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 41368 : modinv_level(long inv)
30 : {
31 41368 : switch (inv) {
32 32189 : case INV_J: return 1;
33 903 : case INV_G2:
34 903 : case INV_W3W3E2:return 3;
35 1119 : case INV_F:
36 : case INV_F2:
37 : case INV_F4:
38 1119 : case INV_F8: return 6;
39 56 : case INV_F3: return 2;
40 532 : 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;
48 322 : case INV_W2W13: return 26;
49 1809 : case INV_W3W7: return 42;
50 655 : case INV_W5W7: return 35;
51 56 : case INV_W3W13: return 39;
52 1008 : case INV_ATKIN3:
53 : case INV_ATKIN5:
54 : case INV_ATKIN7:
55 : case INV_ATKIN11:
56 : case INV_ATKIN13:
57 : case INV_ATKIN17:
58 : case INV_ATKIN19:
59 : case INV_ATKIN23:
60 1008 : case INV_ATKIN29: return inv-100;
61 : }
62 : pari_err_BUG("modinv_level"); return 0;/*LCOV_EXCL_LINE*/
63 : }
64 :
65 : /* Where applicable, returns N=p1*p2 (possibly p2=1) s.t. two j's
66 : * related to the same f are N-isogenous, and 0 otherwise. This is
67 : * often (but not necessarily) equal to the level. */
68 : long
69 7437562 : modinv_degree(long *p1, long *p2, long inv)
70 : {
71 7437562 : switch (inv) {
72 297342 : case INV_W3W5: return (*p1 = 3) * (*p2 = 5);
73 427304 : case INV_W2W3E2:
74 427304 : case INV_W2W3: return (*p1 = 2) * (*p2 = 3);
75 1533918 : case INV_W2W5E2:
76 1533918 : case INV_W2W5: return (*p1 = 2) * (*p2 = 5);
77 947813 : case INV_W2W7E2:
78 947813 : case INV_W2W7: return (*p1 = 2) * (*p2 = 7);
79 1454419 : case INV_W2W13: return (*p1 = 2) * (*p2 = 13);
80 523917 : case INV_W3W7: return (*p1 = 3) * (*p2 = 7);
81 786066 : case INV_W3W3E2:
82 786066 : case INV_W3W3: return (*p1 = 3) * (*p2 = 3);
83 568755 : case INV_W5W7: return (*p1 = 5) * (*p2 = 7);
84 195062 : case INV_W3W13: return (*p1 = 3) * (*p2 = 13);
85 291827 : case INV_ATKIN3:
86 : case INV_ATKIN5:
87 : case INV_ATKIN7:
88 : case INV_ATKIN11:
89 : case INV_ATKIN13:
90 : case INV_ATKIN17:
91 : case INV_ATKIN19:
92 : case INV_ATKIN23:
93 291827 : case INV_ATKIN29: return (*p1 = inv-100) * (*p2 = 1);
94 : }
95 411139 : *p1 = *p2 = 1; return 0;
96 : }
97 :
98 : /* Certain invariants require that D not have 2 in it's conductor, but
99 : * this doesn't apply to every invariant with even level so we handle
100 : * it separately */
101 : INLINE int
102 566569 : modinv_odd_conductor(long inv)
103 : {
104 566569 : switch (inv) {
105 76633 : case INV_F:
106 : case INV_W3W3:
107 76633 : case INV_W3W7: return 1;
108 : }
109 489936 : return 0;
110 : }
111 :
112 : long
113 22917001 : modinv_height_factor(long inv)
114 : {
115 22917001 : switch (inv) {
116 5536 : case INV_J: return 1;
117 7070 : case INV_G2: return 3;
118 3109724 : case INV_F: return 72;
119 28 : case INV_F2: return 36;
120 536382 : case INV_F3: return 24;
121 49 : case INV_F4: return 18;
122 49 : case INV_F8: return 9;
123 63 : case INV_W2W3: return 72;
124 2353463 : case INV_W3W3: return 36;
125 3610845 : case INV_W2W5: return 54;
126 1340998 : case INV_W2W7: return 48;
127 1386 : case INV_W3W5: return 36;
128 3907638 : case INV_W2W13: return 42;
129 1125957 : case INV_W3W7: return 32;
130 1167138 : case INV_W2W3E2:return 36;
131 180796 : case INV_W2W5E2:return 27;
132 1061844 : case INV_W2W7E2:return 24;
133 49 : case INV_W3W3E2:return 18;
134 1127910 : case INV_W5W7: return 24;
135 14 : case INV_W3W13: return 28;
136 3380062 : case INV_ATKIN3:
137 : case INV_ATKIN5:
138 : case INV_ATKIN7:
139 : case INV_ATKIN11:
140 : case INV_ATKIN13:
141 : case INV_ATKIN17:
142 : case INV_ATKIN19:
143 : case INV_ATKIN23:
144 3380062 : case INV_ATKIN29: return (inv-99)/2;
145 : default: pari_err_BUG("modinv_height_factor"); return 0;/*LCOV_EXCL_LINE*/
146 : }
147 : }
148 :
149 : long
150 1907423 : disc_best_modinv(long D)
151 : {
152 : long ret;
153 1907423 : ret = INV_F; if (modinv_good_disc(ret, D)) return ret;
154 1534057 : ret = INV_W2W3; if (modinv_good_disc(ret, D)) return ret;
155 1534057 : ret = INV_W2W5; if (modinv_good_disc(ret, D)) return ret;
156 1238755 : ret = INV_W2W7; if (modinv_good_disc(ret, D)) return ret;
157 1139957 : ret = INV_W2W13; if (modinv_good_disc(ret, D)) return ret;
