc_info *dinfo, long njinvs, GEN surface_js,
1499 : GEN floor_js, ulong n, ulong card, ulong val, norm_eqn_t ne)
1500 : {
1501 : pari_sp av;
1502 40400 : long i, m = dinfo->dl1, njs = lg(surface_js) - 1, inv = dinfo->inv, rev;
1503 40400 : GEN rt_mat = zero_Flm_copy(L + 1, njinvs), rts, cyc;
1504 40400 : ulong p = ne->p, pi = ne->pi, j;
1505 40400 : av = avma;
1506 :
1507 40400 : i = 1;
1508 40400 : cyc = get_Lsqr_cycle(dinfo);
1509 40401 : rts = gel(rt_mat, i);
1510 40401 : vecsmall_pick(rts, floor_js, cyc);
1511 40400 : append_neighbours(rts, surface_js, njs, L, m, i);
1512 :
1513 40400 : i = 2;
1514 40400 : update_Lsqr_cycle(cyc, dinfo);
1515 40400 : rts = gel(rt_mat, i);
1516 40400 : vecsmall_pick(rts, floor_js, cyc);
1517 :
1518 : /* Fix orientation if necessary */
1519 40400 : if (modinv_is_double_eta(inv)) {
1520 : /* TODO: There is potential for refactoring between this,
1521 : * double_eta_initial_js and modfn_preimage. */
1522 6928 : pari_sp av0 = avma;
1523 6928 : GEN F = double_eta_Fl(inv, p);
1524 6928 : pari_sp av = avma;
1525 6928 : ulong r1 = double_eta_power(inv, uel(rts, 1), p, pi);
1526 6928 : GEN r, f = Flx_double_eta_jpoly(F, r1, p, pi);
1527 6928 : if ((j = Flx_oneroot_pre(f, p, pi)) == p) pari_err_BUG("root_matrix");
1528 6928 : j = compute_L_isogenous_curve(L, n, ne, j, card, val, 0);
1529 6928 : set_avma(av);
1530 6928 : r1 = double_eta_power(inv, uel(surface_js, i), p, pi);
1531 6928 : f = Flx_double_eta_jpoly(F, r1, p, pi);
1532 6928 : r = Flx_roots_pre(f, p, pi);
1533 6928 : if (lg(r) != 3) pari_err_BUG("root_matrix");
1534 6928 : rev = (j != uel(r, 1)) && (j != uel(r, 2));
1535 6928 : set_avma(av0);
1536 : } else {
1537 : ulong j1pr, j1;
1538 33472 : j1pr = modfn_preimage(uel(rts, 1), p, pi, dinfo->inv);
1539 33471 : j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
1540 33473 : rev = j1 != modfn_preimage(uel(surface_js, i), p, pi, dinfo->inv);
1541 : }
1542 40401 : if (rev)
1543 19448 : carray_reverse_inplace(surface_js + 2, njs - 1);
1544 40401 : append_neighbours(rts, surface_js, njs, L, m, i);
1545 :
1546 573740 : for (i = 3; i <= njinvs; ++i) {
1547 533339 : update_Lsqr_cycle(cyc, dinfo);
1548 533339 : rts = gel(rt_mat, i);
1549 533339 : vecsmall_pick(rts, floor_js, cyc);
1550 533348 : append_neighbours(rts, surface_js, njs, L, m, i);
1551 : }
1552 40401 : set_avma(av); return rt_mat;
1553 : }
1554 :
1555 : INLINE void
1556 43091 : interpolate_coeffs(GEN phi_modp, ulong p, GEN j_invs, GEN coeff_mat)
1557 : {
1558 43091 : pari_sp av = avma;
1559 : long i;
1560 43091 : GEN pols = Flv_Flm_polint(j_invs, coeff_mat, p, 0);
1561 916234 : for (i = 1; i < lg(pols); ++i) {
1562 873147 : GEN pol = gel(pols, i);
1563 873147 : long k, maxk = lg(pol);
1564 19328514 : for (k = 2; k < maxk; ++k) coeff(phi_modp, k - 1, i) = pol[k];
1565 : }
1566 43087 : set_avma(av);
1567 43092 : }
1568 :
1569 : INLINE long
1570 337608 : Flv_lastnonzero(GEN v)
1571 : {
1572 : long i;
1573 26653170 : for (i = lg(v) - 1; i > 0; --i)
1574 26652487 : if (v[i]) break;
1575 337608 : return i;
1576 : }
1577 :
1578 : /* Assuming the matrix of coefficients in phi corresponds to polynomials
1579 : * phi_k^* satisfying Y^c phi_k^*(Y^s) for c in {0, 1, ..., s} satisfying
1580 : * c + Lk = L + 1 (mod s), change phi so that the coefficients are for the
1581 : * polynomials Y^c phi_k^*(Y^s) (s is the sparsity factor) */
1582 : INLINE void
1583 10047 : inflate_polys(GEN phi, long L, long s)
1584 : {
1585 10047 : long k, deg = L + 1;
1586 : long maxr;
1587 10047 : maxr = nbrows(phi);
1588 347655 : for (k = 0; k <= deg; ) {
1589 337608 : long i, c = umodsu(L * (1 - k) + 1, s);
1590 : /* TODO: We actually know that the last nonzero element of gel(phi, k)
1591 : * can't be later than index n+1, where n is about (L + 1)/s. */
1592 337608 : ++k;
1593 5490714 : for (i = Flv_lastnonzero(gel(phi, k)); i > 0; --i) {
1594 5153106 : long r = c + (i - 1) * s + 1;
1595 5153106 : if (r > maxr) { coeff(phi, i, k) = 0; continue; }
1596 5082612 : if (r != i) {
1597 4979510 : coeff(phi, r, k) = coeff(phi, i, k);
1598 4979510 : coeff(phi, i, k) = 0;
1599 : }
1600 : }
1601 : }
1602 10047 : }
1603 :
1604 : INLINE void
1605 39865 : Flv_powu_inplace_pre(GEN v, ulong n, ulong p, ulong pi)
1606 : {
1607 : long i;
1608 333748 : for (i = 1; i < lg(v); ++i) v[i] = Fl_powu_pre(v[i], n, p, pi);
1609 39859 : }
1610 :
1611 : INLINE void
1612 10047 : normalise_coeffs(GEN coeffs, GEN js, long L, long s, ulong p, ulong pi)
1613 : {
1614 10047 : pari_sp av = avma;
1615 : long k;
1616 : GEN pows, modinv_js;
1617 :
1618 : /* NB: In fact it would be correct to return the coefficients "as is" when
1619 : * s = 1, but we make that an error anyway since this function should never
1620 : * be called with s = 1. */
1621 10047 : if (s <= 1) pari_err_BUG("normalise_coeffs");
1622 :
1623 : /* pows[i + 1] contains 1 / js[i + 1]^i for i = 0, ..., s - 1. */
1624 10047 : pows = cgetg(s + 1, t_VEC);
1625 10047 : gel(pows, 1) = const_vecsmall(lg(js) - 1, 1);
1626 10047 : modinv_js = Flv_inv_pre(js, p, pi);
1627 10047 : gel(pows, 2) = modinv_js;
1628 37688 : for (k = 3; k <= s; ++k) {
1629 27641 : gel(pows, k) = gcopy(modinv_js);
1630 27641 : Flv_powu_inplace_pre(gel(pows, k), k - 1, p, pi);
1631 : }
1632 :
1633 : /* For each column of coefficients coeffs[k] = [a0 .. an],
1634 : * replace ai by ai / js[i]^c.
1635 : * Said in another way, normalise each row i of coeffs by
1636 : * dividing through by js[i - 1]^c (where c depends on i). */
1637 347674 : for (k = 1; k < lg(coeffs); ++k) {
1638 337600 : long i, c = umodsu(L * (1 - (k - 1)) + 1, s);
1639 337598 : GEN col = gel(coeffs, k), C = gel(pows, c + 1);
1640 5855819 : for (i = 1; i < lg(col); ++i)
1641 5518192 : col[i] = Fl_mul_pre(col[i], C[i], p, pi);
1642 : }
1643 10074 : set_avma(av);
1644 10047 : }
1645 :
1646 : INLINE void
1647 6928 : double_eta_initial_js(
1648 : ulong *x0, ulong *x0pr, ulong j0, ulong j0pr, norm_eqn_t ne,
1649 : long inv, ulong L, ulong n, ulong card, ulong val)
1650 : {
1651 6928 : pari_sp av0 = avma;
1652 6928 : ulong p = ne->p, pi = ne->pi, s2 = ne->s2;
1653 6928 : GEN F = double_eta_Fl(inv, p);
1654 6928 : pari_sp av = avma;
1655 : ulong j1pr, j1, r, t;
1656 : GEN f, g;
1657 :
1658 6928 : *x0pr = modinv_double_eta_from_j(F, inv, j0pr, p, pi, s2);
1659 6928 : t = double_eta_power(inv, *x0pr, p, pi);
1660 6928 : f = Flx_div_by_X_x(Flx_double_eta_jpoly(F, t, p, pi), j0pr, p, &r);
1661 6928 : if (r) pari_err_BUG("double_eta_initial_js");
1662 6928 : j1pr = Flx_deg1_root(f, p);
1663 6928 : set_avma(av);
1664 :
1665 6928 : j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
1666 6928 : f = Flx_double_eta_xpoly(F, j0, p, pi);
1667 6928 : g = Flx_double_eta_xpoly(F, j1, p, pi);
1668 : /* x0 is the unique common root of f and g */
1669 6928 : *x0 = Flx_deg1_root(Flx_gcd(f, g, p), p);
1670 6928 : set_avma(av0);
1671 :
1672 6928 : if ( ! double_eta_root(inv, x0, *x0, p, pi, s2))
1673 0 : pari_err_BUG("double_eta_initial_js");
1674 6928 : }
1675 :
1676 : /* This is Sutherland 2012, Algorithm 2.1, p16. */
1677 : static GEN
1678 40394 : polmodular_split_p_Flm(ulong L, GEN hilb, GEN factu, norm_eqn_t ne, GEN db,
1679 : GEN G_surface, GEN G_floor, const disc_info *dinfo)
1680 : {
1681 : ulong j0, j0_rt, j0pr, j0pr_rt;
1682 40394 : ulong n, card, val, p = ne->p, pi = ne->pi;
1683 40394 : long inv = dinfo->inv, s = modinv_sparse_factor(inv);
1684 40395 : long nj_selected = ceil((L + 1)/(double)s) + 1;
1685 : GEN surface_js, floor_js, rts, phi_modp, jdb, fdb;
1686 40395 : long switched_signs = 0;
1687 :
1688 40395 : jdb = polmodular_db_for_inv(db, INV_J);
1689 40396 : fdb = polmodular_db_for_inv(db, inv);
1690 :
1691 : /* Precomputation */
1692 40395 : card = p + 1 - ne->t;
1693 40395 : val = u_lvalrem(card, L, &n); /* n = card / L^{v_L(card)} */
1694 :
1695 40396 : j0 = oneroot_of_classpoly(hilb, factu, ne, jdb);
1696 40398 : j0pr = compute_L_isogenous_curve(L, n, ne, j0, card, val, 1);
1697 40401 : if (modinv_is_double_eta(inv)) {
1698 6928 : double_eta_initial_js(&j0_rt, &j0pr_rt, j0, j0pr, ne, inv, L, n, card, val);
1699 : } else {
1700 33473 : j0_rt = modfn_root(j0, ne, inv);
1701 33473 : j0pr_rt = modfn_root(j0pr, ne, inv);
1702 : }
1703 40401 : surface_js = enum_volcano_surface(ne, j0_rt, fdb, G_surface);
1704 40399 : floor_js = enum_volcano_floor(L, ne, j0pr_rt, fdb, G_floor);
1705 40400 : rts = root_matrix(L, dinfo, nj_selected, surface_js, floor_js,
1706 : n, card, val, ne);
1707 2363 : do {
1708 42764 : pari_sp btop = avma;
1709 : long i;
1710 : GEN coeffs, surf;
1711 :
1712 42764 : coeffs = roots_to_coeffs(rts, p, L);
1713 42763 : surf = vecsmall_shorten(surface_js, nj_selected);
1714 42762 : if (s > 1) {
1715 10047 : normalise_coeffs(coeffs, surf, L, s, p, pi);
1716 10047 : Flv_powu_inplace_pre(surf, s, p, pi);
1717 : }
1718 42762 : phi_modp = zero_Flm_copy(L + 2, L + 2);
1719 42762 : interpolate_coeffs(phi_modp, p, surf, coeffs);
1720 42763 : if (s > 1) inflate_polys(phi_modp, L, s);
1721 :
1722 : /* TODO: Calculate just this coefficient of X^L Y^L, so we can do this
1723 : * test, then calculate the other coefficients; at the moment we are
1724 : * sometimes doing all the roots-to-coeffs, normalisation and interpolation
1725 : * work twice. */
1726 42763 : if (ucoeff(phi_modp, L + 1, L + 1) == p - 1) break;
1727 :
1728 2363 : if (switched_signs) pari_err_BUG("polmodular_split_p_Flm");
1729 :
1730 2363 : set_avma(btop);
1731 28283 : for (i = 1; i < lg(rts); ++i) {
1732 25920 : surface_js[i] = Fl_neg(surface_js[i], p);
1733 25920 : coeff(rts, L, i) = Fl_neg(coeff(rts, L, i), p);
1734 25920 : coeff(rts, L + 1, i) = Fl_neg(coeff(rts, L + 1, i), p);
1735 : }
1736 2363 : switched_signs = 1;
1737 : } while (1);
1738 40400 : dbg_printf(4)(" Phi_%lu(X, Y) (mod %lu) = %Ps\n", L, p, phi_modp);
1739 :
1740 40400 : return phi_modp;
1741 : }
1742 :
1743 : INLINE void
1744 2464 : Flv_deriv_pre_inplace(GEN v, long deg, ulong p, ulong pi)
1745 : {
1746 2464 : long i, ln = lg(v), d = deg % p;
1747 57190 : for (i = ln - 1; i > 1; --i, --d) v[i] = Fl_mul_pre(v[i - 1], d, p, pi);
1748 2463 : v[1] = 0;
1749 2463 : }
1750 :
1751 : INLINE GEN
1752 2674 : eval_modpoly_modp(GEN Tp, GEN j_powers, ulong p, ulong pi, int compute_derivs)
1753 : {
1754 2674 : long L = lg(j_powers) - 3;
1755 2674 : GEN j_pows_p = ZV_to_Flv(j_powers, p);
1756 2674 : GEN tmp = cgetg(2 + 2 * compute_derivs, t_VEC);
1757 : /* We wrap the result in this t_VEC Tp to trick the
1758 : * ZM_*_CRT() functions into thinking it's a matrix. */
1759 2674 : gel(tmp, 1) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1760 2674 : if (compute_derivs) {
1761 1232 : Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
1762 1232 : gel(tmp, 2) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1763 1232 : Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
1764 1232 : gel(tmp, 3) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1765 : }
1766 2674 : return tmp;
1767 : }
1768 :
1769 : /* Parallel interface */
1770 : GEN
1771 40389 : polmodular_worker(GEN tp, ulong L, GEN hilb, GEN factu, GEN vne, GEN vinfo,
1772 : long derivs, GEN j_powers, GEN G_surface, GEN G_floor,
1773 : GEN fdb)
1774 : {
1775 40389 : pari_sp av = avma;
1776 : norm_eqn_t ne;
1777 40389 : long D = vne[1], u = vne[2];
1778 40389 : ulong vL, t = tp[1], p = tp[2];
1779 : GEN Tp;
1780 :
1781 40389 : if (! uissquareall((4 * p - t * t) / -D, &vL))
1782 0 : pari_err_BUG("polmodular_worker");
1783 40394 : norm_eqn_set(ne, D, t, u, vL, NULL, p); /* L | vL */
1784 40392 : Tp = polmodular_split_p_Flm(L, hilb, factu, ne, fdb,
1785 : G_surface, G_floor, (const disc_info*)vinfo);
1786 40399 : if (!isintzero(j_powers))
1787 2674 : Tp = eval_modpoly_modp(Tp, j_powers, ne->p, ne->pi, derivs);
1788 40399 : return gc_upto(av, Tp);
1789 : }
1790 :
1791 : static GEN
1792 24820 : sympol_to_ZM(GEN phi, long L)
1793 : {
1794 24820 : pari_sp av = avma;
1795 24820 : GEN res = zeromatcopy(L + 2, L + 2);
1796 24820 : long i, j, c = 1;
1797 108601 : for (i = 1; i <= L + 1; ++i)
1798 277606 : for (j = 1; j <= i; ++j, ++c)
1799 193825 : gcoeff(res, i, j) = gcoeff(res, j, i) = gel(phi, c);
1800 24820 : gcoeff(res, L + 2, 1) = gcoeff(res, 1, L + 2) = gen_1;
1801 24820 : return gc_GEN(av, res);
1802 : }
1803 :
1804 : static GEN polmodular_small_ZM(long L, long inv, GEN *db);
1805 :
1806 : INLINE long
1807 28145 : modinv_max_internal_level(long inv)
1808 : {
1809 28145 : switch (inv) {
1810 25335 : case INV_J: return 5;
1811 259 : case INV_G2: return 2;
1812 443 : case INV_F:
1813 : case INV_F2:
1814 : case INV_F4:
1815 443 : case INV_F8: return 5;
1816 210 : case INV_W2W5:
1817 210 : case INV_W2W5E2: return 7;
1818 504 : case INV_W2W3:
1819 : case INV_W2W3E2:
1820 : case INV_W3W3:
1821 504 : case INV_W3W7: return 5;
1822 63 : case INV_W3W3E2:return 2;
1823 701 : case INV_F3:
1824 : case INV_W2W7:
1825 : case INV_W2W7E2:
1826 701 : case INV_W2W13: return 3;
1827 630 : case INV_W3W5:
1828 : case INV_W5W7:
1829 : case INV_W3W13:
1830 : case INV_ATKIN3:
1831 : case INV_ATKIN5:
1832 : case INV_ATKIN7:
1833 : case INV_ATKIN11:
1834 : case INV_ATKIN13:
1835 : case INV_ATKIN17:
1836 630 : case INV_ATKIN19: return 2;
1837 : }
1838 : pari_err_BUG("modinv_max_internal_level"); return LONG_MAX;/*LCOV_EXCL_LINE*/
1839 : }
1840 : static void
1841 24 : db_add_levels(GEN *db, GEN P, long inv)
1842 24 : { polmodular_db_add_levels(db, zv_to_longptr(P), lg(P)-1, inv); }
1843 :
1844 : GEN
1845 28026 : polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db)
1846 : {
1847 28026 : pari_sp ltop = avma;
1848 28026 : long k, d, Dcnt, nprimes = 0;
1849 : GEN modpoly, plist, tp, j_powers;
1850 : disc_info Ds[MODPOLY_MAX_DCNT];
1851 28026 : long lvl = modinv_level(inv);
1852 28026 : if (ugcd(L, lvl) != 1)
1853 7 : pari_err_DOMAIN("polmodular0_ZM", "invariant",
1854 : "incompatible with", stoi(L), stoi(lvl));
1855 :
1856 28019 : dbg_printf(1)("Calculating modular polynomial of level %lu for invariant %d\n", L, inv);
1857 28019 : if (L <= modinv_max_internal_level(inv)) return polmodular_small_ZM(L,inv,db);
1858 :
1859 3059 : Dcnt = discriminant_with_classno_at_least(Ds, L, inv, Q, USE_SPARSE_FACTOR);
1860 6136 : for (d = 0; d < Dcnt; d++) nprimes += Ds[d].nprimes;
1861 3059 : modpoly = cgetg(nprimes+1, t_VEC);
1862 3059 : plist = cgetg(nprimes+1, t_VECSMALL);
1863 3059 : tp = mkvec(mkvecsmall2(0,0));
1864 3059 : j_powers = gen_0;
1865 3059 : if (J) {
1866 63 : compute_derivs = !!compute_derivs;
1867 63 : j_powers = Fp_powers(J, L+1, Q);
1868 : }
1869 6136 : for (d = 0, k = 1; d < Dcnt; d++)
1870 : {
1871 3077 : disc_info *dinfo = &Ds[d];
1872 : struct pari_mt pt;
1873 3077 : const long D = dinfo->D1, DK = dinfo->D0;
1874 3077 : const ulong cond = usqrt(D / DK);
1875 3077 : long i, pending = 0;
1876 3077 : GEN worker, hilb, factu = factoru(cond);
1877 :
1878 3077 : polmodular_db_add_level(db, dinfo->L0, inv);
1879 3077 : if (dinfo->L1) polmodular_db_add_level(db, dinfo->L1, inv);
1880 3077 : dbg_printf(1)("Selected discriminant D = %ld = %ld^2 * %ld.\n", D,cond,DK);
1881 3077 : hilb = polclass0(DK, INV_J, 0, db);
1882 3077 : if (cond > 1) db_add_levels(db, gel(factu,1), INV_J);
1883 3077 : dbg_printf(1)("D = %ld, L0 = %lu, L1 = %lu, ", dinfo->D1, dinfo->L0, dinfo->L1);
1884 3077 : dbg_printf(1)("n1 = %lu, n2 = %lu, dl1 = %lu, dl2_0 = %lu, dl2_1 = %lu\n",
1885 : dinfo->n1, dinfo->n2, dinfo->dl1, dinfo->dl2_0, dinfo->dl2_1);
1886 3077 : dbg_printf(0)("Calculating modular polynomial of level %lu:", L);
1887 :
1888 3077 : worker = snm_closure(is_entry("_polmodular_worker"),
1889 : mkvecn(10, utoi(L), hilb, factu, mkvecsmall2(D, cond),
1890 : (GEN)dinfo, stoi(compute_derivs), j_powers,
1891 : make_pcp_surface(dinfo),
1892 : make_pcp_floor(dinfo), *db));
1893 3077 : mt_queue_start_lim(&pt, worker, dinfo->nprimes);
1894 47613 : for (i = 0; i < dinfo->nprimes || pending; i++)
1895 : {
1896 : long workid;
1897 : GEN done;
1898 44536 : if (i < dinfo->nprimes)
1899 : {
1900 40401 : mael(tp, 1, 1) = dinfo->traces[i];
1901 40401 : mael(tp, 1, 2) = dinfo->primes[i];
1902 : }
1903 44536 : mt_queue_submit(&pt, i, i < dinfo->nprimes? tp: NULL);
1904 44536 : done = mt_queue_get(&pt, &workid, &pending);
1905 44536 : if (done)
1906 : {
1907 40401 : plist[k] = dinfo->primes[workid];
1908 40401 : gel(modpoly, k) = done; k++;
1909 40401 : dbg_printf(0)(" %ld%%", k*100/nprimes);
1910 : }
1911 : }
1912 3077 : dbg_printf(0)(" done\n");
1913 3077 : mt_queue_end(&pt);
1914 3077 : killblock((GEN)dinfo->primes);
1915 : }
1916 3059 : modpoly = nmV_chinese_center(modpoly, plist, NULL);
1917 3059 : if (J) modpoly = FpM_red(modpoly, Q);
1918 3059 : return gc_upto(ltop, modpoly);
1919 : }
1920 :
1921 : GEN
1922 19266 : polmodular_ZM(long L, long inv)
1923 : {
1924 : GEN db, Phi;
1925 :
1926 19266 : if (L < 2)
1927 7 : pari_err_DOMAIN("polmodular_ZM", "L", "<", gen_2, stoi(L));
1928 :
1929 : /* TODO: Handle nonprime L. Algorithm 1.1 and Corollary 3.4 in Sutherland,
1930 : * "Class polynomials for nonholomorphic modular functions" */
1931 19259 : if (! uisprime(L)) pari_err_IMPL("composite level");
1932 :
1933 19252 : db = polmodular_db_init(inv);
1934 19252 : Phi = polmodular0_ZM(L, inv, NULL, NULL, 0, &db);
1935 19245 : gunclone_deep(db); return Phi;
1936 : }
1937 :
1938 : GEN
1939 19182 : polmodular_ZXX(long L, long inv, long vx, long vy)
1940 : {
1941 19182 : pari_sp av = avma;
1942 19182 : GEN phi = polmodular_ZM(L, inv);
1943 :
1944 19161 : if (vx < 0) vx = 0;
1945 19161 : if (vy < 0) vy = 1;
1946 19161 : if (varncmp(vx, vy) >= 0)
1947 14 : pari_err_PRIORITY("polmodular_ZXX", pol_x(vx), "<=", vy);
1948 19147 : return gc_GEN(av, RgM_to_RgXX(phi, vx, vy));
1949 : }
1950 :
1951 : INLINE GEN
1952 56 : FpV_deriv(GEN v, long deg, GEN P)
1953 : {
1954 56 : long i, ln = lg(v);
1955 56 : GEN dv = cgetg(ln, t_VEC);
1956 392 : for (i = ln-1; i > 1; i--, deg--) gel(dv, i) = Fp_mulu(gel(v, i-1), deg, P);
1957 56 : gel(dv, 1) = gen_0; return dv;
1958 : }
1959 :
1960 : GEN
1961 126 : Fp_polmodular_evalx(long L, long inv, GEN J, GEN P, long v, int compute_derivs)
1962 : {
1963 126 : pari_sp av = avma;
1964 : GEN db, phi;
1965 :
1966 126 : if (L <= modinv_max_internal_level(inv)) {
1967 : GEN tmp;
1968 63 : GEN phi = RgM_to_FpM(polmodular_ZM(L, inv), P);
1969 63 : GEN j_powers = Fp_powers(J, L + 1, P);
1970 63 : GEN modpol = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1971 63 : if (compute_derivs) {
1972 28 : tmp = cgetg(4, t_VEC);
1973 28 : gel(tmp, 1) = modpol;
1974 28 : j_powers = FpV_deriv(j_powers, L + 1, P);
1975 28 : gel(tmp, 2) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1976 28 : j_powers = FpV_deriv(j_powers, L + 1, P);
1977 28 : gel(tmp, 3) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1978 : } else
1979 35 : tmp = modpol;
1980 63 : return gc_GEN(av, tmp);
1981 : }
1982 :
1983 63 : db = polmodular_db_init(inv);
1984 63 : phi = polmodular0_ZM(L, inv, J, P, compute_derivs, &db);
1985 63 : phi = RgM_to_RgXV(phi, v);
1986 63 : gunclone_deep(db);
1987 63 : return gc_GEN(av, compute_derivs? phi: gel(phi, 1));
1988 : }
1989 :
1990 : GEN
1991 651 : polmodular(long L, long inv, GEN x, long v, long compute_derivs)
1992 : {
1993 651 : pari_sp av = avma;
1994 : long tx;
1995 651 : GEN J = NULL, P = NULL, res = NULL, one = NULL;
1996 :
1997 651 : check_modinv(inv);
1998 644 : if (!x || gequalX(x)) {
1999 504 : long xv = 0;
2000 504 : if (x) xv = varn(x);
2001 504 : if (compute_derivs) pari_err_FLAG("polmodular");
2002 497 : return polmodular_ZXX(L, inv, xv, v);
2003 : }
2004 :
2005 140 : tx = typ(x);
2006 140 : if (tx == t_INTMOD) {
2007 63 : J = gel(x, 2);
2008 63 : P = gel(x, 1);
2009 63 : one = mkintmod(gen_1, P);
2010 77 : } else if (tx == t_FFELT) {
2011 70 : J = FF_to_FpXQ_i(x);
2012 70 : if (degpol(J) > 0)
2013 7 : pari_err_DOMAIN("polmodular", "x", "not in prime subfield ", gen_0, x);
2014 63 : J = constant_coeff(J);
2015 63 : P = FF_p_i(x);
2016 63 : one = FF_1(x);
2017 : } else
2018 7 : pari_err_TYPE("polmodular", x);
2019 :
2020 126 : if (v < 0) v = 1;
2021 126 : res = Fp_polmodular_evalx(L, inv, J, P, v, compute_derivs);
2022 126 : return gc_upto(av, gmul(res, one));
2023 : }
2024 :
2025 : /* SECTION: Modular polynomials of level <= MAX_INTERNAL_MODPOLY_LEVEL. */
2026 :
2027 : /* These functions return a vector of coefficients of classical modular
2028 : * polynomials Phi_L(X,Y) of small level L. The number of such coefficients is
2029 : * (L+1)(L+2)/2 since Phi is symmetric. We omit the common coefficient of
2030 : * X^{L+1} and Y^{L+1} since it is always 1. Use sympol_to_ZM() to get the
2031 : * corresponding desymmetrised matrix of coefficients */
2032 :
2033 : /* Phi2, the modular polynomial of level 2:
2034 : *
2035 : * X^3 + X^2 * (-Y^2 + 1488*Y - 162000)
2036 : * + X * (1488*Y^2 + 40773375*Y + 8748000000)
2037 : * + Y^3 - 162000*Y^2 + 8748000000*Y - 157464000000000
2038 : *
2039 : * [[3, 0, 1],
2040 : * [2, 2, -1],
2041 : * [2, 1, 1488],
2042 : * [2, 0, -162000],
2043 : * [1, 1, 40773375],
2044 : * [1, 0, 8748000000],
2045 : * [0, 0, -157464000000000]], */
2046 : static GEN
2047 20015 : phi2_ZV(void)
2048 : {
2049 20015 : GEN phi2 = cgetg(7, t_VEC);
2050 20015 : gel(phi2, 1) = uu32toi(36662, 1908994048);
2051 20015 : setsigne(gel(phi2, 1), -1);
2052 20015 : gel(phi2, 2) = uu32toi(2, 158065408);
2053 20015 : gel(phi2, 3) = stoi(40773375);
2054 20015 : gel(phi2, 4) = stoi(-162000);
2055 20015 : gel(phi2, 5) = stoi(1488);
2056 20015 : gel(phi2, 6) = gen_m1;
2057 20015 : return phi2;
2058 : }
2059 :
2060 : /* L = 3
2061 : *
2062 : * [4, 0, 1],
2063 : * [3, 3, -1],
2064 : * [3, 2, 2232],
2065 : * [3, 1, -1069956],
2066 : * [3, 0, 36864000],
2067 : * [2, 2, 2587918086],
2068 : * [2, 1, 8900222976000],
2069 : * [2, 0, 452984832000000],
2070 : * [1, 1, -770845966336000000],
2071 : * [1, 0, 1855425871872000000000]
2072 : * [0, 0, 0]
2073 : *
2074 : * 1855425871872000000000 = 2^32 * (100 * 2^32 + 2503270400) */
2075 : static GEN
2076 1910 : phi3_ZV(void)
2077 : {
2078 1910 : GEN phi3 = cgetg(11, t_VEC);
2079 1910 : pari_sp av = avma;
2080 1910 : gel(phi3, 1) = gen_0;
2081 1910 : gel(phi3, 2) = gc_upto(av, shifti(uu32toi(100, 2503270400UL), 32));
2082 1910 : gel(phi3, 3) = uu32toi(179476562, 2147483648UL);
2083 1910 : setsigne(gel(phi3, 3), -1);
2084 1910 : gel(phi3, 4) = uu32toi(105468, 3221225472UL);
2085 1910 : gel(phi3, 5) = uu32toi(2072, 1050738688);
2086 1910 : gel(phi3, 6) = utoi(2587918086UL);
2087 1910 : gel(phi3, 7) = stoi(36864000);
2088 1910 : gel(phi3, 8) = stoi(-1069956);
2089 1910 : gel(phi3, 9) = stoi(2232);
2090 1910 : gel(phi3, 10) = gen_m1;
2091 1910 : return phi3;
2092 : }
2093 :
2094 : static GEN
2095 1880 : phi5_ZV(void)
2096 : {
2097 1880 : GEN phi5 = cgetg(22, t_VEC);
2098 1880 : gel(phi5, 1) = mkintn(5, 0x18c2cc9cUL, 0x484382b2UL, 0xdc000000UL, 0x0UL, 0x0UL);
2099 1880 : gel(phi5, 2) = mkintn(5, 0x2638fUL, 0x2ff02690UL, 0x68026000UL, 0x0UL, 0x0UL);
2100 1880 : gel(phi5, 3) = mkintn(5, 0x308UL, 0xac9d9a4UL, 0xe0fdab12UL, 0xc0000000UL, 0x0UL);
2101 1880 : setsigne(gel(phi5, 3), -1);
2102 1880 : gel(phi5, 4) = mkintn(5, 0x13UL, 0xaae09f9dUL, 0x1b5ef872UL, 0x30000000UL, 0x0UL);
2103 1880 : gel(phi5, 5) = mkintn(4, 0x1b802fa9UL, 0x77ba0653UL, 0xd2f78000UL, 0x0UL);
2104 1880 : gel(phi5, 6) = mkintn(4, 0xfbfdUL, 0x278e4756UL, 0xdf08a7c4UL, 0x40000000UL);
2105 1880 : gel(phi5, 7) = mkintn(4, 0x35f922UL, 0x62ccea6fUL, 0x153d0000UL, 0x0UL);
2106 1880 : gel(phi5, 8) = mkintn(4, 0x97dUL, 0x29203fafUL, 0xc3036909UL, 0x80000000UL);
2107 1880 : setsigne(gel(phi5, 8), -1);
2108 1880 : gel(phi5, 9) = mkintn(3, 0x56e9e892UL, 0xd7781867UL, 0xf2ea0000UL);
2109 1880 : gel(phi5, 10) = mkintn(3, 0x5d6dUL, 0xe0a58f4eUL, 0x9ee68c14UL);
2110 1880 : setsigne(gel(phi5, 10), -1);
2111 1880 : gel(phi5, 11) = mkintn(3, 0x1100dUL, 0x85cea769UL, 0x40000000UL);
2112 1880 : gel(phi5, 12) = mkintn(3, 0x1b38UL, 0x43cf461fUL, 0x3a900000UL);
2113 1880 : gel(phi5, 13) = mkintn(3, 0x14UL, 0xc45a616eUL, 0x4801680fUL);
2114 1880 : gel(phi5, 14) = uu32toi(0x17f4350UL, 0x493ca3e0UL);
2115 1880 : gel(phi5, 15) = uu32toi(0x183UL, 0xe54ce1f8UL);
2116 1880 : gel(phi5, 16) = uu32toi(0x1c9UL, 0x18860000UL);
2117 1880 : gel(phi5, 17) = uu32toi(0x39UL, 0x6f7a2206UL);
2118 1880 : setsigne(gel(phi5, 17), -1);
2119 1880 : gel(phi5, 18) = stoi(2028551200);
2120 1880 : gel(phi5, 19) = stoi(-4550940);
2121 1880 : gel(phi5, 20) = stoi(3720);
2122 1880 : gel(phi5, 21) = gen_m1;
2123 1880 : return phi5;
2124 : }
2125 :
2126 : static GEN
2127 189 : phi5_f_ZV(void)
2128 : {
2129 189 : GEN phi = zerovec(21);
2130 189 : gel(phi, 3) = stoi(4);
2131 189 : gel(phi, 21) = gen_m1;
2132 189 : return phi;
2133 : }
2134 :
2135 : static GEN
2136 21 : phi3_f3_ZV(void)
2137 : {
2138 21 : GEN phi = zerovec(10);
2139 21 : gel(phi, 3) = stoi(8);
2140 21 : gel(phi, 10) = gen_m1;
2141 21 : return phi;
2142 : }
2143 :
2144 : static GEN
2145 105 : phi2_g2_ZV(void)
2146 : {
2147 105 : GEN phi = zerovec(6);
2148 105 : gel(phi, 1) = stoi(-54000);
2149 105 : gel(phi, 3) = stoi(495);
2150 105 : gel(phi, 6) = gen_m1;
2151 105 : return phi;
2152 : }
2153 :
2154 : static GEN
2155 56 : phi5_w2w3_ZV(void)
2156 : {
2157 56 : GEN phi = zerovec(21);
2158 56 : gel(phi, 3) = gen_m1;
2159 56 : gel(phi, 10) = stoi(5);
2160 56 : gel(phi, 21) = gen_m1;
2161 56 : return phi;
2162 : }
2163 :
2164 : static GEN
2165 91 : phi7_w2w5_ZV(void)
2166 : {
2167 91 : GEN phi = zerovec(36);
2168 91 : gel(phi, 3) = gen_m1;
2169 91 : gel(phi, 15) = stoi(56);
2170 91 : gel(phi, 19) = stoi(42);
2171 91 : gel(phi, 24) = stoi(21);
2172 91 : gel(phi, 30) = stoi(7);
2173 91 : gel(phi, 36) = gen_m1;
2174 91 : return phi;
2175 : }
2176 :
2177 : static GEN
2178 63 : phi5_w3w3_ZV(void)
2179 : {
2180 63 : GEN phi = zerovec(21);
2181 63 : gel(phi, 3) = stoi(9);
2182 63 : gel(phi, 6) = stoi(-15);
2183 63 : gel(phi, 15) = stoi(5);
2184 63 : gel(phi, 21) = gen_m1;
2185 63 : return phi;
2186 : }
2187 :
2188 : static GEN
2189 182 : phi3_w2w7_ZV(void)
2190 : {
2191 182 : GEN phi = zerovec(10);
2192 182 : gel(phi, 3) = gen_m1;
2193 182 : gel(phi, 6) = stoi(3);
2194 182 : gel(phi, 10) = gen_m1;
2195 182 : return phi;
2196 : }
2197 :
2198 : static GEN
2199 35 : phi2_w3w5_ZV(void)
2200 : {
2201 35 : GEN phi = zerovec(6);
2202 35 : gel(phi, 3) = gen_1;
2203 35 : gel(phi, 6) = gen_m1;
2204 35 : return phi;
2205 : }
2206 :
2207 : static GEN
2208 49 : phi5_w3w7_ZV(void)
2209 : {
2210 49 : GEN phi = zerovec(21);
2211 49 : gel(phi, 3) = gen_m1;
2212 49 : gel(phi, 6) = stoi(10);
2213 49 : gel(phi, 8) = stoi(5);
2214 49 : gel(phi, 10) = stoi(35);
2215 49 : gel(phi, 13) = stoi(20);
2216 49 : gel(phi, 15) = stoi(10);
2217 49 : gel(phi, 17) = stoi(5);
2218 49 : gel(phi, 19) = stoi(5);
2219 49 : gel(phi, 21) = gen_m1;
2220 49 : return phi;
2221 : }
2222 :
2223 : static GEN
2224 42 : phi3_w2w13_ZV(void)
2225 : {
2226 42 : GEN phi = zerovec(10);
2227 42 : gel(phi, 3) = gen_m1;
2228 42 : gel(phi, 6) = stoi(3);
2229 42 : gel(phi, 8) = stoi(3);
2230 42 : gel(phi, 10) = gen_m1;
2231 42 : return phi;
2232 : }
2233 :
2234 : static GEN
2235 21 : phi2_w3w3e2_ZV(void)
2236 : {
2237 21 : GEN phi = zerovec(6);
2238 21 : gel(phi, 3) = stoi(3);
2239 21 : gel(phi, 6) = gen_m1;
2240 21 : return phi;
2241 : }
2242 :
2243 : static GEN
2244 63 : phi2_w5w7_ZV(void)
2245 : {
2246 63 : GEN phi = zerovec(6);
2247 63 : gel(phi, 3) = gen_1;
2248 63 : gel(phi, 5) = gen_2;
2249 63 : gel(phi, 6) = gen_m1;
2250 63 : return phi;
2251 : }
2252 :
2253 : static GEN
2254 14 : phi2_w3w13_ZV(void)
2255 : {
2256 14 : GEN phi = zerovec(6);
2257 14 : gel(phi, 3) = gen_m1;
2258 14 : gel(phi, 5) = gen_2;
2259 14 : gel(phi, 6) = gen_m1;
2260 14 : return phi;
2261 : }
2262 :
2263 : static GEN
2264 7 : phi2_atkin3_ZV(void)
2265 : {
2266 7 : GEN phi = zerovec(6);
2267 7 : gel(phi, 1) = utoi(28166076);
2268 7 : gel(phi, 2) = utoi(741474);
2269 7 : gel(phi, 3) = utoi(17343);
2270 7 : gel(phi, 4) = utoi(1566);
2271 7 : gel(phi, 6) = gen_m1;
2272 7 : return phi;
2273 : }
2274 :
2275 : static GEN
2276 14 : phi2_atkin5_ZV(void)
2277 : {
2278 14 : GEN phi = zerovec(6);
2279 14 : gel(phi, 1) = utoi(323456);
2280 14 : gel(phi, 2) = utoi(24244);
2281 14 : gel(phi, 3) = utoi(1519);
2282 14 : gel(phi, 4) = utoi(268);
2283 14 : gel(phi, 6) = gen_m1;
2284 14 : return phi;
2285 : }
2286 :
2287 : static GEN
2288 7 : phi2_atkin7_ZV(void)