158 838012 : ret = INV_W3W3; if (modinv_good_disc(ret, D)) return ret;
159 651805 : ret = INV_W2W3E2;if (modinv_good_disc(ret, D)) return ret;
160 579453 : ret = INV_W3W5; if (modinv_good_disc(ret, D)) return ret;
161 579299 : ret = INV_W3W7; if (modinv_good_disc(ret, D)) return ret;
162 511091 : ret = INV_W3W13; if (modinv_good_disc(ret, D)) return ret;
163 511091 : ret = INV_W2W5E2;if (modinv_good_disc(ret, D)) return ret;
164 494753 : ret = INV_F3; if (modinv_good_disc(ret, D)) return ret;
165 464485 : ret = INV_W2W7E2;if (modinv_good_disc(ret, D)) return ret;
166 376656 : ret = INV_W5W7; if (modinv_good_disc(ret, D)) return ret;
167 283836 : ret = INV_W3W3E2;if (modinv_good_disc(ret, D)) return ret;
168 283836 : ret = INV_ATKIN29;if (modinv_good_disc(ret, D)) return ret;
169 134519 : ret = INV_ATKIN23;if (modinv_good_disc(ret, D)) return ret;
170 63098 : ret = INV_ATKIN19;if (modinv_good_disc(ret, D)) return ret;
171 29897 : ret = INV_ATKIN17;if (modinv_good_disc(ret, D)) return ret;
172 14532 : ret = INV_ATKIN13;if (modinv_good_disc(ret, D)) return ret;
173 9009 : ret = INV_ATKIN11;if (modinv_good_disc(ret, D)) return ret;
174 4697 : ret = INV_ATKIN7;if (modinv_good_disc(ret, D)) return ret;
175 3829 : ret = INV_ATKIN5;if (modinv_good_disc(ret, D)) return ret;
176 2191 : ret = INV_G2; if (modinv_good_disc(ret, D)) return ret;
177 1064 : ret = INV_ATKIN3;if (modinv_good_disc(ret, D)) return ret;
178 77 : return INV_J;
179 : }
180 :
181 : INLINE long
182 48096 : modinv_sparse_factor(long inv)
183 : {
184 48096 : switch (inv) {
185 3643 : case INV_G2:
186 : case INV_F8:
187 : case INV_W3W5:
188 : case INV_W2W5E2:
189 : case INV_W3W3E2:
190 3643 : return 3;
191 604 : case INV_F:
192 604 : return 24;
193 357 : case INV_F2:
194 : case INV_W2W3:
195 357 : return 12;
196 112 : case INV_F3:
197 112 : return 8;
198 1645 : case INV_F4:
199 : case INV_W2W3E2:
200 : case INV_W2W5:
201 : case INV_W3W3:
202 1645 : return 6;
203 1046 : case INV_W2W7:
204 1046 : return 4;
205 2914 : case INV_W2W7E2:
206 : case INV_W2W13:
207 : case INV_W3W7:
208 2914 : return 2;
209 : }
210 37775 : return 1;
211 : }
212 :
213 : #define IQ_FILTER_1MOD3 1
214 : #define IQ_FILTER_2MOD3 2
215 : #define IQ_FILTER_1MOD4 4
216 : #define IQ_FILTER_3MOD4 8
217 :
218 : INLINE long
219 15877 : modinv_pfilter(long inv)
220 : {
221 15877 : switch (inv) {
222 2045 : case INV_G2:
223 : case INV_W3W3:
224 : case INV_W3W3E2:
225 : case INV_W3W5:
226 : case INV_W2W5:
227 : case INV_W2W3E2:
228 : case INV_W2W5E2:
229 : case INV_W3W13:
230 2045 : return IQ_FILTER_1MOD3; /* ensure unique cube roots */
231 529 : case INV_W2W7:
232 : case INV_F3:
233 529 : return IQ_FILTER_1MOD4; /* ensure at most two 4th/8th roots */
234 951 : case INV_F:
235 : case INV_F2:
236 : case INV_F4:
237 : case INV_F8:
238 : case INV_W2W3:
239 : /* Ensure unique cube roots and at most two 4th/8th roots */
240 951 : return IQ_FILTER_1MOD3 | IQ_FILTER_1MOD4;
241 : }
242 12352 : return 0;
243 : }
244 :
245 : int
246 11453157 : modinv_good_prime(long inv, long p)
247 : {
248 11453157 : switch (inv) {
249 342781 : case INV_G2:
250 : case INV_W2W3E2:
251 : case INV_W3W3:
252 : case INV_W3W3E2:
253 : case INV_W3W5:
254 : case INV_W2W5E2:
255 : case INV_W2W5:
256 342781 : return (p % 3) == 2;
257 398068 : case INV_W2W7:
258 : case INV_F3:
259 398068 : return (p & 3) != 1;
260 408761 : case INV_F2:
261 : case INV_F4:
262 : case INV_F8:
263 : case INV_F:
264 : case INV_W2W3:
265 408761 : return ((p % 3) == 2) && (p & 3) != 1;
266 : }
267 10303547 : return 1;
268 : }
269 :
270 : /* Returns true if the prime p does not divide the conductor of D */
271 : INLINE int
272 3502361 : prime_to_conductor(long D, long p)
273 : {
274 : long b;
275 3502361 : if (p > 2) return (D % (p * p));
276 1280564 : b = D & 0xF;
277 1280564 : return (b && b != 4); /* 2 divides the conductor of D <=> D=0,4 mod 16 */
278 : }
279 :
280 : INLINE GEN
281 3502361 : red_primeform(long D, long p)
282 : {
283 3502361 : pari_sp av = avma;
284 : GEN P;
285 3502361 : if (!prime_to_conductor(D, p)) return NULL;
286 3502361 : P = primeform_u(stoi(D), p); /* primitive since p \nmid conductor */
287 3502361 : return gc_upto(av, qfi_red(P));