2289 : {
2290 7 : GEN phi = zerovec(6);
2291 7 : gel(phi, 1) = utoi(27100);
2292 7 : gel(phi, 2) = utoi(3810);
2293 7 : gel(phi, 3) = utoi(407);
2294 7 : gel(phi, 4) = utoi(102);
2295 7 : gel(phi, 6) = gen_m1;
2296 7 : return phi;
2297 : }
2298 :
2299 : static GEN
2300 7 : phi2_atkin11_ZV(void)
2301 : {
2302 7 : GEN phi = zerovec(6);
2303 7 : gel(phi, 1) = utoi(1600);
2304 7 : gel(phi, 2) = utoi(470);
2305 7 : gel(phi, 3) = utoi(91);
2306 7 : gel(phi, 4) = utoi(34);
2307 7 : gel(phi, 6) = gen_m1;
2308 7 : return phi;
2309 : }
2310 :
2311 : static GEN
2312 14 : phi2_atkin13_ZV(void)
2313 : {
2314 14 : GEN phi = zerovec(6);
2315 14 : gel(phi, 1) = utoi(656);
2316 14 : gel(phi, 2) = utoi(240);
2317 14 : gel(phi, 3) = utoi(55);
2318 14 : gel(phi, 4) = utoi(24);
2319 14 : gel(phi, 6) = gen_m1;
2320 14 : return phi;
2321 : }
2322 :
2323 : static GEN
2324 21 : phi2_atkin17_ZV(void)
2325 : {
2326 21 : GEN phi = zerovec(6);
2327 21 : gel(phi, 1) = utoi(156);
2328 21 : gel(phi, 2) = utoi(86);
2329 21 : gel(phi, 3) = utoi(27);
2330 21 : gel(phi, 4) = utoi(14);
2331 21 : gel(phi, 6) = gen_m1;
2332 21 : return phi;
2333 : }
2334 :
2335 : static GEN
2336 14 : phi2_atkin19_ZV(void)
2337 : {
2338 14 : GEN phi = zerovec(6);
2339 14 : gel(phi, 1) = utoi(100);
2340 14 : gel(phi, 2) = utoi(60);
2341 14 : gel(phi, 3) = utoi(19);
2342 14 : gel(phi, 4) = utoi(12);
2343 14 : gel(phi, 6) = gen_m1;
2344 14 : return phi;
2345 : }
2346 :
2347 : INLINE long
2348 140 : modinv_parent(long inv)
2349 : {
2350 140 : switch (inv) {
2351 42 : case INV_F2:
2352 : case INV_F4:
2353 42 : case INV_F8: return INV_F;
2354 14 : case INV_W2W3E2: return INV_W2W3;
2355 21 : case INV_W2W5E2: return INV_W2W5;
2356 63 : case INV_W2W7E2: return INV_W2W7;
2357 0 : case INV_W3W3E2: return INV_W3W3;
2358 : default: pari_err_BUG("modinv_parent"); return -1;/*LCOV_EXCL_LINE*/
2359 : }
2360 : }
2361 :
2362 : /* TODO: Think of a better name than "parent power"; sheesh. */
2363 : INLINE long
2364 140 : modinv_parent_power(long inv)
2365 : {
2366 140 : switch (inv) {
2367 14 : case INV_F4: return 4;
2368 14 : case INV_F8: return 8;
2369 112 : case INV_F2:
2370 : case INV_W2W3E2:
2371 : case INV_W2W5E2:
2372 : case INV_W2W7E2:
2373 112 : case INV_W3W3E2: return 2;
2374 : default: pari_err_BUG("modinv_parent_power"); return -1;/*LCOV_EXCL_LINE*/
2375 : }
2376 : }
2377 :
2378 : static GEN
2379 140 : polmodular0_powerup_ZM(long L, long inv, GEN *db)
2380 : {
2381 140 : pari_sp ltop = avma, av;
2382 : long s, D, nprimes, N;
2383 : GEN mp, pol, P, H;
2384 140 : long parent = modinv_parent(inv);
2385 140 : long e = modinv_parent_power(inv);
2386 : disc_info Ds[MODPOLY_MAX_DCNT];
2387 : /* FIXME: We throw away the table of fundamental discriminants here. */
2388 140 : long nDs = discriminant_with_classno_at_least(Ds, L, inv, NULL, IGNORE_SPARSE_FACTOR);
2389 140 : if (nDs != 1) pari_err_BUG("polmodular0_powerup_ZM");
2390 140 : D = Ds[0].D1;
2391 140 : nprimes = Ds[0].nprimes + 1;
2392 140 : mp = polmodular0_ZM(L, parent, NULL, NULL, 0, db);
2393 140 : H = polclass0(D, parent, 0, db);
2394 :
2395 140 : N = L + 2;
2396 140 : if (degpol(H) < N) pari_err_BUG("polmodular0_powerup_ZM");
2397 :
2398 140 : av = avma;
2399 140 : pol = ZM_init_CRT(zero_Flm_copy(N, L + 2), 1);
2400 140 : P = gen_1;
2401 469 : for (s = 1; s < nprimes; ++s) {
2402 : pari_sp av1, av2;
2403 329 : ulong p = Ds[0].primes[s-1], pi = get_Fl_red(p);
2404 : long i;
2405 : GEN Hrts, js, Hp, Phip, coeff_mat, phi_modp;
2406 :
2407 329 : phi_modp = zero_Flm_copy(N, L + 2);
2408 329 : av1 = avma;
2409 329 : Hp = ZX_to_Flx(H, p);
2410 329 : Hrts = Flx_roots_pre(Hp, p, pi);
2411 329 : if (lg(Hrts)-1 < N) pari_err_BUG("polmodular0_powerup_ZM");
2412 329 : js = cgetg(N + 1, t_VECSMALL);
2413 2506 : for (i = 1; i <= N; ++i)
2414 2177 : uel(js, i) = Fl_powu_pre(uel(Hrts, i), e, p, pi);
2415 :
2416 329 : Phip = ZM_to_Flm(mp, p);
2417 329 : coeff_mat = zero_Flm_copy(N, L + 2);
2418 329 : av2 = avma;
2419 2506 : for (i = 1; i <= N; ++i) {
2420 : long k;
2421 : GEN phi_at_ji, mprts;
2422 :
2423 2177 : phi_at_ji = Flm_Fl_polmodular_evalx(Phip, L, uel(Hrts, i), p, pi);
2424 2177 : mprts = Flx_roots_pre(phi_at_ji, p, pi);
2425 2177 : if (lg(mprts) != L + 2) pari_err_BUG("polmodular0_powerup_ZM");
2426 :
2427 2177 : Flv_powu_inplace_pre(mprts, e, p, pi);
2428 2177 : phi_at_ji = Flv_roots_to_pol(mprts, p, 0);
2429 :
2430 17290 : for (k = 1; k <= L + 2; ++k)
2431 15113 : ucoeff(coeff_mat, i, k) = uel(phi_at_ji, k + 1);
2432 2177 : set_avma(av2);
2433 : }
2434 :
2435 329 : interpolate_coeffs(phi_modp, p, js, coeff_mat);
2436 329 : set_avma(av1);
2437 :
2438 329 : (void) ZM_incremental_CRT(&pol, phi_modp, &P, p);
2439 329 : if (gc_needed(av, 2)) (void)gc_all(av, 2, &pol, &P);
2440 : }
2441 140 : killblock((GEN)Ds[0].primes); return gc_upto(ltop, pol);
2442 : }
2443 :
2444 : /* Returns the modular polynomial with the smallest level for the given
2445 : * invariant, except if inv is INV_J, in which case return the modular
2446 : * polynomial of level L in {2,3,5}. NULL is returned if the modular
2447 : * polynomial can be calculated using polmodular0_powerup_ZM. */
2448 : INLINE GEN
2449 24960 : internal_db(long L, long inv)
2450 : {
2451 24960 : switch (inv) {
2452 23805 : case INV_J: switch (L) {
2453 20015 : case 2: return phi2_ZV();
2454 1910 : case 3: return phi3_ZV();
2455 1880 : case 5: return phi5_ZV();
2456 0 : default: break;
2457 : }
2458 189 : case INV_F: return phi5_f_ZV();
2459 14 : case INV_F2: return NULL;
2460 21 : case INV_F3: return phi3_f3_ZV();
2461 14 : case INV_F4: return NULL;
2462 105 : case INV_G2: return phi2_g2_ZV();
2463 56 : case INV_W2W3: return phi5_w2w3_ZV();
2464 14 : case INV_F8: return NULL;
2465 63 : case INV_W3W3: return phi5_w3w3_ZV();
2466 91 : case INV_W2W5: return phi7_w2w5_ZV();
2467 182 : case INV_W2W7: return phi3_w2w7_ZV();
2468 35 : case INV_W3W5: return phi2_w3w5_ZV();
2469 49 : case INV_W3W7: return phi5_w3w7_ZV();
2470 14 : case INV_W2W3E2: return NULL;
2471 21 : case INV_W2W5E2: return NULL;
2472 42 : case INV_W2W13: return phi3_w2w13_ZV();
2473 63 : case INV_W2W7E2: return NULL;
2474 21 : case INV_W3W3E2: return phi2_w3w3e2_ZV();
2475 63 : case INV_W5W7: return phi2_w5w7_ZV();
2476 14 : case INV_W3W13: return phi2_w3w13_ZV();
2477 7 : case INV_ATKIN3: return phi2_atkin3_ZV();
2478 14 : case INV_ATKIN5: return phi2_atkin5_ZV();
2479 7 : case INV_ATKIN7: return phi2_atkin7_ZV();
2480 7 : case INV_ATKIN11: return phi2_atkin11_ZV();
2481 14 : case INV_ATKIN13: return phi2_atkin13_ZV();
2482 21 : case INV_ATKIN17: return phi2_atkin17_ZV();
2483 14 : case INV_ATKIN19: return phi2_atkin19_ZV();
2484 : }
2485 0 : pari_err_BUG("internal_db");
2486 : return NULL;/*LCOV_EXCL_LINE*/
2487 : }
2488 :
2489 : /* NB: Should only be called if L <= modinv_max_internal_level(inv) */
2490 : static GEN
2491 24960 : polmodular_small_ZM(long L, long inv, GEN *db)
2492 : {
2493 24960 : GEN f = internal_db(L, inv);
2494 24960 : if (!f) return polmodular0_powerup_ZM(L, inv, db);
2495 24820 : return sympol_to_ZM(f, L);
2496 : }
2497 :
2498 : /* Each function phi_w?w?_j() returns a vector V containing two
2499 : * vectors u and v, and a scalar k, which together represent the
2500 : * bivariate polnomial
2501 : *
2502 : * phi(X, Y) = \sum_i u[i] X^i + Y \sum_i v[i] X^i + Y^2 X^k
2503 : */
2504 : static GEN
2505 1060 : phi_w2w3_j(void)
2506 : {
2507 : GEN phi, phi0, phi1;
2508 1060 : phi = cgetg(4, t_VEC);
2509 :
2510 1060 : phi0 = cgetg(14, t_VEC);
2511 1060 : gel(phi0, 1) = gen_1;
2512 1060 : gel(phi0, 2) = utoineg(0x3cUL);
2513 1060 : gel(phi0, 3) = utoi(0x702UL);
2514 1060 : gel(phi0, 4) = utoineg(0x797cUL);
2515 1060 : gel(phi0, 5) = utoi(0x5046fUL);
2516 1060 : gel(phi0, 6) = utoineg(0x1be0b8UL);
2517 1060 : gel(phi0, 7) = utoi(0x28ef9cUL);
2518 1060 : gel(phi0, 8) = utoi(0x15e2968UL);
2519 1060 : gel(phi0, 9) = utoi(0x1b8136fUL);
2520 1060 : gel(phi0, 10) = utoi(0xa67674UL);
2521 1060 : gel(phi0, 11) = utoi(0x23982UL);
2522 1060 : gel(phi0, 12) = utoi(0x294UL);
2523 1060 : gel(phi0, 13) = gen_1;
2524 :
2525 1060 : phi1 = cgetg(13, t_VEC);
2526 1060 : gel(phi1, 1) = gen_0;
2527 1060 : gel(phi1, 2) = gen_0;
2528 1060 : gel(phi1, 3) = gen_m1;
2529 1060 : gel(phi1, 4) = utoi(0x23UL);
2530 1060 : gel(phi1, 5) = utoineg(0xaeUL);
2531 1060 : gel(phi1, 6) = utoineg(0x5b8UL);
2532 1060 : gel(phi1, 7) = utoi(0x12d7UL);
2533 1060 : gel(phi1, 8) = utoineg(0x7c86UL);
2534 1060 : gel(phi1, 9) = utoi(0x37c8UL);
2535 1060 : gel(phi1, 10) = utoineg(0x69cUL);
2536 1060 : gel(phi1, 11) = utoi(0x48UL);
2537 1060 : gel(phi1, 12) = gen_m1;
2538 :
2539 1060 : gel(phi, 1) = phi0;
2540 1060 : gel(phi, 2) = phi1;
2541 1060 : gel(phi, 3) = utoi(5); return phi;
2542 : }
2543 :
2544 : static GEN
2545 3825 : phi_w3w3_j(void)
2546 : {
2547 : GEN phi, phi0, phi1;
2548 3825 : phi = cgetg(4, t_VEC);
2549 :
2550 3825 : phi0 = cgetg(14, t_VEC);
2551 3825 : gel(phi0, 1) = utoi(0x2d9UL);
2552 3825 : gel(phi0, 2) = utoi(0x4fbcUL);
2553 3825 : gel(phi0, 3) = utoi(0x5828aUL);
2554 3825 : gel(phi0, 4) = utoi(0x3a7a3cUL);
2555 3825 : gel(phi0, 5) = utoi(0x1bd8edfUL);
2556 3825 : gel(phi0, 6) = utoi(0x8348838UL);
2557 3825 : gel(phi0, 7) = utoi(0x1983f8acUL);
2558 3825 : gel(phi0, 8) = utoi(0x14e4e098UL);
2559 3825 : gel(phi0, 9) = utoi(0x69ed1a7UL);
2560 3825 : gel(phi0, 10) = utoi(0xc3828cUL);
2561 3825 : gel(phi0, 11) = utoi(0x2696aUL);
2562 3825 : gel(phi0, 12) = utoi(0x2acUL);
2563 3825 : gel(phi0, 13) = gen_1;
2564 :
2565 3825 : phi1 = cgetg(13, t_VEC);
2566 3825 : gel(phi1, 1) = gen_0;
2567 3825 : gel(phi1, 2) = utoineg(0x1bUL);
2568 3825 : gel(phi1, 3) = utoineg(0x5d6UL);
2569 3825 : gel(phi1, 4) = utoineg(0x1c7bUL);
2570 3825 : gel(phi1, 5) = utoi(0x7980UL);
2571 3825 : gel(phi1, 6) = utoi(0x12168UL);
2572 3825 : gel(phi1, 7) = utoineg(0x3528UL);
2573 3825 : gel(phi1, 8) = utoineg(0x6174UL);
2574 3825 : gel(phi1, 9) = utoi(0x2208UL);
2575 3825 : gel(phi1, 10) = utoineg(0x41dUL);
2576 3825 : gel(phi1, 11) = utoi(0x36UL);
2577 3825 : gel(phi1, 12) = gen_m1;
2578 :
2579 3825 : gel(phi, 1) = phi0;
2580 3825 : gel(phi, 2) = phi1;
2581 3825 : gel(phi, 3) = gen_2; return phi;
2582 : }
2583 :
2584 : static GEN
2585 2927 : phi_w2w5_j(void)
2586 : {
2587 : GEN phi, phi0, phi1;
2588 2927 : phi = cgetg(4, t_VEC);
2589 :
2590 2927 : phi0 = cgetg(20, t_VEC);
2591 2927 : gel(phi0, 1) = gen_1;
2592 2927 : gel(phi0, 2) = utoineg(0x2aUL);
2593 2927 : gel(phi0, 3) = utoi(0x549UL);
2594 2927 : gel(phi0, 4) = utoineg(0x6530UL);
2595 2927 : gel(phi0, 5) = utoi(0x60504UL);
2596 2927 : gel(phi0, 6) = utoineg(0x3cbbc8UL);
2597 2927 : gel(phi0, 7) = utoi(0x1d1ee74UL);
2598 2927 : gel(phi0, 8) = utoineg(0x7ef9ab0UL);
2599 2927 : gel(phi0, 9) = utoi(0x12b888beUL);
2600 2927 : gel(phi0, 10) = utoineg(0x15fa174cUL);
2601 2927 : gel(phi0, 11) = utoi(0x615d9feUL);
2602 2927 : gel(phi0, 12) = utoi(0xbeca070UL);
2603 2927 : gel(phi0, 13) = utoineg(0x88de74cUL);
2604 2927 : gel(phi0, 14) = utoineg(0x2b3a268UL);
2605 2927 : gel(phi0, 15) = utoi(0x24b3244UL);
2606 2927 : gel(phi0, 16) = utoi(0xb56270UL);
2607 2927 : gel(phi0, 17) = utoi(0x25989UL);
2608 2927 : gel(phi0, 18) = utoi(0x2a6UL);
2609 2927 : gel(phi0, 19) = gen_1;
2610 :
2611 2927 : phi1 = cgetg(19, t_VEC);
2612 2927 : gel(phi1, 1) = gen_0;
2613 2927 : gel(phi1, 2) = gen_0;
2614 2927 : gel(phi1, 3) = gen_m1;
2615 2927 : gel(phi1, 4) = utoi(0x1eUL);
2616 2927 : gel(phi1, 5) = utoineg(0xffUL);
2617 2927 : gel(phi1, 6) = utoi(0x243UL);
2618 2927 : gel(phi1, 7) = utoineg(0xf3UL);
2619 2927 : gel(phi1, 8) = utoineg(0x5c4UL);
2620 2927 : gel(phi1, 9) = utoi(0x107bUL);
2621 2927 : gel(phi1, 10) = utoineg(0x11b2fUL);
2622 2927 : gel(phi1, 11) = utoi(0x48fa8UL);
2623 2927 : gel(phi1, 12) = utoineg(0x6ff7cUL);
2624 2927 : gel(phi1, 13) = utoi(0x4bf48UL);
2625 2927 : gel(phi1, 14) = utoineg(0x187efUL);
2626 2927 : gel(phi1, 15) = utoi(0x404cUL);
2627 2927 : gel(phi1, 16) = utoineg(0x582UL);
2628 2927 : gel(phi1, 17) = utoi(0x3cUL);
2629 2927 : gel(phi1, 18) = gen_m1;
2630 :
2631 2927 : gel(phi, 1) = phi0;
2632 2927 : gel(phi, 2) = phi1;
2633 2927 : gel(phi, 3) = utoi(7); return phi;
2634 : }
2635 :
2636 : static GEN
2637 6628 : phi_w2w7_j(void)
2638 : {
2639 : GEN phi, phi0, phi1;
2640 6628 : phi = cgetg(4, t_VEC);
2641 :
2642 6628 : phi0 = cgetg(26, t_VEC);
2643 6628 : gel(phi0, 1) = gen_1;
2644 6628 : gel(phi0, 2) = utoineg(0x24UL);
2645 6628 : gel(phi0, 3) = utoi(0x4ceUL);
2646 6628 : gel(phi0, 4) = utoineg(0x5d60UL);
2647 6628 : gel(phi0, 5) = utoi(0x62b05UL);
2648 6628 : gel(phi0, 6) = utoineg(0x47be78UL);
2649 6628 : gel(phi0, 7) = utoi(0x2a3880aUL);
2650 6628 : gel(phi0, 8) = utoineg(0x114bccf4UL);
2651 6628 : gel(phi0, 9) = utoi(0x4b95e79aUL);
2652 6628 : gel(phi0, 10) = utoineg(0xe2cfee1cUL);
2653 6628 : gel(phi0, 11) = uu32toi(0x1UL, 0xe43d1126UL);
2654 6628 : gel(phi0, 12) = uu32toineg(0x2UL, 0xf04dc6f8UL);
2655 6628 : gel(phi0, 13) = uu32toi(0x3UL, 0x5384987dUL);
2656 6628 : gel(phi0, 14) = uu32toineg(0x2UL, 0xa5ccbe18UL);
2657 6628 : gel(phi0, 15) = uu32toi(0x1UL, 0x4c52c8a6UL);
2658 6628 : gel(phi0, 16) = utoineg(0x2643fdecUL);
2659 6628 : gel(phi0, 17) = utoineg(0x49f5ab66UL);
2660 6628 : gel(phi0, 18) = utoi(0x33074d3cUL);
2661 6628 : gel(phi0, 19) = utoineg(0x6a3e376UL);
2662 6628 : gel(phi0, 20) = utoineg(0x675aa58UL);
2663 6628 : gel(phi0, 21) = utoi(0x2674005UL);
2664 6628 : gel(phi0, 22) = utoi(0xba5be0UL);
2665 6628 : gel(phi0, 23) = utoi(0x2644eUL);
2666 6628 : gel(phi0, 24) = utoi(0x2acUL);
2667 6628 : gel(phi0, 25) = gen_1;
2668 :
2669 6628 : phi1 = cgetg(25, t_VEC);
2670 6628 : gel(phi1, 1) = gen_0;
2671 6628 : gel(phi1, 2) = gen_0;
2672 6628 : gel(phi1, 3) = gen_m1;
2673 6628 : gel(phi1, 4) = utoi(0x1cUL);
2674 6628 : gel(phi1, 5) = utoineg(0x10aUL);
2675 6628 : gel(phi1, 6) = utoi(0x3f0UL);
2676 6628 : gel(phi1, 7) = utoineg(0x5d3UL);
2677 6628 : gel(phi1, 8) = utoi(0x3efUL);
2678 6628 : gel(phi1, 9) = utoineg(0x102UL);
2679 6628 : gel(phi1, 10) = utoineg(0x5c8UL);
2680 6628 : gel(phi1, 11) = utoi(0x102fUL);
2681 6628 : gel(phi1, 12) = utoineg(0x13f8aUL);
2682 6628 : gel(phi1, 13) = utoi(0x86538UL);
2683 6628 : gel(phi1, 14) = utoineg(0x1bbd10UL);
2684 6628 : gel(phi1, 15) = utoi(0x3614e8UL);
2685 6628 : gel(phi1, 16) = utoineg(0x42f793UL);
2686 6628 : gel(phi1, 17) = utoi(0x364698UL);
2687 6628 : gel(phi1, 18) = utoineg(0x1c7a10UL);
2688 6628 : gel(phi1, 19) = utoi(0x97cc8UL);
2689 6628 : gel(phi1, 20) = utoineg(0x1fc8aUL);
2690 6628 : gel(phi1, 21) = utoi(0x4210UL);
2691 6628 : gel(phi1, 22) = utoineg(0x524UL);
2692 6628 : gel(phi1, 23) = utoi(0x38UL);
2693 6628 : gel(phi1, 24) = gen_m1;
2694 :
2695 6628 : gel(phi, 1) = phi0;
2696 6628 : gel(phi, 2) = phi1;
2697 6628 : gel(phi, 3) = utoi(9); return phi;
2698 : }
2699 :
2700 : static GEN
2701 2402 : phi_w2w13_j(void)
2702 : {
2703 : GEN phi, phi0, phi1;
2704 2402 : phi = cgetg(4, t_VEC);
2705 :
2706 2402 : phi0 = cgetg(44, t_VEC);
2707 2402 : gel(phi0, 1) = gen_1;
2708 2402 : gel(phi0, 2) = utoineg(0x1eUL);
2709 2402 : gel(phi0, 3) = utoi(0x45fUL);
2710 2402 : gel(phi0, 4) = utoineg(0x5590UL);
2711 2402 : gel(phi0, 5) = utoi(0x64407UL);
2712 2402 : gel(phi0, 6) = utoineg(0x53a792UL);
2713 2402 : gel(phi0, 7) = utoi(0x3b21af3UL);
2714 2402 : gel(phi0, 8) = utoineg(0x20d056d0UL);
2715 2402 : gel(phi0, 9) = utoi(0xe02db4a6UL);
2716 2402 : gel(phi0, 10) = uu32toineg(0x4UL, 0xb23400b0UL);
2717 2402 : gel(phi0, 11) = uu32toi(0x14UL, 0x57fbb906UL);
2718 2402 : gel(phi0, 12) = uu32toineg(0x49UL, 0xcf80c00UL);
2719 2402 : gel(phi0, 13) = uu32toi(0xdeUL, 0x84ff421UL);
2720 2402 : gel(phi0, 14) = uu32toineg(0x244UL, 0xc500c156UL);
2721 2402 : gel(phi0, 15) = uu32toi(0x52cUL, 0x79162979UL);
2722 2402 : gel(phi0, 16) = uu32toineg(0xa64UL, 0x8edc5650UL);
2723 2402 : gel(phi0, 17) = uu32toi(0x1289UL, 0x4225bb41UL);
2724 2402 : gel(phi0, 18) = uu32toineg(0x1d89UL, 0x2a15229aUL);
2725 2402 : gel(phi0, 19) = uu32toi(0x2a3eUL, 0x4539f1ebUL);
2726 2402 : gel(phi0, 20) = uu32toineg(0x366aUL, 0xa5ea1130UL);
2727 2402 : gel(phi0, 21) = uu32toi(0x3f47UL, 0xa19fecb4UL);
2728 2402 : gel(phi0, 22) = uu32toineg(0x4282UL, 0x91a3c4a0UL);
2729 2402 : gel(phi0, 23) = uu32toi(0x3f30UL, 0xbaa305b4UL);
2730 2402 : gel(phi0, 24) = uu32toineg(0x3635UL, 0xd11c2530UL);
2731 2402 : gel(phi0, 25) = uu32toi(0x29e2UL, 0x89df27ebUL);
2732 2402 : gel(phi0, 26) = uu32toineg(0x1d03UL, 0x6509d48aUL);
2733 2402 : gel(phi0, 27) = uu32toi(0x11e2UL, 0x272cc601UL);
2734 2402 : gel(phi0, 28) = uu32toineg(0x9b0UL, 0xacd58ff0UL);
2735 2402 : gel(phi0, 29) = uu32toi(0x485UL, 0x608d7db9UL);
2736 2402 : gel(phi0, 30) = uu32toineg(0x1bfUL, 0xa941546UL);
2737 2402 : gel(phi0, 31) = uu32toi(0x82UL, 0x56e48b21UL);
2738 2402 : gel(phi0, 32) = uu32toineg(0x13UL, 0xc36b2340UL);
2739 2402 : gel(phi0, 33) = uu32toineg(0x5UL, 0x6637257aUL);
2740 2402 : gel(phi0, 34) = uu32toi(0x5UL, 0x40f70bd0UL);
2741 2402 : gel(phi0, 35) = uu32toineg(0x1UL, 0xf70842daUL);
2742 2402 : gel(phi0, 36) = utoi(0x53eea5f0UL);
2743 2402 : gel(phi0, 37) = utoi(0xda17bf3UL);
2744 2402 : gel(phi0, 38) = utoineg(0xaf246c2UL);
2745 2402 : gel(phi0, 39) = utoi(0x278f847UL);
2746 2402 : gel(phi0, 40) = utoi(0xbf5550UL);
2747 2402 : gel(phi0, 41) = utoi(0x26f1fUL);
2748 2402 : gel(phi0, 42) = utoi(0x2b2UL);
2749 2402 : gel(phi0, 43) = gen_1;
2750 :
2751 2402 : phi1 = cgetg(43, t_VEC);
2752 2402 : gel(phi1, 1) = gen_0;
2753 2402 : gel(phi1, 2) = gen_0;
2754 2402 : gel(phi1, 3) = gen_m1;
2755 2402 : gel(phi1, 4) = utoi(0x1aUL);
2756 2402 : gel(phi1, 5) = utoineg(0x111UL);
2757 2402 : gel(phi1, 6) = utoi(0x5e4UL);
2758 2402 : gel(phi1, 7) = utoineg(0x1318UL);
2759 2402 : gel(phi1, 8) = utoi(0x2804UL);
2760 2402 : gel(phi1, 9) = utoineg(0x3cd6UL);
2761 2402 : gel(phi1, 10) = utoi(0x467cUL);
2762 2402 : gel(phi1, 11) = utoineg(0x3cd6UL);
2763 2402 : gel(phi1, 12) = utoi(0x2804UL);
2764 2402 : gel(phi1, 13) = utoineg(0x1318UL);
2765 2402 : gel(phi1, 14) = utoi(0x5e3UL);
2766 2402 : gel(phi1, 15) = utoineg(0x10dUL);
2767 2402 : gel(phi1, 16) = utoineg(0x5ccUL);
2768 2402 : gel(phi1, 17) = utoi(0x100bUL);
2769 2402 : gel(phi1, 18) = utoineg(0x160e1UL);
2770 2402 : gel(phi1, 19) = utoi(0xd2cb0UL);
2771 2402 : gel(phi1, 20) = utoineg(0x4c85fcUL);
2772 2402 : gel(phi1, 21) = utoi(0x137cb98UL);
2773 2402 : gel(phi1, 22) = utoineg(0x3c75568UL);
2774 2402 : gel(phi1, 23) = utoi(0x95c69c8UL);
2775 2402 : gel(phi1, 24) = utoineg(0x131557bcUL);
2776 2402 : gel(phi1, 25) = utoi(0x20aacfd0UL);
2777 2402 : gel(phi1, 26) = utoineg(0x2f9164e6UL);
2778 2402 : gel(phi1, 27) = utoi(0x3b6a5e40UL);
2779 2402 : gel(phi1, 28) = utoineg(0x3ff54344UL);
2780 2402 : gel(phi1, 29) = utoi(0x3b6a9140UL);
2781 2402 : gel(phi1, 30) = utoineg(0x2f927fa6UL);
2782 2402 : gel(phi1, 31) = utoi(0x20ae6450UL);
2783 2402 : gel(phi1, 32) = utoineg(0x131cd87cUL);
2784 2402 : gel(phi1, 33) = utoi(0x967d1e8UL);
2785 2402 : gel(phi1, 34) = utoineg(0x3d48ca8UL);
2786 2402 : gel(phi1, 35) = utoi(0x14333b8UL);
2787 2402 : gel(phi1, 36) = utoineg(0x5406bcUL);
2788 2402 : gel(phi1, 37) = utoi(0x10c130UL);
2789 2402 : gel(phi1, 38) = utoineg(0x27ba1UL);
2790 2402 : gel(phi1, 39) = utoi(0x433cUL);
2791 2402 : gel(phi1, 40) = utoineg(0x4c6UL);
2792 2402 : gel(phi1, 41) = utoi(0x34UL);
2793 2402 : gel(phi1, 42) = gen_m1;
2794 :
2795 2402 : gel(phi, 1) = phi0;
2796 2402 : gel(phi, 2) = phi1;
2797 2402 : gel(phi, 3) = utoi(15); return phi;
2798 : }
2799 :
2800 : static GEN
2801 1160 : phi_w3w5_j(void)
2802 : {
2803 : GEN phi, phi0, phi1;
2804 1160 : phi = cgetg(4, t_VEC);
2805 :
2806 1160 : phi0 = cgetg(26, t_VEC);
2807 1160 : gel(phi0, 1) = gen_1;
2808 1160 : gel(phi0, 2) = utoi(0x18UL);
2809 1160 : gel(phi0, 3) = utoi(0xb4UL);
2810 1160 : gel(phi0, 4) = utoineg(0x178UL);
2811 1160 : gel(phi0, 5) = utoineg(0x2d7eUL);
2812 1160 : gel(phi0, 6) = utoineg(0x89b8UL);
2813 1160 : gel(phi0, 7) = utoi(0x35c24UL);
2814 1160 : gel(phi0, 8) = utoi(0x128a18UL);
2815 1160 : gel(phi0, 9) = utoineg(0x12a911UL);
2816 1160 : gel(phi0, 10) = utoineg(0xcc0190UL);
2817 1160 : gel(phi0, 11) = utoi(0x94368UL);
2818 1160 : gel(phi0, 12) = utoi(0x1439d0UL);
2819 1160 : gel(phi0, 13) = utoi(0x96f931cUL);
2820 1160 : gel(phi0, 14) = utoineg(0x1f59ff0UL);
2821 1160 : gel(phi0, 15) = utoi(0x20e7e8UL);
2822 1160 : gel(phi0, 16) = utoineg(0x25fdf150UL);
2823 1160 : gel(phi0, 17) = utoineg(0x7091511UL);
2824 1160 : gel(phi0, 18) = utoi(0x1ef52f8UL);
2825 1160 : gel(phi0, 19) = utoi(0x341f2de4UL);
2826 1160 : gel(phi0, 20) = utoi(0x25d72c28UL);
2827 1160 : gel(phi0, 21) = utoi(0x95d2082UL);
2828 1160 : gel(phi0, 22) = utoi(0xd2d828UL);
2829 1160 : gel(phi0, 23) = utoi(0x281f4UL);
2830 1160 : gel(phi0, 24) = utoi(0x2b8UL);
2831 1160 : gel(phi0, 25) = gen_1;
2832 :
2833 1160 : phi1 = cgetg(25, t_VEC);
2834 1160 : gel(phi1, 1) = gen_0;
2835 1160 : gel(phi1, 2) = gen_0;
2836 1160 : gel(phi1, 3) = gen_0;
2837 1160 : gel(phi1, 4) = gen_1;
2838 1160 : gel(phi1, 5) = utoi(0xfUL);
2839 1160 : gel(phi1, 6) = utoi(0x2eUL);
2840 1160 : gel(phi1, 7) = utoineg(0x1fUL);
2841 1160 : gel(phi1, 8) = utoineg(0x2dUL);
2842 1160 : gel(phi1, 9) = utoineg(0x5caUL);
2843 1160 : gel(phi1, 10) = utoineg(0x358UL);
2844 1160 : gel(phi1, 11) = utoi(0x2f1cUL);
2845 1160 : gel(phi1, 12) = utoi(0xd8eaUL);
2846 1160 : gel(phi1, 13) = utoineg(0x38c70UL);
2847 1160 : gel(phi1, 14) = utoineg(0x1a964UL);
2848 1160 : gel(phi1, 15) = utoi(0x93512UL);
2849 1160 : gel(phi1, 16) = utoineg(0x58f2UL);
2850 1160 : gel(phi1, 17) = utoineg(0x5af1eUL);
2851 1160 : gel(phi1, 18) = utoi(0x1afb8UL);
2852 1160 : gel(phi1, 19) = utoi(0xc084UL);
2853 1160 : gel(phi1, 20) = utoineg(0x7fcbUL);
2854 1160 : gel(phi1, 21) = utoi(0x1c89UL);
2855 1160 : gel(phi1, 22) = utoineg(0x32aUL);
2856 1160 : gel(phi1, 23) = utoi(0x2dUL);
2857 1160 : gel(phi1, 24) = gen_m1;
2858 :
2859 1160 : gel(phi, 1) = phi0;
2860 1160 : gel(phi, 2) = phi1;
2861 1160 : gel(phi, 3) = utoi(8); return phi;
2862 : }
2863 :
2864 : static GEN
2865 2986 : phi_w3w7_j(void)
2866 : {
2867 : GEN phi, phi0, phi1;
2868 2986 : phi = cgetg(4, t_VEC);
2869 :
2870 2986 : phi0 = cgetg(34, t_VEC);
2871 2986 : gel(phi0, 1) = gen_1;
2872 2986 : gel(phi0, 2) = utoineg(0x14UL);
2873 2986 : gel(phi0, 3) = utoi(0x82UL);
2874 2986 : gel(phi0, 4) = utoi(0x1f8UL);
2875 2986 : gel(phi0, 5) = utoineg(0x2a45UL);
2876 2986 : gel(phi0, 6) = utoi(0x9300UL);
2877 2986 : gel(phi0, 7) = utoi(0x32abeUL);
2878 2986 : gel(phi0, 8) = utoineg(0x19c91cUL);
2879 2986 : gel(phi0, 9) = utoi(0xc1ba9UL);
2880 2986 : gel(phi0, 10) = utoi(0x1788f68UL);
2881 2986 : gel(phi0, 11) = utoineg(0x2b1989cUL);
2882 2986 : gel(phi0, 12) = utoineg(0x7a92408UL);
2883 2986 : gel(phi0, 13) = utoi(0x1238d56eUL);
2884 2986 : gel(phi0, 14) = utoi(0x13dd66a0UL);
2885 2986 : gel(phi0, 15) = utoineg(0x2dbedca8UL);
2886 2985 : gel(phi0, 16) = utoineg(0x34282eb8UL);
2887 2985 : gel(phi0, 17) = utoi(0x2c2a54d2UL);
2888 2985 : gel(phi0, 18) = utoi(0x98db81a8UL);
2889 2985 : gel(phi0, 19) = utoineg(0x4088be8UL);
2890 2985 : gel(phi0, 20) = utoineg(0xe424a220UL);
2891 2985 : gel(phi0, 21) = utoineg(0x67bbb232UL);
2892 2985 : gel(phi0, 22) = utoi(0x7dd8bb98UL);
2893 2985 : gel(phi0, 23) = uu32toi(0x1UL, 0xcaff744UL);
2894 2985 : gel(phi0, 24) = utoineg(0x1d46a378UL);
2895 2985 : gel(phi0, 25) = utoineg(0x82fa50f7UL);
2896 2985 : gel(phi0, 26) = utoineg(0x700ef38cUL);
2897 2985 : gel(phi0, 27) = utoi(0x20aa202eUL);
2898 2985 : gel(phi0, 28) = utoi(0x299b3440UL);
2899 2985 : gel(phi0, 29) = utoi(0xa476c4bUL);
2900 2986 : gel(phi0, 30) = utoi(0xd80558UL);
2901 2986 : gel(phi0, 31) = utoi(0x28a32UL);
2902 2986 : gel(phi0, 32) = utoi(0x2bcUL);
2903 2986 : gel(phi0, 33) = gen_1;
2904 :
2905 2986 : phi1 = cgetg(33, t_VEC);
2906 2986 : gel(phi1, 1) = gen_0;
2907 2986 : gel(phi1, 2) = gen_0;
2908 2986 : gel(phi1, 3) = gen_0;
2909 2986 : gel(phi1, 4) = gen_m1;
2910 2986 : gel(phi1, 5) = utoi(0xeUL);
2911 2986 : gel(phi1, 6) = utoineg(0x31UL);
2912 2986 : gel(phi1, 7) = utoineg(0xeUL);
2913 2986 : gel(phi1, 8) = utoi(0x99UL);
2914 2986 : gel(phi1, 9) = utoineg(0x8UL);
2915 2986 : gel(phi1, 10) = utoineg(0x2eUL);
2916 2986 : gel(phi1, 11) = utoineg(0x5ccUL);
2917 2986 : gel(phi1, 12) = utoi(0x308UL);
2918 2986 : gel(phi1, 13) = utoi(0x2904UL);
2919 2986 : gel(phi1, 14) = utoineg(0x15700UL);
2920 2986 : gel(phi1, 15) = utoineg(0x2b9ecUL);
2921 2986 : gel(phi1, 16) = utoi(0xf0966UL);
2922 2986 : gel(phi1, 17) = utoi(0xb3cc8UL);
2923 2986 : gel(phi1, 18) = utoineg(0x38241cUL);
2924 2986 : gel(phi1, 19) = utoineg(0x8604cUL);
2925 2986 : gel(phi1, 20) = utoi(0x578a64UL);
2926 2986 : gel(phi1, 21) = utoineg(0x11a798UL);
2927 2986 : gel(phi1, 22) = utoineg(0x39c85eUL);
2928 2986 : gel(phi1, 23) = utoi(0x1a5084UL);
2929 2986 : gel(phi1, 24) = utoi(0xcdeb4UL);
2930 2986 : gel(phi1, 25) = utoineg(0xb0364UL);
2931 2986 : gel(phi1, 26) = utoi(0x129d4UL);
2932 2986 : gel(phi1, 27) = utoi(0x126fcUL);
2933 2986 : gel(phi1, 28) = utoineg(0x8649UL);
2934 2986 : gel(phi1, 29) = utoi(0x1aa2UL);
2935 2986 : gel(phi1, 30) = utoineg(0x2dfUL);
2936 2986 : gel(phi1, 31) = utoi(0x2aUL);
2937 2986 : gel(phi1, 32) = gen_m1;
2938 :
2939 2986 : gel(phi, 1) = phi0;
2940 2986 : gel(phi, 2) = phi1;
2941 2986 : gel(phi, 3) = utoi(10); return phi;
2942 : }
2943 :
2944 : static GEN
2945 210 : phi_w3w13_j(void)
2946 : {
2947 : GEN phi, phi0, phi1;
2948 210 : phi = cgetg(4, t_VEC);
2949 :
2950 210 : phi0 = cgetg(58, t_VEC);
2951 210 : gel(phi0, 1) = gen_1;
2952 210 : gel(phi0, 2) = utoineg(0x10UL);
2953 210 : gel(phi0, 3) = utoi(0x58UL);
2954 210 : gel(phi0, 4) = utoi(0x258UL);
2955 210 : gel(phi0, 5) = utoineg(0x270cUL);
2956 210 : gel(phi0, 6) = utoi(0x9c00UL);
2957 210 : gel(phi0, 7) = utoi(0x2b40cUL);
2958 210 : gel(phi0, 8) = utoineg(0x20e250UL);
2959 210 : gel(phi0, 9) = utoi(0x4f46baUL);
2960 210 : gel(phi0, 10) = utoi(0x1869448UL);
2961 210 : gel(phi0, 11) = utoineg(0xa49ab68UL);
2962 210 : gel(phi0, 12) = utoi(0x96c7630UL);
2963 210 : gel(phi0, 13) = utoi(0x4f7e0af6UL);
2964 210 : gel(phi0, 14) = utoineg(0xea093590UL);
2965 210 : gel(phi0, 15) = utoineg(0x6735bc50UL);
2966 210 : gel(phi0, 16) = uu32toi(0x5UL, 0x971a2e08UL);
2967 210 : gel(phi0, 17) = uu32toineg(0x6UL, 0x29c9d965UL);
2968 210 : gel(phi0, 18) = uu32toineg(0xdUL, 0xeb9aa360UL);
2969 210 : gel(phi0, 19) = uu32toi(0x26UL, 0xe9c0584UL);
2970 210 : gel(phi0, 20) = uu32toineg(0x1UL, 0xb0cadce8UL);
2971 210 : gel(phi0, 21) = uu32toineg(0x62UL, 0x73586014UL);
2972 210 : gel(phi0, 22) = uu32toi(0x66UL, 0xaf672e38UL);
2973 210 : gel(phi0, 23) = uu32toi(0x6bUL, 0x93c28cdcUL);
2974 210 : gel(phi0, 24) = uu32toineg(0x11eUL, 0x4f633080UL);
2975 210 : gel(phi0, 25) = uu32toi(0x3cUL, 0xcc42461bUL);
2976 210 : gel(phi0, 26) = uu32toi(0x17bUL, 0xdec0a78UL);
2977 210 : gel(phi0, 27) = uu32toineg(0x166UL, 0x910d8bd0UL);
2978 210 : gel(phi0, 28) = uu32toineg(0xd4UL, 0x47873030UL);
2979 210 : gel(phi0, 29) = uu32toi(0x204UL, 0x811828baUL);
2980 210 : gel(phi0, 30) = uu32toineg(0x50UL, 0x5d713960UL);
2981 210 : gel(phi0, 31) = uu32toineg(0x198UL, 0xa27e42b0UL);
2982 210 : gel(phi0, 32) = uu32toi(0xe1UL, 0x25685138UL);
2983 210 : gel(phi0, 33) = uu32toi(0xe3UL, 0xaa5774bbUL);
2984 210 : gel(phi0, 34) = uu32toineg(0xcfUL, 0x392a9a00UL);
2985 210 : gel(phi0, 35) = uu32toineg(0x81UL, 0xfb334d04UL);
2986 210 : gel(phi0, 36) = uu32toi(0xabUL, 0x59594a68UL);
2987 210 : gel(phi0, 37) = uu32toi(0x42UL, 0x356993acUL);
2988 210 : gel(phi0, 38) = uu32toineg(0x86UL, 0x307ba678UL);
2989 210 : gel(phi0, 39) = uu32toineg(0xbUL, 0x7a9e59dcUL);
2990 210 : gel(phi0, 40) = uu32toi(0x4cUL, 0x27935f20UL);
2991 210 : gel(phi0, 41) = uu32toineg(0x2UL, 0xe0ac9045UL);
2992 210 : gel(phi0, 42) = uu32toineg(0x24UL, 0x14495758UL);
2993 210 : gel(phi0, 43) = utoi(0x20973410UL);
2994 210 : gel(phi0, 44) = uu32toi(0x13UL, 0x99ff4e00UL);
2995 210 : gel(phi0, 45) = uu32toineg(0x1UL, 0xa710d34aUL);
2996 210 : gel(phi0, 46) = uu32toineg(0x7UL, 0xfe5405c0UL);
2997 210 : gel(phi0, 47) = uu32toi(0x1UL, 0xcdee0f8UL);
2998 210 : gel(phi0, 48) = uu32toi(0x2UL, 0x660c92a8UL);
2999 210 : gel(phi0, 49) = utoi(0x3f13a35aUL);
3000 210 : gel(phi0, 50) = utoineg(0xe4eb4ba0UL);
3001 210 : gel(phi0, 51) = utoineg(0x6420f4UL);
3002 210 : gel(phi0, 52) = utoi(0x2c624370UL);
3003 210 : gel(phi0, 53) = utoi(0xb31b814UL);
3004 210 : gel(phi0, 54) = utoi(0xdd3ad8UL);
3005 210 : gel(phi0, 55) = utoi(0x29278UL);