288 : }
289 :
290 : /* Computes product of primeforms over primes appearing in the prime
291 : * factorization of n (including multiplicity) */
292 : GEN
293 144613 : qfb_nform(long D, long n)
294 : {
295 144613 : pari_sp av = avma;
296 144613 : GEN N = NULL, fa = factoru(n), P = gel(fa,1), E = gel(fa,2);
297 144613 : long i, l = lg(P);
298 :
299 433587 : for (i = 1; i < l; ++i)
300 : {
301 : long j, e;
302 288974 : GEN Q = red_primeform(D, P[i]);
303 288974 : if (!Q) return gc_NULL(av);
304 288974 : e = E[i];
305 288974 : if (i == 1) { N = Q; j = 1; } else j = 0;
306 433419 : for (; j < e; ++j) N = qfbcomp_i(Q, N);
307 : }
308 144613 : return gc_upto(av, N);
309 : }
310 :
311 : INLINE int
312 1717114 : qfb_is_two_torsion(GEN x)
313 : {
314 3434228 : return equali1(gel(x,1)) || !signe(gel(x,2))
315 3434228 : || equalii(gel(x,1), gel(x,2)) || equalii(gel(x,1), gel(x,3));
316 : }
317 :
318 : /* Returns true iff the products p1*p2, p1*p2^-1, p1^-1*p2, and
319 : * p1^-1*p2^-1 are all distinct in cl(D) */
320 : INLINE int
321 235817 : qfb_distinct_prods(long D, long p1, long p2)
322 : {
323 : GEN P1, P2;
324 :
325 235817 : P1 = red_primeform(D, p1);
326 235817 : if (!P1) return 0;
327 235817 : P1 = qfbsqr_i(P1);
328 :
329 235817 : P2 = red_primeform(D, p2);
330 235817 : if (!P2) return 0;
331 235817 : P2 = qfbsqr_i(P2);
332 :
333 235817 : return !(equalii(gel(P1,1), gel(P2,1)) && absequalii(gel(P1,2), gel(P2,2)));
334 : }
335 :
336 : /* By Corollary 3.1 of Enge-Schertz Constructing elliptic curves over finite
337 : * fields using double eta-quotients, we need p1 != p2 to both be noninert
338 : * and prime to the conductor, and if p1=p2=p we want p split and prime to the
339 : * conductor. We exclude the case that p1=p2 divides the conductor, even
340 : * though this does yield class invariants */
341 : INLINE int
342 5500283 : modinv_double_eta_good_disc(long D, long inv)
343 : {
344 5500283 : pari_sp av = avma;
345 : GEN P;
346 : long i1, i2, p1, p2, N;
347 :
348 5500283 : N = modinv_degree(&p1, &p2, inv);
349 5500283 : if (! N) return 0;
350 5500283 : i1 = kross(D, p1);
351 5500283 : if (i1 < 0) return 0;
352 : /* Exclude ramified case for w_{p,p} */
353 2518939 : if (p1 == p2 && !i1) return 0;
354 2518939 : i2 = kross(D, p2);
355 2518939 : if (i2 < 0) return 0;
356 : /* this also verifies that p1 is prime to the conductor */
357 1403828 : P = red_primeform(D, p1);
358 1403828 : if (!P || gequal1(gel(P,1)) /* don't allow p1 to be principal */
359 : /* if p1 is unramified, require it to have order > 2 */
360 1403828 : || (i1 && qfb_is_two_torsion(P))) return gc_bool(av,0);
361 1402036 : if (p1 == p2) /* if p1=p2 we need p1*p1 to be distinct from its inverse */
362 222621 : return gc_bool(av, !qfb_is_two_torsion(qfbsqr_i(P)));
363 :
364 : /* this also verifies that p2 is prime to the conductor */
365 1179415 : P = red_primeform(D, p2);
366 1179415 : if (!P || gequal1(gel(P,1)) /* don't allow p2 to be principal */
367 : /* if p2 is unramified, require it to have order > 2 */
368 1179415 : || (i2 && qfb_is_two_torsion(P))) return gc_bool(av,0);
369 1177875 : set_avma(av);
370 :
371 : /* if p1 and p2 are split, we also require p1*p2, p1*p2^-1, p1^-1*p2,
372 : * and p1^-1*p2^-1 to be distinct */
373 1177875 : if (i1>0 && i2>0 && !qfb_distinct_prods(D, p1, p2)) return gc_bool(av,0);
374 1174815 : if (!i1 && !i2) {
375 : /* if both p1 and p2 are ramified, make sure their product is not
376 : * principal */
377 144060 : P = qfb_nform(D, N);
378 144060 : if (equali1(gel(P,1))) return gc_bool(av,0);
379 143829 : set_avma(av);
380 : }
381 1174584 : return 1;
382 : }
383 :
384 : /* Assumes D is a good discriminant for inv, which implies that the
385 : * level is prime to the conductor */
386 : long
387 798 : modinv_ramified(long D, long inv, long *pN)
388 : {
389 798 : long p1, p2; *pN = modinv_degree(&p1, &p2, inv);
390 798 : if (*pN <= 1) return 0;
391 798 : return !(D % p1) && !(D % p2);
392 : }
393 :
394 : static int
395 665182 : modinv_good_atkin(long L, long D)
396 : {
397 665182 : long L2 = L*L;
398 : GEN q;
399 665182 : if (kross(D,L) < 0 || -D%L2==0) return 0;
400 351911 : if (-D > 4*L2) return 1;