3006 210 : gel(phi0, 56) = utoi(0x2c0UL);
3007 210 : gel(phi0, 57) = gen_1;
3008 :
3009 210 : phi1 = cgetg(57, t_VEC);
3010 210 : gel(phi1, 1) = gen_0;
3011 210 : gel(phi1, 2) = gen_0;
3012 210 : gel(phi1, 3) = gen_0;
3013 210 : gel(phi1, 4) = gen_m1;
3014 210 : gel(phi1, 5) = utoi(0xdUL);
3015 210 : gel(phi1, 6) = utoineg(0x34UL);
3016 210 : gel(phi1, 7) = utoi(0x1aUL);
3017 210 : gel(phi1, 8) = utoi(0xf7UL);
3018 210 : gel(phi1, 9) = utoineg(0x16cUL);
3019 210 : gel(phi1, 10) = utoineg(0xddUL);
3020 210 : gel(phi1, 11) = utoi(0x28aUL);
3021 210 : gel(phi1, 12) = utoineg(0xddUL);
3022 210 : gel(phi1, 13) = utoineg(0x16cUL);
3023 210 : gel(phi1, 14) = utoi(0xf6UL);
3024 210 : gel(phi1, 15) = utoi(0x1dUL);
3025 210 : gel(phi1, 16) = utoineg(0x31UL);
3026 210 : gel(phi1, 17) = utoineg(0x5ceUL);
3027 210 : gel(phi1, 18) = utoi(0x2e4UL);
3028 210 : gel(phi1, 19) = utoi(0x252cUL);
3029 210 : gel(phi1, 20) = utoineg(0x1b34cUL);
3030 210 : gel(phi1, 21) = utoi(0xaf80UL);
3031 210 : gel(phi1, 22) = utoi(0x1cc5f9UL);
3032 210 : gel(phi1, 23) = utoineg(0x3e1aa5UL);
3033 210 : gel(phi1, 24) = utoineg(0x86d17aUL);
3034 210 : gel(phi1, 25) = utoi(0x2427264UL);
3035 210 : gel(phi1, 26) = utoineg(0x691c1fUL);
3036 210 : gel(phi1, 27) = utoineg(0x862ad4eUL);
3037 210 : gel(phi1, 28) = utoi(0xab21e1fUL);
3038 210 : gel(phi1, 29) = utoi(0xbc19ddcUL);
3039 210 : gel(phi1, 30) = utoineg(0x24331db8UL);
3040 210 : gel(phi1, 31) = utoi(0x972c105UL);
3041 210 : gel(phi1, 32) = utoi(0x363d7107UL);
3042 210 : gel(phi1, 33) = utoineg(0x39696450UL);
3043 210 : gel(phi1, 34) = utoineg(0x1bce7c48UL);
3044 210 : gel(phi1, 35) = utoi(0x552ecba0UL);
3045 210 : gel(phi1, 36) = utoineg(0x1c7771b8UL);
3046 210 : gel(phi1, 37) = utoineg(0x393029b8UL);
3047 210 : gel(phi1, 38) = utoi(0x3755be97UL);
3048 210 : gel(phi1, 39) = utoi(0x83402a9UL);
3049 210 : gel(phi1, 40) = utoineg(0x24d5be62UL);
3050 210 : gel(phi1, 41) = utoi(0xdb6d90aUL);
3051 210 : gel(phi1, 42) = utoi(0xa0ef177UL);
3052 210 : gel(phi1, 43) = utoineg(0x99ff162UL);
3053 210 : gel(phi1, 44) = utoi(0xb09e27UL);
3054 210 : gel(phi1, 45) = utoi(0x26a7adcUL);
3055 210 : gel(phi1, 46) = utoineg(0x116e2fcUL);
3056 210 : gel(phi1, 47) = utoineg(0x1383b5UL);
3057 210 : gel(phi1, 48) = utoi(0x35a9e7UL);
3058 210 : gel(phi1, 49) = utoineg(0x1082a0UL);
3059 210 : gel(phi1, 50) = utoineg(0x4696UL);
3060 210 : gel(phi1, 51) = utoi(0x19f98UL);
3061 210 : gel(phi1, 52) = utoineg(0x8bb3UL);
3062 210 : gel(phi1, 53) = utoi(0x18bbUL);
3063 210 : gel(phi1, 54) = utoineg(0x297UL);
3064 210 : gel(phi1, 55) = utoi(0x27UL);
3065 210 : gel(phi1, 56) = gen_m1;
3066 :
3067 210 : gel(phi, 1) = phi0;
3068 210 : gel(phi, 2) = phi1;
3069 210 : gel(phi, 3) = utoi(16); return phi;
3070 : }
3071 :
3072 : static GEN
3073 3003 : phi_w5w7_j(void)
3074 : {
3075 : GEN phi, phi0, phi1;
3076 3003 : phi = cgetg(4, t_VEC);
3077 :
3078 3003 : phi0 = cgetg(50, t_VEC);
3079 3003 : gel(phi0, 1) = gen_1;
3080 3003 : gel(phi0, 2) = utoi(0xcUL);
3081 3003 : gel(phi0, 3) = utoi(0x2aUL);
3082 3003 : gel(phi0, 4) = utoi(0x10UL);
3083 3003 : gel(phi0, 5) = utoineg(0x69UL);
3084 3003 : gel(phi0, 6) = utoineg(0x318UL);
3085 3003 : gel(phi0, 7) = utoineg(0x148aUL);
3086 3003 : gel(phi0, 8) = utoineg(0x17c4UL);
3087 3003 : gel(phi0, 9) = utoi(0x1a73UL);
3088 3003 : gel(phi0, 10) = gen_0;
3089 3003 : gel(phi0, 11) = utoi(0x338a0UL);
3090 3003 : gel(phi0, 12) = utoi(0x61698UL);
3091 3003 : gel(phi0, 13) = utoineg(0x96e8UL);
3092 3003 : gel(phi0, 14) = utoi(0x140910UL);
3093 3003 : gel(phi0, 15) = utoineg(0x45f6b4UL);
3094 3003 : gel(phi0, 16) = utoineg(0x309f50UL);
3095 3003 : gel(phi0, 17) = utoineg(0xef9f8bUL);
3096 3003 : gel(phi0, 18) = utoineg(0x283167cUL);
3097 3003 : gel(phi0, 19) = utoi(0x625e20aUL);
3098 3003 : gel(phi0, 20) = utoineg(0x16186350UL);
3099 3003 : gel(phi0, 21) = utoi(0x46861281UL);
3100 3003 : gel(phi0, 22) = utoineg(0x754b96a0UL);
3101 3003 : gel(phi0, 23) = uu32toi(0x1UL, 0x421ca02aUL);
3102 3003 : gel(phi0, 24) = uu32toineg(0x2UL, 0xdb76a5cUL);
3103 3003 : gel(phi0, 25) = uu32toi(0x4UL, 0xf6afd8eUL);
3104 3003 : gel(phi0, 26) = uu32toineg(0x6UL, 0xaafd3cb4UL);
3105 3003 : gel(phi0, 27) = uu32toi(0x8UL, 0xda2539caUL);
3106 3003 : gel(phi0, 28) = uu32toineg(0xfUL, 0x84343790UL);
3107 3003 : gel(phi0, 29) = uu32toi(0xfUL, 0x914ff421UL);
3108 3003 : gel(phi0, 30) = uu32toineg(0x19UL, 0x3c123950UL);
3109 3003 : gel(phi0, 31) = uu32toi(0x15UL, 0x381f722aUL);
3110 3003 : gel(phi0, 32) = uu32toineg(0x15UL, 0xe01c0c24UL);
3111 3003 : gel(phi0, 33) = uu32toi(0x19UL, 0x3360b375UL);
3112 3003 : gel(phi0, 34) = utoineg(0x59fda9c0UL);
3113 3003 : gel(phi0, 35) = uu32toi(0x20UL, 0xff55024cUL);
3114 3003 : gel(phi0, 36) = uu32toi(0x16UL, 0xcc600800UL);
3115 3003 : gel(phi0, 37) = uu32toi(0x24UL, 0x1879c898UL);
3116 3003 : gel(phi0, 38) = uu32toi(0x1cUL, 0x37f97498UL);
3117 3003 : gel(phi0, 39) = uu32toi(0x19UL, 0x39ec4b60UL);
3118 3003 : gel(phi0, 40) = uu32toi(0x10UL, 0x52c660d0UL);
3119 3003 : gel(phi0, 41) = uu32toi(0x9UL, 0xcab00333UL);
3120 3003 : gel(phi0, 42) = uu32toi(0x4UL, 0x7fe69be4UL);
3121 3003 : gel(phi0, 43) = uu32toi(0x1UL, 0xa0c6f116UL);
3122 3003 : gel(phi0, 44) = utoi(0x69244638UL);
3123 3003 : gel(phi0, 45) = utoi(0xed560f7UL);
3124 3002 : gel(phi0, 46) = utoi(0xe7b660UL);
3125 3002 : gel(phi0, 47) = utoi(0x29d8aUL);
3126 3002 : gel(phi0, 48) = utoi(0x2c4UL);
3127 3002 : gel(phi0, 49) = gen_1;
3128 :
3129 3002 : phi1 = cgetg(49, t_VEC);
3130 3002 : gel(phi1, 1) = gen_0;
3131 3002 : gel(phi1, 2) = gen_0;
3132 3002 : gel(phi1, 3) = gen_0;
3133 3002 : gel(phi1, 4) = gen_0;
3134 3002 : gel(phi1, 5) = gen_0;
3135 3002 : gel(phi1, 6) = gen_1;
3136 3002 : gel(phi1, 7) = utoi(0x7UL);
3137 3002 : gel(phi1, 8) = utoi(0x8UL);
3138 3002 : gel(phi1, 9) = utoineg(0x9UL);
3139 3003 : gel(phi1, 10) = gen_0;
3140 3003 : gel(phi1, 11) = utoineg(0x13UL);
3141 3003 : gel(phi1, 12) = utoineg(0x7UL);
3142 3003 : gel(phi1, 13) = utoineg(0x5ceUL);
3143 3003 : gel(phi1, 14) = utoineg(0xb0UL);
3144 3003 : gel(phi1, 15) = utoi(0x460UL);
3145 3003 : gel(phi1, 16) = utoineg(0x194bUL);
3146 3003 : gel(phi1, 17) = utoi(0x87c3UL);
3147 3003 : gel(phi1, 18) = utoi(0x3cdeUL);
3148 3003 : gel(phi1, 19) = utoineg(0xd683UL);
3149 3003 : gel(phi1, 20) = utoi(0x6099bUL);
3150 3002 : gel(phi1, 21) = utoineg(0x111ea8UL);
3151 3002 : gel(phi1, 22) = utoi(0xfa113UL);
3152 3002 : gel(phi1, 23) = utoineg(0x1a6561UL);
3153 3002 : gel(phi1, 24) = utoineg(0x1e997UL);
3154 3002 : gel(phi1, 25) = utoi(0x214e54UL);
3155 3002 : gel(phi1, 26) = utoineg(0x29c3f4UL);
3156 3002 : gel(phi1, 27) = utoi(0x67e102UL);
3157 3002 : gel(phi1, 28) = utoineg(0x227eaaUL);
3158 3003 : gel(phi1, 29) = utoi(0x191d10UL);
3159 3003 : gel(phi1, 30) = utoi(0x1a9cd5UL);
3160 3003 : gel(phi1, 31) = utoineg(0x58386fUL);
3161 3003 : gel(phi1, 32) = utoi(0x2e49f6UL);
3162 3003 : gel(phi1, 33) = utoineg(0x31194bUL);
3163 3003 : gel(phi1, 34) = utoi(0x9e07aUL);
3164 3003 : gel(phi1, 35) = utoi(0x260d59UL);
3165 3003 : gel(phi1, 36) = utoineg(0x189921UL);
3166 3003 : gel(phi1, 37) = utoi(0xeca4aUL);
3167 3003 : gel(phi1, 38) = utoineg(0xa3d9cUL);
3168 3003 : gel(phi1, 39) = utoineg(0x426daUL);
3169 3003 : gel(phi1, 40) = utoi(0x91875UL);
3170 3003 : gel(phi1, 41) = utoineg(0x3b55bUL);
3171 3003 : gel(phi1, 42) = utoineg(0x56f4UL);
3172 3003 : gel(phi1, 43) = utoi(0xcd1bUL);
3173 3003 : gel(phi1, 44) = utoineg(0x5159UL);
3174 3003 : gel(phi1, 45) = utoi(0x10f4UL);
3175 3003 : gel(phi1, 46) = utoineg(0x20dUL);
3176 3003 : gel(phi1, 47) = utoi(0x23UL);
3177 3003 : gel(phi1, 48) = gen_m1;
3178 :
3179 3003 : gel(phi, 1) = phi0;
3180 3003 : gel(phi, 2) = phi1;
3181 3003 : gel(phi, 3) = utoi(12); return phi;
3182 : }
3183 :
3184 : static GEN
3185 924 : phi_atkin3_j(void)
3186 : {
3187 : GEN phi, phi0, phi1;
3188 924 : phi = cgetg(4, t_VEC);
3189 :
3190 924 : phi0 = cgetg(6, t_VEC);
3191 924 : gel(phi0, 1) = utoi(538141968);
3192 924 : gel(phi0, 2) = utoi(19712160);
3193 924 : gel(phi0, 3) = utoi(193752);
3194 924 : gel(phi0, 4) = utoi(744);
3195 924 : gel(phi0, 5) = gen_1;
3196 :
3197 924 : phi1 = cgetg(5, t_VEC);
3198 924 : gel(phi1, 1) = utoi(24528);
3199 924 : gel(phi1, 2) = utoi(2348);
3200 924 : gel(phi1, 3) = gen_0;
3201 924 : gel(phi1, 4) = gen_m1;
3202 :
3203 924 : gel(phi, 1) = phi0;
3204 924 : gel(phi, 2) = phi1;
3205 924 : gel(phi, 3) = gen_0; return phi;
3206 : }
3207 :
3208 : static GEN
3209 1190 : phi_atkin5_j(void)
3210 : {
3211 : GEN phi, phi0, phi1;
3212 1190 : phi = cgetg(4, t_VEC);
3213 :
3214 1190 : phi0 = cgetg(8, t_VEC);
3215 1190 : gel(phi0, 1) = uu32toi(0xd,0x595d1000UL);
3216 1190 : gel(phi0, 2) = uu32toi(0x2,0x935de800UL);
3217 1190 : gel(phi0, 3) = utoi(756084480);
3218 1190 : gel(phi0, 4) = utoi(20990720);
3219 1190 : gel(phi0, 5) = utoi(196080);
3220 1190 : gel(phi0, 6) = utoi(744);
3221 1190 : gel(phi0, 7) = gen_1;
3222 :
3223 1190 : phi1 = cgetg(7, t_VEC);
3224 1190 : gel(phi1, 1) = utoineg(449408);
3225 1190 : gel(phi1, 2) = utoineg(73056);
3226 1190 : gel(phi1, 3) = utoi(3800);
3227 1190 : gel(phi1, 4) = utoi(670);
3228 1190 : gel(phi1, 5) = gen_0;
3229 1190 : gel(phi1, 6) = gen_m1;
3230 :
3231 1190 : gel(phi, 1) = phi0;
3232 1190 : gel(phi, 2) = phi1;
3233 1190 : gel(phi, 3) = gen_0; return phi;
3234 : }
3235 :
3236 : static GEN
3237 301 : phi_atkin7_j(void)
3238 : {
3239 : GEN phi, phi0, phi1;
3240 301 : phi = cgetg(4, t_VEC);
3241 :
3242 301 : phi0 = cgetg(10, t_VEC);
3243 301 : gel(phi0, 1) = uu32toi(0x136,0xe07f9221UL);
3244 301 : gel(phi0, 2) = uu32toi(0x9d,0xc4224ba8UL);
3245 301 : gel(phi0, 3) = uu32toi(0x20,0x58246d3cUL);
3246 301 : gel(phi0, 4) = uu32toi(0x3,0x631e2dd8UL);
3247 301 : gel(phi0, 5) = utoi(803037606);
3248 301 : gel(phi0, 6) = utoi(21226520);
3249 301 : gel(phi0, 7) = utoi(196476);
3250 301 : gel(phi0, 8) = utoi(744);
3251 301 : gel(phi0, 9) = gen_1;
3252 :
3253 301 : phi1 = cgetg(9, t_VEC);
3254 301 : gel(phi1, 1) = utoi(2128500);
3255 301 : gel(phi1, 2) = utoi(186955);
3256 301 : gel(phi1, 3) = utoineg(204792);
3257 301 : gel(phi1, 4) = utoineg(31647);
3258 301 : gel(phi1, 5) = utoi(1428);
3259 301 : gel(phi1, 6) = utoi(357);
3260 301 : gel(phi1, 7) = gen_0;
3261 301 : gel(phi1, 8) = gen_m1;
3262 :
3263 301 : gel(phi, 1) = phi0;
3264 301 : gel(phi, 2) = phi1;
3265 301 : gel(phi, 3) = gen_0; return phi;
3266 : }
3267 :
3268 : static GEN
3269 469 : phi_atkin11_j(void)
3270 : {
3271 : GEN phi, phi0, phi1;
3272 469 : phi = cgetg(4, t_VEC);
3273 :
3274 469 : phi0 = cgetg(14, t_VEC);
3275 469 : gel(phi0, 1) = uu32toi(0x351f,0xe3329000);
3276 470 : gel(phi0, 2) = uu32toi(0x5a09,0xb4cae000);
3277 470 : gel(phi0, 3) = uu32toi(0x4386,0xeec9c800);
3278 470 : gel(phi0, 4) = uu32toi(0x1d6c,0x110f8800);
3279 470 : gel(phi0, 5) = uu32toi(0x836,0xd0d89f00);
3280 470 : gel(phi0, 6) = uu32toi(0x186,0xd34d0c00);
3281 470 : gel(phi0, 7) = uu32toi(0x30,0x8f70b700);
3282 470 : gel(phi0, 8) = uu32toi(0x3,0xedd91100);
3283 470 : gel(phi0, 9) = utoi(830467440);
3284 470 : gel(phi0, 10) = utoi(21354080);
3285 470 : gel(phi0, 11) = utoi(196680);
3286 470 : gel(phi0, 12) = utoi(744);
3287 470 : gel(phi0, 13) = gen_1;
3288 :
3289 470 : phi1 = cgetg(13, t_VEC);
3290 470 : gel(phi1, 1) = utoineg(8720000);
3291 470 : gel(phi1, 2) = utoineg(19849600);
3292 470 : gel(phi1, 3) = utoineg(8252640);
3293 470 : gel(phi1, 4) = utoi(1867712);
3294 470 : gel(phi1, 5) = utoi(1675784);
3295 470 : gel(phi1, 6) = utoi(184184);
3296 470 : gel(phi1, 7) = utoineg(57442);
3297 470 : gel(phi1, 8) = utoineg(11440);
3298 470 : gel(phi1, 9) = utoi(506);
3299 470 : gel(phi1, 10) = utoi(187);
3300 470 : gel(phi1, 11) = gen_0;
3301 470 : gel(phi1, 12) = gen_m1;
3302 :
3303 470 : gel(phi, 1) = phi0;
3304 470 : gel(phi, 2) = phi1;
3305 470 : gel(phi, 3) = gen_0; return phi;
3306 : }
3307 :
3308 : static GEN
3309 2682 : phi_atkin13_j(void)
3310 : {
3311 : GEN phi, phi0, phi1;
3312 2682 : phi = cgetg(4, t_VEC);
3313 :
3314 2682 : phi0 = cgetg(16, t_VEC);
3315 2682 : gel(phi0, 1) = uu32toi(0x8954,0x40000000);
3316 2682 : gel(phi0, 2) = uu32toi(0x169eb,0x5e000000);
3317 2682 : gel(phi0, 3) = uu32toi(0x1ae7f,0x36e00000);
3318 2682 : gel(phi0, 4) = uu32toi(0x13107,0x840d8000);
3319 2682 : gel(phi0, 5) = uu32toi(0x8f0a,0xa4ccb800);
3320 2682 : gel(phi0, 6) = uu32toi(0x2e9f,0x7cfb8de0);
3321 2682 : gel(phi0, 7) = uu32toi(0xac8,0xedcc81b1);
3322 2682 : gel(phi0, 8) = uu32toi(0x1c6,0x36bee68);
3323 2682 : gel(phi0, 9) = uu32toi(0x34,0x377ed40c);
3324 2682 : gel(phi0, 10) = uu32toi(0x4,0xa132b38);
3325 2682 : gel(phi0, 11) = utoi(835688022);
3326 2682 : gel(phi0, 12) = utoi(21377304);
3327 2682 : gel(phi0, 13) = utoi(196716);
3328 2682 : gel(phi0, 14) = utoi(744);
3329 2682 : gel(phi0, 15) = gen_1;
3330 :
3331 2682 : phi1 = cgetg(15, t_VEC);
3332 2682 : gel(phi1, 1) = utoi(24576000);
3333 2682 : gel(phi1, 2) = utoi(32384000);
3334 2682 : gel(phi1, 3) = utoineg(5859360);
3335 2682 : gel(phi1, 4) = utoineg(23669490);
3336 2682 : gel(phi1, 5) = utoineg(9614956);
3337 2682 : gel(phi1, 6) = utoi(700323);
3338 2682 : gel(phi1, 7) = utoi(1161420);
3339 2682 : gel(phi1, 8) = utoi(149786);
3340 2682 : gel(phi1, 9) = utoineg(37596);
3341 2682 : gel(phi1, 10) = utoineg(8502);
3342 2682 : gel(phi1, 11) = utoi(364);
3343 2682 : gel(phi1, 12) = utoi(156);
3344 2682 : gel(phi1, 13) = gen_0;
3345 2682 : gel(phi1, 14) = gen_m1;
3346 :
3347 2682 : gel(phi, 1) = phi0;
3348 2682 : gel(phi, 2) = phi1;
3349 2682 : gel(phi, 3) = gen_0; return phi;
3350 : }
3351 :
3352 : static GEN
3353 4110 : phi_atkin17_j(void)
3354 : {
3355 : GEN phi, phi0, phi1;
3356 4110 : phi = cgetg(4, t_VEC);
3357 :
3358 4110 : phi0 = cgetg(20, t_VEC);
3359 4110 : gel(phi0, 1) = uu32toi(0x1657c,0x54a85640);
3360 4110 : gel(phi0, 2) = uu32toi(0x700a8,0xf0f3e240);
3361 4110 : gel(phi0, 3) = uu32toi(0x104ffa,0x16a394f0);
3362 4110 : gel(phi0, 4) = uu32toi(0x176924,0x252cada0);
3363 4110 : gel(phi0, 5) = uu32toi(0x172465,0xa95c437c);
3364 4110 : gel(phi0, 6) = uu32toi(0x10afa6,0x44a03d44);
3365 4110 : gel(phi0, 7) = uu32toi(0x90fff,0xc76052b1);
3366 4110 : gel(phi0, 8) = uu32toi(0x3c625,0x26e00dfc);
3367 4110 : gel(phi0, 9) = uu32toi(0x136f3,0xc7587fe);
3368 4110 : gel(phi0, 10) = uu32toi(0x4d55,0x39993e90);
3369 4110 : gel(phi0, 11) = uu32toi(0xebe,0x56879c1f);
3370 4110 : gel(phi0, 12) = uu32toi(0x21e,0x4cf30138);
3371 4110 : gel(phi0, 13) = uu32toi(0x39,0x6108ad0);
3372 4110 : gel(phi0, 14) = uu32toi(0x4,0x2dd68d04);
3373 4110 : gel(phi0, 15) = utoi(842077983);
3374 4110 : gel(phi0, 16) = utoi(21404972);
3375 4110 : gel(phi0, 17) = utoi(196758);
3376 4110 : gel(phi0, 18) = utoi(744);
3377 4110 : gel(phi0, 19) = gen_1;
3378 :
3379 4110 : phi1 = cgetg(19, t_VEC);
3380 4110 : gel(phi1, 1) = utoineg(25608112);
3381 4110 : gel(phi1, 2) = utoineg(128884056);
3382 4110 : gel(phi1, 3) = utoineg(169635044);
3383 4110 : gel(phi1, 4) = utoineg(18738794);
3384 4110 : gel(phi1, 5) = utoi(125706976);
3385 4110 : gel(phi1, 6) = utoi(98725154);
3386 4110 : gel(phi1, 7) = utoi(13049914);
3387 4110 : gel(phi1, 8) = utoineg(16023299);
3388 4110 : gel(phi1, 9) = utoineg(7118240);
3389 4110 : gel(phi1, 10) = utoi(70737);
3390 4110 : gel(phi1, 11) = utoi(630836);
3391 4110 : gel(phi1, 12) = utoi(91766);
3392 4110 : gel(phi1, 13) = utoineg(20808);
3393 4110 : gel(phi1, 14) = utoineg(5338);
3394 4110 : gel(phi1, 15) = utoi(238);
3395 4110 : gel(phi1, 16) = utoi(119);
3396 4110 : gel(phi1, 17) = gen_0;
3397 4110 : gel(phi1, 18) = gen_m1;
3398 :
3399 4110 : gel(phi, 1) = phi0;
3400 4110 : gel(phi, 2) = phi1;
3401 4110 : gel(phi, 3) = gen_0; return phi;
3402 : }
3403 :
3404 : static GEN
3405 1535 : phi_atkin19_j(void)
3406 : {
3407 : GEN phi, phi0, phi1;
3408 1535 : phi = cgetg(4, t_VEC);
3409 :
3410 1535 : phi0 = cgetg(22, t_VEC);
3411 1535 : gel(phi0, 1) = uu32toi(0x8954,0x40000000);
3412 1535 : gel(phi0, 2) = uu32toi(0x3f55f,0xd4000000);
3413 1535 : gel(phi0, 3) = uu32toi(0xd919c,0xfec00000);
3414 1535 : gel(phi0, 4) = uu32toi(0x1caf6f,0x559c0000);
3415 1535 : gel(phi0, 5) = uu32toi(0x29e098,0x33660000);
3416 1535 : gel(phi0, 6) = uu32toi(0x2ccab4,0x9d840000);
3417 1535 : gel(phi0, 7) = uu32toi(0x2456c7,0x80a1b000);
3418 1535 : gel(phi0, 8) = uu32toi(0x16d60a,0xd745d000);
3419 1535 : gel(phi0, 9) = uu32toi(0xb4073,0xd4d99000);
3420 1535 : gel(phi0, 10) = uu32toi(0x45efb,0xfafc9940);
3421 1535 : gel(phi0, 11) = uu32toi(0x156b5,0xc5077760);
3422 1535 : gel(phi0, 12) = uu32toi(0x524a,0x36e3a250);
3423 1535 : gel(phi0, 13) = uu32toi(0xf4f,0x2f2d5961);
3424 1535 : gel(phi0, 14) = uu32toi(0x229,0xdaeee798);
3425 1534 : gel(phi0, 15) = uu32toi(0x39,0x9e6319bc);
3426 1535 : gel(phi0, 16) = uu32toi(0x4,0x322f8d88);
3427 1535 : gel(phi0, 17) = utoi(842900838);
3428 1535 : gel(phi0, 18) = utoi(21408744);
3429 1535 : gel(phi0, 19) = utoi(196764);
3430 1535 : gel(phi0, 20) = utoi(744);
3431 1535 : gel(phi0, 21) = gen_1;
3432 :
3433 1535 : phi1 = cgetg(21, t_VEC);
3434 1535 : gel(phi1, 1) = utoi(24576000);
3435 1535 : gel(phi1, 2) = utoi(90675200);
3436 1535 : gel(phi1, 3) = utoi(51363840);
3437 1535 : gel(phi1, 4) = utoineg(196605312);
3438 1535 : gel(phi1, 5) = utoineg(358921248);
3439 1535 : gel(phi1, 6) = utoineg(190349904);
3440 1535 : gel(phi1, 7) = utoi(54954270);
3441 1535 : gel(phi1, 8) = utoi(101838024);
3442 1535 : gel(phi1, 9) = utoi(30202704);
3443 1535 : gel(phi1, 10) = utoineg(9356265);
3444 1535 : gel(phi1, 11) = utoineg(6935646);
3445 1535 : gel(phi1, 12) = utoineg(444030);
3446 1535 : gel(phi1, 13) = utoi(519042);
3447 1535 : gel(phi1, 14) = utoi(97983);
3448 1535 : gel(phi1, 15) = utoineg(16416);
3449 1535 : gel(phi1, 16) = utoineg(5073);
3450 1535 : gel(phi1, 17) = utoi(190);
3451 1535 : gel(phi1, 18) = utoi(114);
3452 1535 : gel(phi1, 19) = gen_0;
3453 1535 : gel(phi1, 20) = gen_m1;
3454 :
3455 1535 : gel(phi, 1) = phi0;
3456 1535 : gel(phi, 2) = phi1;
3457 1535 : gel(phi, 3) = gen_0; return phi;
3458 : }
3459 :
3460 : GEN
3461 35412 : double_eta_raw(long inv)
3462 : {
3463 35412 : switch (inv) {
3464 1060 : case INV_W2W3:
3465 1060 : case INV_W2W3E2: return phi_w2w3_j();
3466 3825 : case INV_W3W3:
3467 3825 : case INV_W3W3E2: return phi_w3w3_j();
3468 2927 : case INV_W2W5:
3469 2927 : case INV_W2W5E2: return phi_w2w5_j();
3470 6628 : case INV_W2W7:
3471 6628 : case INV_W2W7E2: return phi_w2w7_j();
3472 1160 : case INV_W3W5: return phi_w3w5_j();
3473 2986 : case INV_W3W7: return phi_w3w7_j();
3474 2402 : case INV_W2W13: return phi_w2w13_j();
3475 210 : case INV_W3W13: return phi_w3w13_j();
3476 3003 : case INV_W5W7: return phi_w5w7_j();
3477 924 : case INV_ATKIN3: return phi_atkin3_j();
3478 1190 : case INV_ATKIN5: return phi_atkin5_j();
3479 301 : case INV_ATKIN7: return phi_atkin7_j();
3480 469 : case INV_ATKIN11: return phi_atkin11_j();
3481 2682 : case INV_ATKIN13: return phi_atkin13_j();
3482 4110 : case INV_ATKIN17: return phi_atkin17_j();
3483 1535 : case INV_ATKIN19: return phi_atkin19_j();
3484 : default: pari_err_BUG("double_eta_raw"); return NULL;/*LCOV_EXCL_LINE*/
3485 : }
3486 : }
3487 :
3488 : /* SECTION: Select discriminant for given modpoly level. */
3489 :
3490 : /* require an L1, useful for multi-threading */
3491 : #define MODPOLY_USE_L1 1
3492 : /* no bound on L1 other than the fixed bound MAX_L1 - needed to
3493 : * handle small L for certain invariants (but not for j) */
3494 : #define MODPOLY_NO_MAX_L1 2
3495 : /* don't use any auxilliary primes - needed to handle small L for
3496 : * certain invariants (but not for j) */
3497 : #define MODPOLY_NO_AUX_L 4
3498 : #define MODPOLY_IGNORE_SPARSE_FACTOR 8
3499 :
3500 : INLINE double
3501 3199 : modpoly_height_bound(long L, long inv)
3502 : {
3503 : double nbits, nbits2;
3504 : double c;
3505 : long hf;
3506 :
3507 : /* proven bound (in bits), derived from: 6l*log(l)+16*l+13*sqrt(l)*log(l) */
3508 3199 : nbits = 6.0*L*log2(L)+16/M_LN2*L+8.0*sqrt((double)L)*log2(L);
3509 : /* alternative proven bound (in bits), derived from: 6l*log(l)+17*l */
3510 3199 : nbits2 = 6.0*L*log2(L)+17/M_LN2*L;
3511 3199 : if ( nbits2 < nbits ) nbits = nbits2;
3512 3199 : hf = modinv_height_factor(inv);
3513 3199 : if (hf > 1) {
3514 : /* IMPORTANT: when dividing by the height factor, we only want to reduce
3515 : terms related to the bound on j (the roots of Phi_l(X,y)), not terms arising
3516 : from binomial coefficients. These arise in lemmas 2 and 3 of the height
3517 : bound paper, terms of (log 2)*L and 2.085*(L+1) which we convert here to
3518 : binary logs */
3519 : /* Massive overestimate: if you care about speed, determine a good height
3520 : * bound empirically as done for INV_F below */
3521 1795 : nbits2 = nbits - 4.01*L -3.0;
3522 1795 : nbits = nbits2/hf + 4.01*L + 3.0;
3523 : }
3524 3199 : if (inv == INV_F) {
3525 142 : if (L < 30) c = 45;
3526 35 : else if (L < 100) c = 36;
3527 21 : else if (L < 300) c = 32;
3528 7 : else if (L < 600) c = 26;
3529 0 : else if (L < 1200) c = 24;
3530 0 : else if (L < 2400) c = 22;
3531 0 : else c = 20;
3532 142 : nbits = (6.0*L*log2(L) + c*L)/hf;
3533 : }
3534 3199 : return nbits;
3535 : }
3536 :
3537 : /* small enough to write the factorization of a smooth in a BIL bit integer */
3538 : #define SMOOTH_PRIMES ((BITS_IN_LONG >> 1) - 1)
3539 :
3540 : #define MAX_ATKIN 255
3541 :
3542 : #define MAX_L1 255
3543 :
3544 : typedef struct D_entry_struct {
3545 : ulong m;
3546 : long D, h;
3547 : } D_entry;
3548 :
3549 : /* Returns a form that generates the classes of norm p^2 in cl(p^2D)
3550 : * (i.e. one with order p-1), where p is an odd prime that splits in D
3551 : * and does not divide its conductor (but this is not verified) */
3552 : INLINE GEN
3553 83180 : qform_primeform2(long p, long D)
3554 : {
3555 83180 : GEN a = sqru(p), Dp2 = mulis(a, D), M = Z_factor(utoipos(p - 1));
3556 83180 : pari_sp av = avma;
3557 : long k;
3558 :
3559 167530 : for (k = D & 1; k <= p; k += 2)
3560 : {
3561 167530 : long ord, c = (k * k - D) / 4;
3562 : GEN Q, q;
3563 :
3564 167530 : if (!(c % p)) continue;
3565 144717 : q = mkqfis(a, k * p, c, Dp2); Q = qfi_red(q);
3566 : /* TODO: How do we know that Q has order dividing p - 1? If we don't, then
3567 : * the call to gen_order should be replaced with a call to something with
3568 : * fastorder semantics (i.e. return 0 if ord(Q) \ndiv M). */
3569 144717 : ord = itos(qfi_order(Q, M));
3570 144717 : if (ord == p - 1) {
3571 : /* TODO: This check that gen_order returned the correct result should be
3572 : * removed when gen_order is replaced with fastorder semantics. */
3573 83180 : if (qfb_equal1(gpowgs(Q, p - 1))) return q;
3574 0 : break;
3575 : }
3576 61537 : set_avma(av);
3577 : }
3578 0 : return NULL;
3579 : }
3580 :
3581 : /* Let n = #cl(D); return x such that [L0]^x = [L] in cl(D), or -1 if x was
3582 : * not found */
3583 : INLINE long
3584 210552 : primeform_discrete_log(long L0, long L, long n, long D)
3585 : {
3586 210552 : pari_sp av = avma;
3587 210552 : GEN X, Q, R, DD = stoi(D);
3588 210552 : Q = primeform_u(DD, L0);
3589 210552 : R = primeform_u(DD, L);
3590 210552 : X = qfi_Shanks(R, Q, n);
3591 210552 : return gc_long(av, X? itos(X): -1);
3592 : }
3593 :
3594 : /* Return the norm of a class group generator appropriate for a discriminant
3595 : * that will be used to calculate the modular polynomial of level L and
3596 : * invariant inv. Don't consider norms less than initial_L0 */
3597 : static long
3598 3199 : select_L0(long L, long inv, long initial_L0)
3599 : {
3600 3199 : long L0, modinv_N = modinv_level(inv);
3601 :
3602 3199 : if (modinv_N % L == 0) pari_err_BUG("select_L0");
3603 :
3604 : /* TODO: Clean up these anomolous L0 choices */
3605 :
3606 : /* I've no idea why the discriminant-finding code fails with L0=5
3607 : * when L=19 and L=29, nor why L0=7 and L0=11 don't work for L=19
3608 : * either, nor why this happens for the otherwise unrelated
3609 : * invariants Weber-f and (2,3) double-eta. */
3610 :
3611 3199 : if (inv == INV_F || inv == INV_F2 || inv == INV_F4 || inv == INV_F8
3612 2945 : || inv == INV_W2W3 || inv == INV_W2W3E2
3613 2882 : || inv == INV_W3W3) {
3614 429 : if (L == 19) return 13;
3615 379 : else if (L == 29) return 7;
3616 : }
3617 3142 : if ((inv == INV_W2W5) && (L == 19)) return 13;
3618 3128 : if ((inv == INV_W2W5E2)
3619 49 : && (L == 7 || L == 19)) return 13;
3620 3107 : if ((inv == INV_W2W7 || inv == INV_W2W7E2)
3621 358 : && L == 11) return 13;
3622 3079 : if (inv == INV_W3W5) {
3623 63 : if (L == 7) return 13;
3624 56 : else if (L == 17) return 7;
3625 : }
3626 3072 : if (inv == INV_W3W7) {
3627 161 : if (L == 29 || L == 101) return 11;
3628 133 : if (L == 11 || L == 19) return 13;
3629 : }
3630 :
3631 : /* L0 = smallest small prime different from L that doesn't divide modinv_N */
3632 3009 : for (L0 = unextprime(initial_L0 + 1);
3633 4748 : L0 == L || modinv_N % L0 == 0;
3634 1739 : L0 = unextprime(L0 + 1))
3635 : ;
3636 3009 : return L0;
3637 : }
3638 :
3639 : /* Return the order of [L]^n in cl(D), where #cl(D) = ord. */
3640 : INLINE long
3641 1114438 : primeform_exp_order(long L, long n, long D, long ord)
3642 : {
3643 1114438 : pari_sp av = avma;
3644 1114438 : GEN Q = gpowgs(primeform_u(stoi(D), L), n);
3645 1114438 : long m = itos(qfi_order(Q, Z_factor(stoi(ord))));
3646 1114438 : return gc_long(av,m);
3647 : }
3648 :
3649 : /* If an ideal of norm modinv_deg is equivalent to an ideal of norm L0, we
3650 : * have an orientation ambiguity that we need to avoid. Note that we need to
3651 : * check all the possibilities (up to 8), but we can cheaply check inverses
3652 : * (so at most 2) */
3653 : static long
3654 54932 : orientation_ambiguity(long D1, long L0, long modinv_p1, long modinv_p2, long modinv_N)
3655 : {
3656 54932 : pari_sp av = avma;
3657 54932 : long ambiguity = 0;
3658 54932 : GEN Q1 = red_primeform(D1, modinv_p1), Q2 = NULL;
3659 :
3660 54932 : if (modinv_p2 > 1)
3661 : {
3662 33682 : if (modinv_p1 == modinv_p2) Q1 = qfbsqr(Q1);
3663 : else
3664 : {
3665 27047 : GEN P2 = red_primeform(D1, modinv_p2);
3666 27047 : GEN Q = qfbsqr(P2), R = qfbsqr(Q1);
3667 : /* check that p1^2 != p2^{+/-2}, since this leads to
3668 : * ambiguities when converting j's to f's */
3669 27047 : if (equalii(gel(Q,1), gel(R,1)) && absequalii(gel(Q,2), gel(R,2)))
3670 : {
3671 0 : dbg_printf(3)("Bad D=%ld, a^2=b^2 problem between modinv_p1=%ld and modinv_p2=%ld\n",
3672 : D1, modinv_p1, modinv_p2);
3673 0 : ambiguity = 1;
3674 : }
3675 : else
3676 : { /* generate both p1*p2 and p1*p2^{-1} */
3677 27047 : Q2 = qfbcomp(Q1, P2);
3678 27047 : P2 = ginv(P2);
3679 27047 : Q1 = qfbcomp(Q1, P2);
3680 : }
3681 : }
3682 : }
3683 54932 : if (!ambiguity)
3684 : {
3685 54932 : GEN P = qfbsqr(red_primeform(D1, L0));
3686 54932 : if (equalii(gel(P,1), gel(Q1,1))
3687 53776 : || (modinv_p2 > 1 && modinv_p1 != modinv_p2
3688 26101 : && equalii(gel(P,1), gel(Q2,1)))) {
3689 1648 : dbg_printf(3)("Bad D=%ld, a=b^{+/-2} problem between modinv_N=%ld and L0=%ld\n",
3690 : D1, modinv_N, L0);
3691 1648 : ambiguity = 1;
3692 : }
3693 : }
3694 54932 : return gc_long(av, ambiguity);
3695 : }
3696 :
3697 : static long
3698 809918 : check_generators(
3699 : long *n1_, long *m_,
3700 : long D, long h, long n, long subgrp_sz, long L0, long L1)
3701 : {
3702 809918 : long n1, m = primeform_exp_order(L0, n, D, h);
3703 809918 : if (m_) *m_ = m;
3704 809918 : n1 = n * m;
3705 809918 : if (!n1) pari_err_BUG("check_generators");
3706 809918 : *n1_ = n1;
3707 809918 : if (n1 < subgrp_sz/2 || ( ! L1 && n1 < subgrp_sz)) {
3708 32634 : dbg_printf(3)("Bad D1=%ld with n1=%ld, h1=%ld, L1=%ld: "
3709 : "L0 and L1 don't span subgroup of size d in cl(D1)\n",
3710 : D, n, h, L1);
3711 32634 : return 0;
3712 : }
3713 777284 : if (n1 < subgrp_sz && ! (n1 & 1)) {
3714 : int res;
3715 : /* check whether L1 is generated by L0, use the fact that it has order 2 */
3716 20833 : pari_sp av = avma;
3717 20833 : GEN D1 = stoi(D);
3718 20833 : GEN Q = gpowgs(primeform_u(D1, L0), n1 / 2);
3719 20833 : res = gequal(Q, qfi_red(primeform_u(D1, L1)));
3720 20833 : set_avma(av);
3721 20833 : if (res) {
3722 6145 : dbg_printf(3)("Bad D1=%ld, with n1=%ld, h1=%ld, L1=%ld: "
3723 : "L1 generated by L0 in cl(D1)\n", D, n, h, L1);
3724 6145 : return 0;
3725 : }
3726 : }
3727 771139 : return 1;
3728 : }
3729 :
3730 : /* Calculate solutions (p, t) to the norm equation
3731 : * 4 p = t^2 - v^2 L^2 D (*)
3732 : * corresponding to the descriminant described by Dinfo.