401 33565 : q = red_primeform(D,L);
402 33565 : if (equali1(gel(q,1))) return 0;
403 29988 : if (D%L==0) return 1;
404 26726 : q = qfbsqr(q);
405 26726 : if (equali1(gel(q,1))) return 0;
406 20895 : return 1;
407 : }
408 :
409 : int
410 15170644 : modinv_good_disc(long inv, long D)
411 : {
412 15170644 : switch (inv) {
413 923311 : case INV_J:
414 923311 : return 1;
415 98728 : case INV_G2:
416 98728 : return !!(D % 3);
417 502845 : case INV_F3:
418 502845 : return (-D & 7) == 7;
419 2058390 : case INV_F:
420 : case INV_F2:
421 : case INV_F4:
422 : case INV_F8:
423 2058390 : return ((-D & 7) == 7) && (D % 3);
424 622069 : case INV_W3W5:
425 622069 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
426 310919 : case INV_W3W3E2:
427 310919 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
428 901663 : case INV_W3W3:
429 901663 : return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
430 667688 : case INV_W2W3E2:
431 667688 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
432 1554721 : case INV_W2W3:
433 1554721 : return ((-D & 7) == 7) && (D % 3) && modinv_double_eta_good_disc(D, inv);
434 1577387 : case INV_W2W5:
435 1577387 : return ((-D % 80) != 20) && (D % 3) && modinv_double_eta_good_disc(D, inv);
436 540722 : case INV_W2W5E2:
437 540722 : return (D % 3) && modinv_double_eta_good_disc(D, inv);
438 566027 : case INV_W2W7E2:
439 566027 : return ((-D % 112) != 84) && modinv_double_eta_good_disc(D, inv);
440 1324607 : case INV_W2W7:
441 1324607 : return ((-D & 7) == 7) && modinv_double_eta_good_disc(D, inv);
442 1181782 : case INV_W2W13:
443 1181782 : return ((-D % 208) != 52) && modinv_double_eta_good_disc(D, inv);
444 679735 : case INV_W3W7:
445 679735 : return (D & 1) && (-D % 21) && modinv_double_eta_good_disc(D, inv);
446 474180 : case INV_W5W7: /* NB: This is a guess; avs doesn't have an entry */
447 474180 : return modinv_double_eta_good_disc(D, inv);
448 520688 : case INV_W3W13: /* NB: This is a guess; avs doesn't have an entry */
449 520688 : return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
450 665182 : case INV_ATKIN3:
451 : case INV_ATKIN5:
452 : case INV_ATKIN7:
453 : case INV_ATKIN11:
454 : case INV_ATKIN13:
455 : case INV_ATKIN17:
456 : case INV_ATKIN19:
457 : case INV_ATKIN23:
458 : case INV_ATKIN29:
459 665182 : return modinv_good_atkin(inv-100, D);
460 : }
461 0 : pari_err_BUG("modinv_good_disc");
462 : return 0;/*LCOV_EXCL_LINE*/
463 : }
464 :
465 : int
466 1078 : modinv_is_Weber(long inv)
467 : {
468 0 : return inv == INV_F || inv == INV_F2 || inv == INV_F3 || inv == INV_F4
469 1078 : || inv == INV_F8;
470 : }
471 :
472 : int
473 259174 : modinv_is_double_eta(long inv)
474 : {
475 259174 : switch (inv) {
476 42162 : case INV_W2W3:
477 : case INV_W2W3E2:
478 : case INV_W2W5:
479 : case INV_W2W5E2:
480 : case INV_W2W7:
481 : case INV_W2W7E2:
482 : case INV_W2W13:
483 : case INV_W3W3:
484 : case INV_W3W3E2:
485 : case INV_W3W5:
486 : case INV_W3W7:
487 : case INV_W5W7:
488 : case INV_W3W13:
489 : case INV_ATKIN3: /* as far as we are concerned */
490 : case INV_ATKIN5: /* as far as we are concerned */
491 : case INV_ATKIN7: /* as far as we are concerned */
492 : case INV_ATKIN11: /* as far as we are concerned */
493 : case INV_ATKIN13: /* as far as we are concerned */
494 : case INV_ATKIN17: /* as far as we are concerned */
495 : case INV_ATKIN19: /* as far as we are concerned */
496 : case INV_ATKIN23: /* as far as we are concerned */
497 : case INV_ATKIN29: /* as far as we are concerned */
498 42162 : return 1;
499 : }
500 217012 : return 0;
501 : }
502 :
503 : /* END Code from "class_inv.h" */
504 :
505 : INLINE int
506 10064 : safe_abs_sqrt(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
507 : {
508 10064 : if (krouu(x, p) == -1)
509 : {
510 4513 : if (p%4 == 1) return 0;
511 4513 : x = Fl_neg(x, p);
512 : }
513 10064 : *r = Fl_sqrt_pre_i(x, s2, p, pi);
514 10064 : return 1;
515 : }
516 :
517 : INLINE int
518 5021 : eighth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
519 : {
520 : ulong s;
521 5021 : if (krouu(x, p) == -1) return 0;
522 2811 : s = Fl_sqrt_pre_i(x, s2, p, pi);