3733 : *
3734 : * INPUT:
3735 : * - max: length of primes and traces
3736 : * - xprimes: p to exclude from primes (if they arise)
3737 : * - xcnt: length of xprimes
3738 : * - minbits: sum of log2(p) must be larger than this
3739 : * - Dinfo: discriminant, invariant and L for which we seek solutions to (*)
3740 : *
3741 : * OUTPUT:
3742 : * - primes: array of p in (*)
3743 : * - traces: array of t in (*)
3744 : * - totbits: sum of log2(p) for p in primes.
3745 : *
3746 : * RETURN:
3747 : * - the number of primes and traces found (these are always the same).
3748 : *
3749 : * NOTE: primes and traces are both NULL or both non-NULL.
3750 : * xprimes can be zero, in which case it is treated as empty. */
3751 : static long
3752 13196 : modpoly_pickD_primes(
3753 : ulong *primes, ulong *traces, long max, ulong *xprimes, long xcnt,
3754 : long *totbits, long minbits, disc_info *Dinfo)
3755 : {
3756 : double bits;
3757 : long D, m, n, vcnt, pfilter, one_prime, inv;
3758 : ulong maxp;
3759 : ulong a1, a2, v, t, p, a1_start, a1_delta, L0, L1, L, absD;
3760 13196 : ulong FF_BITS = BITS_IN_LONG - 2; /* BITS_IN_LONG - NAIL_BITS */
3761 :
3762 13196 : D = Dinfo->D1; absD = -D;
3763 13196 : L0 = Dinfo->L0;
3764 13196 : L1 = Dinfo->L1;
3765 13196 : L = Dinfo->L;
3766 13196 : inv = Dinfo->inv;
3767 :
3768 : /* make sure pfilter and D don't preclude the possibility of p=(t^2-v^2D)/4 being prime */
3769 13196 : pfilter = modinv_pfilter(inv);
3770 13196 : if ((pfilter & IQ_FILTER_1MOD3) && ! (D % 3)) return 0;
3771 13161 : if ((pfilter & IQ_FILTER_1MOD4) && ! (D & 0xF)) return 0;
3772 :
3773 : /* Naively estimate the number of primes satisfying 4p=t^2-L^2D with
3774 : * t=2 mod L and pfilter. This is roughly
3775 : * #{t: t^2 < max p and t=2 mod L} / pi(max p) * filter_density,
3776 : * where filter_density is 1, 2, or 4 depending on pfilter. If this quantity
3777 : * is already more than twice the number of bits we need, assume that,
3778 : * barring some obstruction, we should have no problem getting enough primes.
3779 : * In this case we just verify we can get one prime (which should always be
3780 : * true, assuming we chose D properly). */
3781 13161 : one_prime = 0;
3782 13161 : *totbits = 0;
3783 13161 : if (max <= 1 && ! one_prime) {
3784 9942 : p = ((pfilter & IQ_FILTER_1MOD3) ? 2 : 1) * ((pfilter & IQ_FILTER_1MOD4) ? 2 : 1);
3785 9942 : one_prime = (1UL << ((FF_BITS+1)/2)) * (log2(L*L*(-D))-1)
3786 9942 : > p*L*minbits*FF_BITS*M_LN2;
3787 9942 : if (one_prime) *totbits = minbits+1; /* lie */
3788 : }
3789 :
3790 13161 : m = n = 0;
3791 13161 : bits = 0.0;
3792 13161 : maxp = 0;
3793 32303 : for (v = 1; v < 100 && bits < minbits; v++) {
3794 : /* Don't allow v dividing the conductor. */
3795 29032 : if (ugcd(absD, v) != 1) continue;
3796 : /* Avoid v dividing the level. */
3797 28834 : if (v > 2 && modinv_is_double_eta(inv) && ugcd(modinv_level(inv), v) != 1)
3798 953 : continue;
3799 : /* can't get odd p with D=1 mod 8 unless v is even */
3800 27881 : if ((v & 1) && (D & 7) == 1) continue;
3801 : /* disallow 4 | v for L0=2 (removing this restriction is costly) */
3802 13779 : if (L0 == 2 && !(v & 3)) continue;
3803 : /* can't get p=3mod4 if v^2D is 0 mod 16 */
3804 13536 : if ((pfilter & IQ_FILTER_1MOD4) && !((v*v*D) & 0xF)) continue;
3805 13453 : if ((pfilter & IQ_FILTER_1MOD3) && !(v%3) ) continue;
3806 : /* avoid L0-volcanos with nonzero height */
3807 13399 : if (L0 != 2 && ! (v % L0)) continue;
3808 : /* ditto for L1 */
3809 13378 : if (L1 && !(v % L1)) continue;
3810 13378 : vcnt = 0;
3811 13378 : if ((v*v*absD)/4 > (1L<<FF_BITS)/(L*L)) break;
3812 13298 : if (both_odd(v,D)) {
3813 0 : a1_start = 1;
3814 0 : a1_delta = 2;
3815 : } else {
3816 13298 : a1_start = ((v*v*D) & 7)? 2: 0;
3817 13298 : a1_delta = 4;
3818 : }
3819 591552 : for (a1 = a1_start; bits < minbits; a1 += a1_delta) {
3820 588295 : a2 = (a1*a1 + v*v*absD) >> 2;
3821 588295 : if (!(a2 % L)) continue;
3822 497952 : t = a1*L + 2;
3823 497952 : p = a2*L*L + t - 1;
3824 : /* double check calculation just in case of overflow or other weirdness */
3825 497952 : if (!odd(p) || t*t + v*v*L*L*absD != 4*p)
3826 0 : pari_err_BUG("modpoly_pickD_primes");
3827 497952 : if (p > (1UL<<FF_BITS)) break;
3828 497721 : if (xprimes) {
3829 369531 : while (m < xcnt && xprimes[m] < p) m++;
3830 369105 : if (m < xcnt && p == xprimes[m]) {
3831 0 : dbg_printf(1)("skipping duplicate prime %ld\n", p);
3832 0 : continue;
3833 : }
3834 : }
3835 497721 : if (!modinv_good_prime(inv, p) || !uisprime(p)) continue;
3836 55721 : if (primes) {
3837 40754 : if (n >= max) goto done;
3838 : /* TODO: Implement test to filter primes that lead to
3839 : * L-valuation != 2 */
3840 40754 : primes[n] = p;
3841 40754 : traces[n] = t;
3842 : }
3843 55721 : n++;
3844 55721 : vcnt++;
3845 55721 : bits += log2(p);
3846 55721 : if (p > maxp) maxp = p;
3847 55721 : if (one_prime) goto done;
3848 : }
3849 3488 : if (vcnt)
3850 3485 : dbg_printf(3)("%ld primes with v=%ld, maxp=%ld (%.2f bits)\n",
3851 : vcnt, v, maxp, log2(maxp));
3852 : }
3853 3271 : done:
3854 13161 : if (!n) {
3855 9 : dbg_printf(3)("check_primes failed completely for D=%ld\n", D);
3856 9 : return 0;
3857 : }
3858 13152 : dbg_printf(3)("D=%ld: Found %ld primes totalling %0.2f of %ld bits\n",
3859 : D, n, bits, minbits);
3860 13152 : if (!*totbits) *totbits = (long)bits;
3861 13152 : return n;
3862 : }
3863 :
3864 : #define MAX_VOLCANO_FLOOR_SIZE 100000000
3865 :
3866 : static long
3867 3201 : calc_primes_for_discriminants(disc_info Ds[], long Dcnt, long L, long minbits)
3868 : {
3869 3201 : pari_sp av = avma;
3870 : long i, j, k, m, n, D1, pcnt, totbits;
3871 : ulong *primes, *Dprimes, *Dtraces;
3872 :
3873 : /* D1 is the discriminant with smallest absolute value among those we found */
3874 3201 : D1 = Ds[0].D1;
3875 9933 : for (i = 1; i < Dcnt; i++)
3876 6732 : if (Ds[i].D1 > D1) D1 = Ds[i].D1;
3877 :
3878 : /* n is an upper bound on the number of primes we might get. */
3879 3201 : n = ceil(minbits / (log2(L * L * (-D1)) - 2)) + 1;
3880 3201 : primes = (ulong *) stack_malloc(n * sizeof(*primes));
3881 3201 : Dprimes = (ulong *) stack_malloc(n * sizeof(*Dprimes));
3882 3201 : Dtraces = (ulong *) stack_malloc(n * sizeof(*Dtraces));
3883 3219 : for (i = 0, totbits = 0, pcnt = 0; i < Dcnt && totbits < minbits; i++)
3884 : {
3885 3219 : long np = modpoly_pickD_primes(Dprimes, Dtraces, n, primes, pcnt,
3886 3219 : &Ds[i].bits, minbits - totbits, Ds + i);
3887 3219 : ulong *T = (ulong *)newblock(2*np);
3888 3219 : Ds[i].nprimes = np;
3889 3219 : Ds[i].primes = T; memcpy(T , Dprimes, np * sizeof(*Dprimes));
3890 3219 : Ds[i].traces = T+np; memcpy(T+np, Dtraces, np * sizeof(*Dtraces));
3891 :
3892 3219 : totbits += Ds[i].bits;
3893 3219 : pcnt += np;
3894 :
3895 3219 : if (totbits >= minbits || i == Dcnt - 1) { Dcnt = i + 1; break; }
3896 : /* merge lists */
3897 589 : for (j = pcnt - np - 1, k = np - 1, m = pcnt - 1; m >= 0; m--) {
3898 571 : if (k >= 0) {
3899 546 : if (j >= 0 && primes[j] > Dprimes[k])
3900 301 : primes[m] = primes[j--];
3901 : else
3902 245 : primes[m] = Dprimes[k--];
3903 : } else {
3904 25 : primes[m] = primes[j--];
3905 : }
3906 : }
3907 : }
3908 3201 : if (totbits < minbits) {
3909 2 : dbg_printf(1)("Only obtained %ld of %ld bits using %ld discriminants\n",
3910 : totbits, minbits, Dcnt);
3911 4 : for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
3912 2 : Dcnt = 0;
3913 : }
3914 3201 : return gc_long(av, Dcnt);
3915 : }
3916 :
3917 : /* Select discriminant(s) to use when calculating the modular
3918 : * polynomial of level L and invariant inv.
3919 : *
3920 : * INPUT:
3921 : * - L: level of modular polynomial (must be odd)
3922 : * - inv: invariant of modular polynomial
3923 : * - L0: result of select_L0(L, inv)
3924 : * - minbits: height of modular polynomial
3925 : * - flags: see below
3926 : * - tab: result of scanD0(L0)
3927 : * - tablen: length of tab
3928 : *
3929 : * OUTPUT:
3930 : * - Ds: the selected discriminant(s)
3931 : *
3932 : * RETURN:
3933 : * - the number of Ds found
3934 : *
3935 : * The flags parameter is constructed by ORing zero or more of the
3936 : * following values:
3937 : * - MODPOLY_USE_L1: force use of second class group generator
3938 : * - MODPOLY_NO_AUX_L: don't use auxillary class group elements
3939 : * - MODPOLY_IGNORE_SPARSE_FACTOR: obtain D for which h(D) > L + 1
3940 : * rather than h(D) > (L + 1)/s */
3941 : static long
3942 3201 : modpoly_pickD(disc_info Ds[MODPOLY_MAX_DCNT], long L, long inv,
3943 : long L0, long max_L1, long minbits, long flags, D_entry *tab, long tablen)
3944 : {
3945 3201 : pari_sp ltop = avma, btop;
3946 : disc_info Dinfo;
3947 : pari_timer T;
3948 : long modinv_p1, modinv_p2; /* const after next line */
3949 3201 : const long modinv_deg = modinv_degree(&modinv_p1, &modinv_p2, inv);
3950 3201 : const long pfilter = modinv_pfilter(inv), modinv_N = modinv_level(inv);
3951 : long i, k, use_L1, Dcnt, D0_i, d, cost, enum_cost, best_cost, totbits;
3952 3201 : const double L_bits = log2(L);
3953 :
3954 3201 : if (!odd(L)) pari_err_BUG("modpoly_pickD");
3955 :
3956 3201 : timer_start(&T);
3957 3201 : if (flags & MODPOLY_IGNORE_SPARSE_FACTOR) d = L+2;
3958 3061 : else d = ceildivuu(L+1, modinv_sparse_factor(inv)) + 1;
3959 :
3960 : /* Now set level to 0 unless we will need to compute N-isogenies */
3961 3201 : dbg_printf(1)("Using L0=%ld for L=%ld, d=%ld, modinv_N=%ld, modinv_deg=%ld\n",
3962 : L0, L, d, modinv_N, modinv_deg);
3963 :
3964 : /* We use L1 if (L0|L) == 1 or if we are forced to by flags. */
3965 3201 : use_L1 = (kross(L0,L) > 0 || (flags & MODPOLY_USE_L1));
3966 :
3967 3201 : Dcnt = best_cost = totbits = 0;
3968 3201 : dbg_printf(3)("use_L1=%ld\n", use_L1);
3969 3201 : dbg_printf(3)("minbits = %ld\n", minbits);
3970 :
3971 : /* Iterate over the fundamental discriminants for L0 */
3972 1962741 : for (D0_i = 0; D0_i < tablen; D0_i++)
3973 : {
3974 1959540 : D_entry D0_entry = tab[D0_i];
3975 1959540 : long m, n0, h0, deg, L1, H_cost, twofactor, D0 = D0_entry.D;
3976 : double D0_bits;
3977 3028969 : if (! modinv_good_disc(inv, D0)) continue;
3978 1288634 : dbg_printf(3)("D0=%ld\n", D0);
3979 : /* don't allow either modinv_p1 or modinv_p2 to ramify */
3980 1288634 : if (kross(D0, L) < 1
3981 580679 : || (modinv_p1 > 1 && kross(D0, modinv_p1) < 1)
3982 572998 : || (modinv_p2 > 1 && kross(D0, modinv_p2) < 1)) {
3983 725935 : dbg_printf(3)("Bad D0=%ld due to nonsplit L or ramified level\n", D0);
3984 725935 : continue;
3985 : }
3986 562699 : deg = D0_entry.h; /* class poly degree */
3987 562699 : h0 = ((D0_entry.m & 2) ? 2*deg : deg); /* class number */
3988 : /* (D0_entry.m & 1) is 1 if ord(L0) < h0 (hence = h0/2),
3989 : * is 0 if ord(L0) = h0 */
3990 562699 : n0 = h0 / ((D0_entry.m & 1) + 1); /* = ord(L0) */
3991 :
3992 : /* Look for L1: for each smooth prime p */
3993 562699 : L1 = 0;
3994 13570062 : for (i = 1 ; i <= SMOOTH_PRIMES; i++)
3995 : {
3996 13125723 : long p = (long)pari_PRIMES[i];
3997 13125723 : if (p <= L0) continue;
3998 : /* If 1 + (D0 | p) = 1, i.e. p | D0 */
3999 12383597 : if (((D0_entry.m >> (2*i)) & 3) == 1) {
4000 : /* XXX: Why (p | L) = -1? Presumably so (L^2 v^2 D0 | p) = -1? */
4001 409582 : if (p <= max_L1 && modinv_N % p && kross(p,L) < 0) { L1 = p; break; }
4002 : }
4003 : }
4004 562699 : if (i > SMOOTH_PRIMES && (n0 < h0 || use_L1))
4005 : { /* Didn't find suitable L1 though we need one */
4006 258179 : dbg_printf(3)("Bad D0=%ld because there is no good L1\n", D0);
4007 258179 : continue;
4008 : }
4009 304520 : dbg_printf(3)("Good D0=%ld with L1=%ld, n0=%ld, h0=%ld, d=%ld\n",
4010 : D0, L1, n0, h0, d);
4011 :
4012 : /* We're finished if we have sufficiently many discriminants that satisfy
4013 : * the cost requirement */
4014 304520 : if (totbits > minbits && best_cost && h0*(L-1) > 3*best_cost) break;
4015 :
4016 304520 : D0_bits = log2(-D0);
4017 : /* If L^2 D0 is too big to fit in a BIL bit integer, skip D0. */
4018 304520 : if (D0_bits + 2 * L_bits > (BITS_IN_LONG - 1)) continue;
4019 :
4020 : /* m is the order of L0^n0 in L^2 D0? */
4021 304520 : m = primeform_exp_order(L0, n0, L * L * D0, n0 * (L-1));
4022 304520 : if (m < (L-1)/2) {
4023 85315 : dbg_printf(3)("Bad D0=%ld because %ld is less than (L-1)/2=%ld\n",
4024 0 : D0, m, (L - 1)/2);
4025 85315 : continue;
4026 : }
4027 : /* Heuristic. Doesn't end up contributing much. */
4028 219205 : H_cost = 2 * deg * deg;
4029 :
4030 : /* 0xc = 0b1100, so D0_entry.m & 0xc == 1 + (D0 | 2) */
4031 219205 : if ((D0 & 7) == 5) /* D0 = 5 (mod 8) */
4032 6303 : twofactor = ((D0_entry.m & 0xc) ? 1 : 3);
4033 : else
4034 212902 : twofactor = 0;
4035 :
4036 219205 : btop = avma;
4037 : /* For each small prime... */
4038 768746 : for (i = 0; i <= SMOOTH_PRIMES; i++) {
4039 : long h1, h2, D1, D2, n1, n2, dl1, dl20, dl21, p, q, j;
4040 : double p_bits;
4041 768641 : set_avma(btop);
4042 : /* i = 0 corresponds to 1, which we do not want to skip! (i.e. DK = D) */
4043 768641 : if (i) {
4044 1087700 : if (modinv_odd_conductor(inv) && i == 1) continue;
4045 538792 : p = (long)pari_PRIMES[i];
4046 : /* Don't allow large factors in the conductor. */
4047 657124 : if (p > max_L1) break;
4048 438024 : if (p == L0 || p == L1 || p == L || p == modinv_p1 || p == modinv_p2)
4049 152777 : continue;
4050 285247 : p_bits = log2(p);
4051 : /* h1 is the class number of D1 = q^2 D0, where q = p^j (j defined in the loop below) */
4052 285247 : h1 = h0 * (p - ((D0_entry.m >> (2*i)) & 0x3) + 1);
4053 : /* q is the smallest power of p such that h1 >= d ~ "L + 1". */
4054 288217 : for (j = 1, q = p; h1 < d; j++, q *= p, h1 *= p)
4055 : ;
4056 285247 : D1 = q * q * D0;
4057 : /* can't have D1 = 0 mod 16 and hope to get any primes congruent to 3 mod 4 */
4058 285247 : if ((pfilter & IQ_FILTER_1MOD4) && !(D1 & 0xF)) continue;
4059 : } else {
4060 : /* i = 0, corresponds to "p = 1". */
4061 219205 : h1 = h0;
4062 219205 : D1 = D0;
4063 219205 : p = q = j = 1;
4064 219205 : p_bits = 0;
4065 : }
4066 : /* include a factor of 4 if D1 is 5 mod 8 */
4067 : /* XXX: No idea why he does this. */
4068 504382 : if (twofactor && (q & 1)) {
4069 15656 : if (modinv_odd_conductor(inv)) continue;
4070 119 : D1 *= 4;
4071 119 : h1 *= twofactor;
4072 : }
4073 : /* heuristic early abort; we may miss good D1's, but this saves time */
4074 488845 : if (totbits > minbits && best_cost && h1*(L-1) > 2.2*best_cost) continue;