523 2811 : return safe_abs_sqrt(&s, s, p, pi, s2) && safe_abs_sqrt(r, s, p, pi, s2);
524 : }
525 :
526 : INLINE ulong
527 3259 : modinv_f_from_j(ulong j, ulong p, ulong pi, ulong s2, long only_residue)
528 : {
529 3259 : pari_sp av = avma;
530 : GEN pol, r;
531 : long i;
532 3259 : ulong g2, f = ULONG_MAX;
533 :
534 : /* f^8 must be a root of X^3 - \gamma_2 X - 16 */
535 3259 : g2 = Fl_sqrtl_pre(j, 3, p, pi);
536 :
537 3259 : pol = mkvecsmall5(0UL, Fl_neg(16 % p, p), Fl_neg(g2, p), 0UL, 1UL);
538 3259 : r = Flx_roots_pre(pol, p, pi);
539 5825 : for (i = 1; i < lg(r); ++i)
540 5825 : if (only_residue)
541 1177 : { if (krouu(r[i], p) != -1) return gc_ulong(av,r[i]); }
542 4648 : else if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
543 0 : pari_err_BUG("modinv_f_from_j");
544 : return 0;/*LCOV_EXCL_LINE*/
545 : }
546 :
547 : INLINE ulong
548 168 : modinv_f3_from_j(ulong j, ulong p, ulong pi, ulong s2)
549 : {
550 168 : pari_sp av = avma;
551 : GEN pol, r;
552 : long i;
553 168 : ulong f = ULONG_MAX;
554 :
555 168 : pol = mkvecsmall5(0UL,
556 168 : Fl_neg(4096 % p, p), Fl_sub(768 % p, j, p), Fl_neg(48 % p, p), 1UL);
557 168 : r = Flx_roots_pre(pol, p, pi);
558 373 : for (i = 1; i < lg(r); ++i)
559 373 : if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
560 0 : pari_err_BUG("modinv_f3_from_j");
561 : return 0;/*LCOV_EXCL_LINE*/
562 : }
563 :
564 : /* Return the exponent e for the double-eta "invariant" w such that
565 : * w^e is a class invariant. For example w2w3^12 is a class
566 : * invariant, so double_eta_exponent(INV_W2W3) is 12 and
567 : * double_eta_exponent(INV_W2W3E2) is 6. */
568 : INLINE ulong
569 67341 : double_eta_exponent(long inv)
570 : {
571 67341 : switch (inv) {
572 2446 : case INV_W2W3: return 12;
573 13012 : case INV_W2W3E2:
574 : case INV_W2W5:
575 13012 : case INV_W3W3: return 6;
576 9730 : case INV_W2W7: return 4;
577 5419 : case INV_W3W5:
578 : case INV_W2W5E2:
579 5419 : case INV_W3W3E2: return 3;
580 15351 : case INV_W2W7E2:
581 : case INV_W2W13:
582 15351 : case INV_W3W7: return 2;
583 21383 : default: return 1;
584 : }
585 : }
586 :
587 : INLINE ulong
588 77 : weber_exponent(long inv)
589 : {
590 77 : switch (inv)
591 : {
592 77 : case INV_F: return 24;
593 0 : case INV_F2: return 12;
594 0 : case INV_F3: return 8;
595 0 : case INV_F4: return 6;
596 0 : case INV_F8: return 3;
597 0 : default: return 1;
598 : }
599 : }
600 :
601 : INLINE ulong
602 32113 : double_eta_power(long inv, ulong w, ulong p, ulong pi)
603 : {
604 32113 : return Fl_powu_pre(w, double_eta_exponent(inv), p, pi);
605 : }
606 :
607 : static GEN
608 455 : double_eta_raw_to_Fp(GEN f, GEN p)
609 : {
610 455 : GEN u = FpX_red(RgV_to_RgX(gel(f,1), 0), p);
611 455 : GEN v = FpX_red(RgV_to_RgX(gel(f,2), 0), p);
612 455 : return mkvec3(u, v, gel(f,3));
613 : }
614 :
615 : /* Given a root x of polclass(D, inv) modulo N, returns a root of polclass(D,0)
616 : * modulo N by plugging x to a modular polynomial. For double-eta quotients,
617 : * this is done by plugging x into the modular polynomial Phi(INV_WpWq, j)
618 : * Enge, Morain 2013: Generalised Weber Functions. */
619 : GEN
620 1133 : Fp_modinv_to_j(GEN x, long inv, GEN p)
621 : {
622 1133 : switch(inv)
623 : {
624 258 : case INV_J: return Fp_red(x, p);
625 343 : case INV_G2: return Fp_powu(x, 3, p);
626 77 : case INV_F: case INV_F2: case INV_F3: case INV_F4: case INV_F8:
627 : {
628 77 : GEN xe = Fp_powu(x, weber_exponent(inv), p);
629 77 : return Fp_div(Fp_powu(subiu(xe, 16), 3, p), xe, p);
630 : }
631 455 : default:
632 455 : if (modinv_is_double_eta(inv))
633 : {
634 455 : GEN xe = Fp_powu(x, double_eta_exponent(inv), p);
635 455 : GEN uvk = double_eta_raw_to_Fp(double_eta_raw(inv), p);
636 455 : GEN J0 = FpX_eval(gel(uvk,1), xe, p);
637 455 : GEN J1 = FpX_eval(gel(uvk,2), xe, p);
638 455 : GEN J2 = Fp_pow(xe, gel(uvk,3), p);
639 455 : GEN phi = mkvec3(J0, J1, J2);
640 455 : return FpX_oneroot(RgX_to_FpX(RgV_to_RgX(phi,1), p),p);
641 : }
642 : pari_err_BUG("Fp_modinv_to_j"); return NULL;/* LCOV_EXCL_LINE */
643 : }
644 : }
645 :
646 : /* Assuming p = 2 (mod 3) and p = 3 (mod 4): if the two 12th roots of
647 : * x (mod p) exist, set *r to one of them and return 1, otherwise