4075 :
4076 : /* log2(D0 * (p^j)^2 * L^2 * twofactor) > (BIL - 1) -- params too big. */
4077 963897 : if (D0_bits + 2*j*p_bits + 2*L_bits
4078 481046 : + (twofactor && (q & 1) ? 2.0 : 0.0) > (BITS_IN_LONG-1)) continue;
4079 :
4080 479241 : if (! check_generators(&n1, NULL, D1, h1, n0, d, L0, L1)) continue;
4081 :
4082 458699 : if (n1 >= h1) dl1 = -1; /* fill it in later */
4083 207359 : else if ((dl1 = primeform_discrete_log(L0, L, n1, D1)) < 0) continue;
4084 332325 : dbg_printf(3)("Good D0=%ld, D1=%ld with q=%ld, L1=%ld, n1=%ld, h1=%ld\n",
4085 : D0, D1, q, L1, n1, h1);
4086 332325 : if (modinv_deg && orientation_ambiguity(D1, L0, modinv_p1, modinv_p2, modinv_N))
4087 1648 : continue;
4088 :
4089 330677 : D2 = L * L * D1;
4090 330677 : h2 = h1 * (L-1);
4091 : /* m is the order of L0^n1 in cl(D2) */
4092 330677 : if (!check_generators(&n2, &m, D2, h2, n1, d*(L-1), L0, L1)) continue;
4093 :
4094 : /* This restriction on m is not necessary, but simplifies life later */
4095 312440 : if (m < (L-1)/2 || (!L1 && m < L-1)) {
4096 152779 : dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4097 : "order of L0^n1 in cl(D2) is too small\n", D2, D1, D0, n2, h2, L1);
4098 152779 : continue;
4099 : }
4100 159661 : dl20 = n1;
4101 159661 : dl21 = 0;
4102 159661 : if (m < L-1) {
4103 83180 : GEN Q1 = qform_primeform2(L, D1), Q2, X;
4104 83180 : if (!Q1) pari_err_BUG("modpoly_pickD");
4105 83180 : Q2 = primeform_u(stoi(D2), L1);
4106 83180 : Q2 = qfbcomp(Q1, Q2); /* we know this element has order L-1 */
4107 83180 : Q1 = primeform_u(stoi(D2), L0);
4108 83180 : k = ((n2 & 1) ? 2*n2 : n2)/(L-1);
4109 83180 : Q1 = gpowgs(Q1, k);
4110 83180 : X = qfi_Shanks(Q2, Q1, L-1);
4111 83180 : if (!X) {
4112 12682 : dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4113 : "form of norm L^2 not generated by L0 and L1\n",
4114 : D2, D1, D0, n2, h2, L1);
4115 12682 : continue;
4116 : }
4117 70498 : dl20 = itos(X) * k;
4118 70498 : dl21 = 1;
4119 : }
4120 146979 : if (! (m < L-1 || n2 < d*(L-1)) && n1 >= d && ! use_L1)
4121 75943 : L1 = 0; /* we don't need L1 */
4122 :
4123 146979 : if (!L1 && use_L1) {
4124 0 : dbg_printf(3)("not using D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4125 : "because we don't need L1 but must use it\n",
4126 : D2, D1, D0, n2, h2, L1);
4127 0 : continue;
4128 : }
4129 : /* don't allow zero dl21 with L1 for the moment, since
4130 : * modpoly doesn't handle it - we may change this in the future */
4131 146979 : if (L1 && ! dl21) continue;
4132 146441 : dbg_printf(3)("Good D0=%ld, D1=%ld, D2=%ld with s=%ld^%ld, L1=%ld, dl2=%ld, n2=%ld, h2=%ld\n",
4133 : D0, D1, D2, p, j, L1, dl20, n2, h2);
4134 :
4135 : /* This estimate is heuristic and fiddling with the
4136 : * parameters 5 and 0.25 can change things quite a bit. */
4137 146441 : enum_cost = n2 * (5 * L0 * L0 + 0.25 * L1 * L1);
4138 146441 : cost = enum_cost + H_cost;
4139 146441 : if (best_cost && cost > 2.2*best_cost) break;
4140 37409 : if (best_cost && cost >= 0.99*best_cost) continue;
4141 :
4142 9977 : Dinfo.GENcode0 = evaltyp(t_VECSMALL)|_evallg(13);
4143 9977 : Dinfo.inv = inv;
4144 9977 : Dinfo.L = L;
4145 9977 : Dinfo.D0 = D0;
4146 9977 : Dinfo.D1 = D1;
4147 9977 : Dinfo.L0 = L0;
4148 9977 : Dinfo.L1 = L1;
4149 9977 : Dinfo.n1 = n1;
4150 9977 : Dinfo.n2 = n2;
4151 9977 : Dinfo.dl1 = dl1;
4152 9977 : Dinfo.dl2_0 = dl20;
4153 9977 : Dinfo.dl2_1 = dl21;
4154 9977 : Dinfo.cost = cost;
4155 :
4156 9977 : if (!modpoly_pickD_primes(NULL, NULL, 0, NULL, 0, &Dinfo.bits, minbits, &Dinfo))
4157 44 : continue;
4158 9933 : dbg_printf(2)("Best D2=%ld, D1=%ld, D0=%ld with s=%ld^%ld, L1=%ld, "
4159 : "n1=%ld, n2=%ld, cost ratio %.2f, bits=%ld\n",
4160 : D2, D1, D0, p, j, L1, n1, n2,
4161 0 : (double)cost/(d*(L-1)), Dinfo.bits);
4162 : /* Insert Dinfo into the Ds array. Ds is sorted by ascending cost. */
4163 55265 : for (j = 0; j < Dcnt; j++)
4164 52054 : if (Dinfo.cost < Ds[j].cost) break;
4165 9933 : if (n2 > MAX_VOLCANO_FLOOR_SIZE && n2*(L1 ? 2 : 1) > 1.2* (d*(L-1)) ) {
4166 0 : dbg_printf(3)("Not using D1=%ld, D2=%ld for space reasons\n", D1, D2);
4167 0 : continue;
4168 : }
4169 9933 : if (j == Dcnt && Dcnt == MODPOLY_MAX_DCNT)
4170 0 : continue;
4171 9933 : totbits += Dinfo.bits;
4172 9933 : if (Dcnt == MODPOLY_MAX_DCNT) totbits -= Ds[Dcnt-1].bits;
4173 9933 : if (Dcnt < MODPOLY_MAX_DCNT) Dcnt++;
4174 9933 : if (n2 > MAX_VOLCANO_FLOOR_SIZE)
4175 0 : dbg_printf(3)("totbits=%ld, minbits=%ld\n", totbits, minbits);
4176 24140 : for (k = Dcnt-1; k > j; k--) Ds[k] = Ds[k-1];
4177 9933 : Ds[k] = Dinfo;
4178 9933 : best_cost = (totbits > minbits)? Ds[Dcnt-1].cost: 0;
4179 : /* if we were able to use D1 with s = 1, there is no point in
4180 : * using any larger D1 for the same D0 */
4181 9933 : if (!i) break;
4182 : } /* END FOR over small primes */
4183 : } /* END WHILE over D0's */
4184 3201 : dbg_printf(2)(" checked %ld of %ld fundamental discriminants to find suitable "
4185 : "discriminant (Dcnt = %ld)\n", D0_i, tablen, Dcnt);
4186 3201 : if ( ! Dcnt) {
4187 0 : dbg_printf(1)("failed completely for L=%ld\n", L);
4188 0 : return 0;
4189 : }
4190 :
4191 3201 : Dcnt = calc_primes_for_discriminants(Ds, Dcnt, L, minbits);
4192 :
4193 : /* fill in any missing dl1's */
4194 6418 : for (i = 0 ; i < Dcnt; i++)
4195 3217 : if (Ds[i].dl1 < 0 &&
4196 3193 : (Ds[i].dl1 = primeform_discrete_log(L0, L, Ds[i].n1, Ds[i].D1)) < 0)
4197 0 : pari_err_BUG("modpoly_pickD");
4198 3201 : if (DEBUGLEVEL > 1+3) {
4199 0 : err_printf("Selected %ld discriminants using %ld msecs\n", Dcnt, timer_delay(&T));
4200 0 : for (i = 0 ; i < Dcnt ; i++)
4201 : {
4202 0 : GEN H = classno(stoi(Ds[i].D0));
4203 0 : long h0 = itos(H);
4204 0 : err_printf (" D0=%ld, h(D0)=%ld, D=%ld, L0=%ld, L1=%ld, "
4205 : "cost ratio=%.2f, enum ratio=%.2f,",
4206 0 : Ds[i].D0, h0, Ds[i].D1, Ds[i].L0, Ds[i].L1,
4207 0 : (double)Ds[i].cost/(d*(L-1)),
4208 0 : (double)(Ds[i].n2*(Ds[i].L1 ? 2 : 1))/(d*(L-1)));
4209 0 : err_printf (" %ld primes, %ld bits\n", Ds[i].nprimes, Ds[i].bits);
4210 : }
4211 : }
4212 3201 : return gc_long(ltop, Dcnt);
4213 : }
4214 :
4215 : static int
4216 15283378 : _qsort_cmp(const void *a, const void *b)
4217 : {
4218 15283378 : D_entry *x = (D_entry *)a, *y = (D_entry *)b;
4219 : long u, v;
4220 :
4221 : /* u and v are the class numbers of x and y */
4222 15283378 : u = x->h * (!!(x->m & 2) + 1);
4223 15283378 : v = y->h * (!!(y->m & 2) + 1);
4224 : /* Sort by class number */
4225 15283378 : if (u < v) return -1;
4226 10641922 : if (u > v) return 1;
4227 : /* Sort by discriminant (which is < 0, hence the sign reversal) */
4228 3201658 : if (x->D > y->D) return -1;
4229 0 : if (x->D < y->D) return 1;
4230 0 : return 0;
4231 : }
4232 :
4233 : /* Build a table containing fundamental D, |D| <= maxD whose class groups
4234 : * - are cyclic generated by an element of norm L0
4235 : * - have class number at most maxh
4236 : * The table is ordered using _qsort_cmp above, which ranks the discriminants
4237 : * by class number, then by absolute discriminant.
4238 : *
4239 : * INPUT:
4240 : * - maxd: largest allowed discriminant
4241 : * - maxh: largest allowed class number
4242 : * - L0: norm of class group generator (2, 3, 5, or 7)
4243 : *
4244 : * OUTPUT:
4245 : * - tablelen: length of return value
4246 : *
4247 : * RETURN:
4248 : * - array of {D, h(D), kronecker symbols for small p} */
4249 : static D_entry *
4250 3201 : scanD0(long *tablelen, long *minD, long maxD, long maxh, long L0)
4251 : {
4252 : pari_sp av;
4253 : D_entry *tab;
4254 : long i, lF, cnt;
4255 : GEN F;
4256 :
4257 : /* NB: As seen in the loop below, the real class number of D can be */
4258 : /* 2*maxh if cl(D) is cyclic. */
4259 3201 : tab = (D_entry *) stack_malloc((maxD/4)*sizeof(*tab)); /* Overestimate */
4260 3201 : F = vecfactorsquarefreeu_coprime(*minD, maxD, mkvecsmall(2));
4261 3201 : lF = lg(F);
4262 31993995 : for (av = avma, cnt = 0, i = 1; i < lF; i++, set_avma(av))
4263 : {
4264 31990794 : GEN DD, ordL, f, q = gel(F,i);
4265 : long j, k, n, h, L1, d, D;
4266 : ulong m;
4267 :
4268 31990794 : if (!q) continue; /* not square-free */
4269 : /* restrict to possibly cyclic class groups */
4270 12973637 : k = lg(q) - 1; if (k > 2) continue;
4271 10108278 : d = i + *minD - 1; /* q = prime divisors of d */
4272 10108278 : if ((d & 3) == 1) continue;
4273 5086135 : D = -d; /* d = 3 (mod 4), D = 1 mod 4 fundamental */
4274 5086135 : if (kross(D, L0) < 1) continue;
4275 :
4276 : /* L1 initially the first factor of d if small enough, otherwise ignored */
4277 2453845 : L1 = (k > 1 && q[1] <= MAX_L1)? q[1]: 0;
4278 :
4279 : /* Check if h(D) is too big */
4280 2453845 : h = hclassno6u(d) / 6;
4281 2453845 : if (h > 2*maxh || (!L1 && h > maxh)) continue;
4282 :
4283 : /* Check if ord(f) is not big enough to generate at least half the
4284 : * class group (where f is the L0-primeform). */
4285 2279518 : DD = stoi(D);
4286 2279518 : f = primeform_u(DD, L0);
4287 2279518 : ordL = qfi_order(qfi_red(f), stoi(h));
4288 2279518 : n = itos(ordL);
4289 2279518 : if (n < h/2 || (!L1 && n < h)) continue;
4290 :
4291 : /* If f is big enough, great! Otherwise, for each potential L1,
4292 : * do a discrete log to see if it is NOT in the subgroup generated
4293 : * by L0; stop as soon as such is found. */
4294 1959540 : for (j = 1;; j++) {
4295 2215363 : if (n == h || (L1 && !qfi_Shanks(primeform_u(DD, L1), f, n))) {
4296 1859163 : dbg_printf(2)("D0=%ld good with L1=%ld\n", D, L1);
4297 1859163 : break;
4298 : }
4299 356200 : if (!L1) break;
4300 255823 : L1 = (j <= k && k > 1 && q[j] <= MAX_L1 ? q[j] : 0);
4301 : }
4302 : /* The first bit of m is set iff f generates a proper subgroup of cl(D)
4303 : * (hence implying that we need L1). */
4304 1959540 : m = (n < h ? 1 : 0);
4305 : /* bits j and j+1 give the 2-bit number 1 + (D|p) where p = prime(j) */
4306 58280064 : for (j = 1 ; j <= SMOOTH_PRIMES; j++)
4307 : {
4308 56320524 : ulong x = (ulong) (1 + kross(D, (long) pari_PRIMES[j]));
4309 56320524 : m |= x << (2*j);
4310 : }
4311 :
4312 : /* Insert d, h and m into the table */
4313 1959540 : tab[cnt].D = D;
4314 1959540 : tab[cnt].h = h;
4315 1959540 : tab[cnt].m = m; cnt++;
4316 : }
4317 :
4318 : /* Sort the table */
4319 3201 : qsort(tab, cnt, sizeof(*tab), _qsort_cmp);
4320 3201 : *tablelen = cnt;
4321 3201 : *minD = maxD + 3 - (maxD & 3); /* smallest d >= maxD, d = 3 (mod 4) */
4322 3201 : return tab;
4323 : }
4324 :
4325 : /* Populate Ds with discriminants (and attached data) that can be
4326 : * used to calculate the modular polynomial of level L and invariant
4327 : * inv. Return the number of discriminants found. */
4328 : static long
4329 3199 : discriminant_with_classno_at_least(disc_info bestD[MODPOLY_MAX_DCNT],
4330 : long L, long inv, GEN Q, long ignore_sparse)
4331 : {
4332 : enum { SMALL_L_BOUND = 101 };
4333 3199 : long max_max_D = 160000 * (inv ? 2 : 1);
4334 : long minD, maxD, maxh, L0, max_L1, minbits, Dcnt, flags, s, d, i, tablen;
4335 : D_entry *tab;
4336 3199 : double eps, cost, best_eps = -1.0, best_cost = -1.0;
4337 : disc_info Ds[MODPOLY_MAX_DCNT];
4338 3199 : long best_cnt = 0;
4339 : pari_timer T;
4340 3199 : timer_start(&T);
4341 :
4342 3199 : s = modinv_sparse_factor(inv);
4343 3199 : d = ceildivuu(L+1, s) + 1;
4344 :
4345 : /* maxD of 10000 allows us to get a satisfactory discriminant in
4346 : * under 250ms in most cases. */
4347 3199 : maxD = 10000;
4348 : /* Allow the class number to overshoot L by 50%. Must be at least
4349 : * 1.1*L, and higher values don't seem to provide much benefit,
4350 : * except when L is small, in which case it's necessary to get any
4351 : * discriminant at all in some cases. */
4352 3199 : maxh = (L / s < SMALL_L_BOUND) ? 10 * L : 1.5 * L;
4353 :
4354 3199 : flags = ignore_sparse ? MODPOLY_IGNORE_SPARSE_FACTOR : 0;
4355 3199 : L0 = select_L0(L, inv, 0);
4356 3199 : max_L1 = L / 2 + 2; /* for L=11 we need L1=7 for j */
4357 3199 : minbits = modpoly_height_bound(L, inv);
4358 3199 : if (Q) minbits += expi(Q);
4359 3199 : minD = 7;
4360 :
4361 6398 : while ( ! best_cnt) {
4362 3201 : while (maxD <= max_max_D) {
4363 : /* TODO: Find a way to re-use tab when we need multiple modpolys */
4364 3201 : tab = scanD0(&tablen, &minD, maxD, maxh, L0);
4365 3201 : dbg_printf(1)("Found %ld potential fundamental discriminants\n", tablen);
4366 :
4367 3201 : Dcnt = modpoly_pickD(Ds, L, inv, L0, max_L1, minbits, flags, tab, tablen);
4368 3201 : eps = 0.0;
4369 3201 : cost = 0.0;
4370 :
4371 3201 : if (Dcnt) {
4372 3199 : long n1 = 0;
4373 6416 : for (i = 0; i < Dcnt; i++) {
4374 3217 : n1 = maxss(n1, Ds[i].n1);
4375 3217 : cost += Ds[i].cost;
4376 : }
4377 3199 : eps = (n1 * s - L) / (double)L;
4378 :
4379 3199 : if (best_cost < 0.0 || cost < best_cost) {
4380 3199 : if (best_cnt)
4381 0 : for (i = 0; i < best_cnt; i++) killblock((GEN)bestD[i].primes);
4382 3199 : (void) memcpy(bestD, Ds, Dcnt * sizeof(disc_info));
4383 3199 : best_cost = cost;
4384 3199 : best_cnt = Dcnt;
4385 3199 : best_eps = eps;
4386 : /* We're satisfied if n1 is within 5% of L. */
4387 3199 : if (L / s <= SMALL_L_BOUND || eps < 0.05) break;
4388 : } else {
4389 0 : for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
4390 : }
4391 : } else {
4392 2 : if (log2(maxD) > BITS_IN_LONG - 2 * (log2(L) + 2))
4393 : {
4394 0 : char *err = stack_sprintf("modular polynomial of level %ld and invariant %ld",L,inv);
4395 0 : pari_err(e_ARCH, err);
4396 : }
4397 : }
4398 2 : maxD *= 2;
4399 2 : minD += 4;
4400 2 : dbg_printf(0)(" Doubling discriminant search space (closest: %.1f%%, cost ratio: %.1f)...\n", eps*100, cost/(double)(d*(L-1)));
4401 : }
4402 3199 : max_max_D *= 2;
4403 : }
4404 :
4405 3199 : if (DEBUGLEVEL > 3) {
4406 0 : pari_sp av = avma;
4407 0 : err_printf("Found discriminant(s):\n");
4408 0 : for (i = 0; i < best_cnt; ++i) {
4409 0 : long h = itos(classno(stoi(bestD[i].D1)));
4410 0 : set_avma(av);
4411 0 : err_printf(" D = %ld, h = %ld, u = %ld, L0 = %ld, L1 = %ld, n1 = %ld, n2 = %ld, cost = %ld\n",
4412 0 : bestD[i].D1, h, usqrt(bestD[i].D1 / bestD[i].D0), bestD[i].L0,
4413 0 : bestD[i].L1, bestD[i].n1, bestD[i].n2, bestD[i].cost);
4414 : }
4415 0 : err_printf("(off target by %.1f%%, cost ratio: %.1f)\n",
4416 0 : best_eps*100, best_cost/(double)(d*(L-1)));
4417 : }
4418 3199 : return best_cnt;
4419 : }
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