648 : * return 0 (without touching *r). */
649 : INLINE int
650 893 : twelth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
651 : {
652 893 : ulong t = Fl_sqrtl_pre(x, 3, p, pi);
653 893 : if (krouu(t, p) == -1) return 0;
654 850 : t = Fl_sqrt_pre_i(t, s2, p, pi);
655 850 : return safe_abs_sqrt(r, t, p, pi, s2);
656 : }
657 :
658 : INLINE int
659 5537 : sixth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
660 : {
661 5537 : ulong t = Fl_sqrtl_pre(x, 3, p, pi);
662 5536 : if (krouu(t, p) == -1) return 0;
663 5349 : *r = Fl_sqrt_pre_i(t, s2, p, pi);
664 5352 : return 1;
665 : }
666 :
667 : INLINE int
668 3926 : fourth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
669 : {
670 : ulong s;
671 3926 : if (krouu(x, p) == -1) return 0;
672 3592 : s = Fl_sqrt_pre_i(x, s2, p, pi);
673 3592 : return safe_abs_sqrt(r, s, p, pi, s2);
674 : }
675 :
676 : INLINE int
677 34774 : double_eta_root(long inv, ulong *r, ulong w, ulong p, ulong pi, ulong s2)
678 : {
679 34774 : switch (double_eta_exponent(inv)) {
680 893 : case 12: return twelth_root(r, w, p, pi, s2);
681 5537 : case 6: return sixth_root(r, w, p, pi, s2);
682 3926 : case 4: return fourth_root(r, w, p, pi, s2);
683 2343 : case 3: *r = Fl_sqrtl_pre(w, 3, p, pi); return 1;
684 8310 : case 2: return krouu(w, p) != -1 && !!(*r = Fl_sqrt_pre_i(w, s2, p, pi));
685 13764 : default: *r = w; return 1; /* case 1 */
686 : }
687 : }
688 :
689 : /* F = double_eta_Fl(inv, p) */
690 : static GEN
691 61086 : Flx_double_eta_xpoly(GEN F, ulong j, ulong p, ulong pi)
692 : {
693 61086 : GEN u = gel(F,1), v = gel(F,2), w;
694 61086 : long i, k = itos(gel(F,3)), lu = lg(u), lv = lg(v), lw = lu + 1;
695 :
696 61086 : w = cgetg(lw, t_VECSMALL); /* lu >= max(lv,k) */
697 61087 : w[1] = 0; /* variable number */
698 1600603 : 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);
699 122176 : for ( ; i < lu; i++) uel(w, i+1) = uel(u,i);
700 61088 : uel(w, k+2) = Fl_add(uel(w, k+2), Fl_sqr_pre(j, p, pi), p);
701 61089 : return Flx_renormalize(w, lw);
702 : }
703 :
704 : /* F = double_eta_Fl(inv, p) */
705 : static GEN
706 32113 : Flx_double_eta_jpoly(GEN F, ulong x, ulong p, ulong pi)
707 : {
708 32113 : pari_sp av = avma;
709 32113 : GEN u = gel(F,1), v = gel(F,2), xs;
710 32113 : long k = itos(gel(F,3));
711 : ulong a, b, c;
712 :
713 : /* u is always longest and the length is bigger than k */
714 32113 : xs = Fl_powers_pre(x, lg(u) - 1, p, pi);
715 32113 : c = Flv_dotproduct_pre(u, xs, p, pi);
716 32113 : b = Flv_dotproduct_pre(v, xs, p, pi);
717 32113 : a = uel(xs, k + 1);
718 32113 : set_avma(av);
719 32113 : return mkvecsmall4(0, c, b, a);
720 : }
721 :
722 : /* reduce F = double_eta_raw(inv) mod p */
723 : static GEN
724 39903 : double_eta_raw_to_Fl(GEN f, ulong p)
725 : {
726 39903 : GEN u = ZV_to_Flv(gel(f,1), p);
727 39903 : GEN v = ZV_to_Flv(gel(f,2), p);
728 39903 : return mkvec3(u, v, gel(f,3));
729 : }
730 : /* double_eta_raw(inv) mod p */
731 : static GEN
732 33889 : double_eta_Fl(long inv, ulong p)
733 33889 : { return double_eta_raw_to_Fl(double_eta_raw(inv), p); }
734 :
735 : /* Go through roots of Psi(X,j) until one has an double_eta_exponent(inv)-th
736 : * root, and return that root. F = double_eta_Fl(inv,p) */
737 : INLINE ulong
738 6697 : modinv_double_eta_from_j(GEN F, long inv, ulong j, ulong p, ulong pi, ulong s2)
739 : {
740 6697 : pari_sp av = avma;
741 : long i;
742 6697 : ulong f = ULONG_MAX;
743 6697 : GEN a = Flx_double_eta_xpoly(F, j, p, pi);
744 6697 : a = Flx_roots_pre(a, p, pi);
745 7582 : for (i = 1; i < lg(a); ++i)
746 7582 : if (double_eta_root(inv, &f, uel(a, i), p, pi, s2)) break;
747 6697 : if (i == lg(a)) pari_err_BUG("modinv_double_eta_from_j");
748 6697 : return gc_ulong(av,f);
749 : }
750 :
751 : /* assume j1 != j2 */
752 : static long
753 20496 : modinv_double_eta_from_2j(
754 : ulong *r, long inv, ulong j1, ulong j2, ulong p, ulong pi, ulong s2)
755 : {
756 20496 : GEN f, g, d, F = double_eta_Fl(inv, p);
757 20498 : f = Flx_double_eta_xpoly(F, j1, p, pi);
758 20497 : g = Flx_double_eta_xpoly(F, j2, p, pi);
759 20498 : d = Flx_gcd(f, g, p);
760 : /* we should have deg(d) = 1, but because j1 or j2 may not have the correct
761 : * endomorphism ring, we use the less strict conditional underneath */
762 40990 : return (degpol(d) > 2 || (*r = Flx_oneroot_pre(d, p, pi)) == p
763 40991 : || ! double_eta_root(inv, r, *r, p, pi, s2));
764 : }
765 :
766 : long
767 20577 : modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb)
768 : {
769 20577 : pari_sp av = avma;
770 20577 : long p1, p2, v = ne->v, p1_depth;
771 20577 : ulong j1, p = ne->p, pi = ne->pi, s2 = ne->s2;
772 : GEN phi;
773 :
774 20577 : (void) modinv_degree(&p1, &p2, inv);
775 20577 : p1_depth = u_lval(v, p1);
776 :
777 20577 : phi = polmodular_db_getp(jdb, p1, p);
778 20577 : if (!next_surface_nbr(&j1, phi, p1, p1_depth, j0, NULL, p, pi))
779 0 : pari_err_BUG("modfn_unambiguous_root");
780 20573 : if (p2 == p1) {
781 1989 : if (!next_surface_nbr(&j1, phi, p1, p1_depth, j1, &j0, p, pi))
782 0 : pari_err_BUG("modfn_unambiguous_root");
783 18584 : } else if (p2 > 1)
784 : {
785 10190 : long p2_depth = u_lval(v, p2);
786 10190 : phi = polmodular_db_getp(jdb, p2, p);
787 10190 : if (!next_surface_nbr(&j1, phi, p2, p2_depth, j1, NULL, p, pi))
788 0 : pari_err_BUG("modfn_unambiguous_root");
789 : }
790 23525 : return gc_long(av, j1 != j0
791 20566 : && !modinv_double_eta_from_2j(r, inv, j0, j1, p, pi, s2));
792 : }
793 :
794 : ulong
795 205999 : modfn_root(ulong j, norm_eqn_t ne, long inv)
796 : {
797 205999 : ulong f, p = ne->p, pi = ne->pi, s2 = ne->s2;
798 205999 : switch (inv) {
799 197898 : case INV_J: return j;
800 4675 : case INV_G2: return Fl_sqrtl_pre(j, 3, p, pi);
801 1894 : case INV_F: return modinv_f_from_j(j, p, pi, s2, 0);
802 196 : case INV_F2:
803 196 : f = modinv_f_from_j(j, p, pi, s2, 0);
804 196 : return Fl_sqr_pre(f, p, pi);
805 168 : case INV_F3: return modinv_f3_from_j(j, p, pi, s2);
806 553 : case INV_F4:
807 553 : f = modinv_f_from_j(j, p, pi, s2, 0);
808 553 : return Fl_sqr_pre(Fl_sqr_pre(f, p, pi), p, pi);
809 616 : case INV_F8: return modinv_f_from_j(j, p, pi, s2, 1);
810 : }
811 0 : if (modinv_is_double_eta(inv))
812 : {
813 0 : pari_sp av = avma;
814 0 : ulong f = modinv_double_eta_from_j(double_eta_Fl(inv,p), inv, j, p, pi, s2);
815 0 : return gc_ulong(av,f);
816 : }
817 : pari_err_BUG("modfn_root"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
818 : }
819 :
820 : /* F = double_eta_raw(inv) */
821 : long
822 6011 : modinv_j_from_2double_eta(
823 : GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi)
824 : {
825 : GEN f, g, d;
826 :
827 6011 : x0 = double_eta_power(inv, x0, p, pi);
828 6011 : x1 = double_eta_power(inv, x1, p, pi);
829 6011 : F = double_eta_raw_to_Fl(F, p);
830 6011 : f = Flx_double_eta_jpoly(F, x0, p, pi);
831 6011 : g = Flx_double_eta_jpoly(F, x1, p, pi);
832 6011 : d = Flx_gcd(f, g, p); /* >= 1 */
833 6011 : return degpol(d) == 1;
834 : }
835 :
836 : /* x root of (X^24 - 16)^3 - X^24 * j = 0 => j = (x^24 - 16)^3 / x^24 */
837 : INLINE ulong
838 1844 : modinv_j_from_f(ulong x, ulong n, ulong p, ulong pi)
839 : {
840 1844 : ulong x24 = Fl_powu_pre(x, 24 / n, p, pi);
841 1844 : return Fl_div(Fl_powu_pre(Fl_sub(x24, 16 % p, p), 3, p, pi), x24, p);
842 : }
843 : /* should never be called if modinv_double_eta(inv) is true */
844 : INLINE ulong
845 70203 : modfn_preimage(ulong x, ulong p, ulong pi, long inv)
846 : {
847 70203 : switch (inv) {
848 64433 : case INV_J: return x;
849 3926 : case INV_G2: return Fl_powu_pre(x, 3, p, pi);
850 : /* NB: could replace these with a single call modinv_j_from_f(x,inv,p,pi)
851 : * but avoid the dependence on the actual value of inv */
852 640 : case INV_F: return modinv_j_from_f(x, 1, p, pi);
853 196 : case INV_F2: return modinv_j_from_f(x, 2, p, pi);
854 168 : case INV_F3: return modinv_j_from_f(x, 3, p, pi);
855 392 : case INV_F4: return modinv_j_from_f(x, 4, p, pi);
856 448 : case INV_F8: return modinv_j_from_f(x, 8, p, pi);
857 : }
858 : pari_err_BUG("modfn_preimage"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
859 : }
860 :
861 : /* SECTION: class group bb_group. */
862 :
863 : INLINE GEN
864 152847 : mkqfis(GEN a, ulong b, ulong c, GEN D) { retmkqfb(a, utoi(b), utoi(c), D); }
865 :
866 : /* SECTION: dot-product-like functions on Fl's with precomputed inverse. */
867 :
868 : /* Computes x0y1 + y0x1 (mod p); assumes p < 2^63. */
869 : INLINE ulong
870 63715116 : Fl_addmul2(
871 : ulong x0, ulong x1, ulong y0, ulong y1,
872 : ulong p, ulong pi)
873 : {
874 63715116 : return Fl_addmulmul_pre(x0,y1,y0,x1,p,pi);
875 : }
876 :
877 : /* Computes x0y2 + x1y1 + x2y0 (mod p); assumes p < 2^62. */
878 : INLINE ulong
879 12612029 : Fl_addmul3(
880 : ulong x0, ulong x1, ulong x2, ulong y0, ulong y1, ulong y2,
881 : ulong p, ulong pi)
882 : {
883 : ulong l0, l1, h0, h1;
884 : LOCAL_OVERFLOW;
885 : LOCAL_HIREMAINDER;
886 12612029 : l0 = mulll(x0, y2); h0 = hiremainder;
887 12612029 : l1 = mulll(x1, y1); h1 = hiremainder;
888 12612029 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
889 12612029 : l0 = mulll(x2, y0); h0 = hiremainder;
890 12612029 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
891 12612029 : return remll_pre(h1, l1, p, pi);
892 : }
893 :
894 : /* Computes x0y3 + x1y2 + x2y1 + x3y0 (mod p); assumes p < 2^62. */
895 : INLINE ulong
896 5317745 : Fl_addmul4(
897 : ulong x0, ulong x1, ulong x2, ulong x3,
898 : ulong y0, ulong y1, ulong y2, ulong y3,
899 : ulong p, ulong pi)
900 : {
901 : ulong l0, l1, h0, h1;
902 : LOCAL_OVERFLOW;
903 : LOCAL_HIREMAINDER;
904 5317745 : l0 = mulll(x0, y3); h0 = hiremainder;
905 5317745 : l1 = mulll(x1, y2); h1 = hiremainder;
906 5317745 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
907 5317745 : l0 = mulll(x2, y1); h0 = hiremainder;
908 5317745 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
909 5317745 : l0 = mulll(x3, y0); h0 = hiremainder;
910 5317745 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
911 5317745 : return remll_pre(h1, l1, p, pi);
912 : }
913 :
914 : /* Computes x0y4 + x1y3 + x2y2 + x3y1 + x4y0 (mod p); assumes p < 2^62. */
915 : INLINE ulong
916 26435367 : Fl_addmul5(
917 : ulong x0, ulong x1, ulong x2, ulong x3, ulong x4,
918 : ulong y0, ulong y1, ulong y2, ulong y3, ulong y4,
919 : ulong p, ulong pi)
920 : {
921 : ulong l0, l1, h0, h1;
922 : LOCAL_OVERFLOW;
923 : LOCAL_HIREMAINDER;
924 26435367 : l0 = mulll(x0, y4); h0 = hiremainder;
925 26435367 : l1 = mulll(x1, y3); h1 = hiremainder;
926 26435367 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
927 26435367 : l0 = mulll(x2, y2); h0 = hiremainder;
928 26435367 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
929 26435367 : l0 = mulll(x3, y1); h0 = hiremainder;
930 26435367 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
931 26435367 : l0 = mulll(x4, y0); h0 = hiremainder;
932 26435367 : l1 = addll(l0, l1); h1 = addllx(h0, h1);
933 26435367 : return remll_pre(h1, l1, p, pi);
934 : }
935 :
936 : /* A polmodular database for a given class invariant consists of a t_VEC whose
937 : * L-th entry is 0 or a GEN pointing to Phi_L. This function produces a pair
938 : * of databases corresponding to the j-invariant and inv */
939 : GEN
940 21492 : polmodular_db_init(long inv)
941 : {
942 21492 : const long LEN = 32;
943 21492 : GEN res = cgetg_block(3, t_VEC);
944 21492 : gel(res, 1) = zerovec_block(LEN);
945 21492 : gel(res, 2) = (inv == INV_J)? gen_0: zerovec_block(LEN);
946 21492 : return res;
947 : }
948 :
949 : void
950 27200 : polmodular_db_add_level(GEN *DB, long L, long inv)
951 : {
952 27200 : GEN db = gel(*DB, (inv == INV_J)? 1: 2);
953 27200 : long max_L = lg(db) - 1;
954 27200 : if (L > max_L) {
955 : GEN newdb;
956 43 : long i, newlen = 2 * L;
957 :
958 43 : newdb = cgetg_block(newlen + 1, t_VEC);
959 1419 : for (i = 1; i <= max_L; ++i) gel(newdb, i) = gel(db, i);
960 2941 : for ( ; i <= newlen; ++i) gel(newdb, i) = gen_0;
961 43 : killblock(db);
962 43 : gel(*DB, (inv == INV_J)? 1: 2) = db = newdb;
963 : }
964 27200 : if (typ(gel(db, L)) == t_INT) {
965 8584 : pari_sp av = avma;
966 8584 : GEN x = polmodular0_ZM(L, inv, NULL, NULL, 0, DB); /* may set db[L] */
967 8584 : GEN y = gel(db, L);
968 8584 : gel(db, L) = gclone(x);
969 8584 : if (typ(y) != t_INT) gunclone(y);
970 8584 : set_avma(av);
971 : }
972 27200 : }
973 :
974 : void
975 5277 : polmodular_db_add_levels(GEN *db, long *levels, long k, long inv)
976 : {
977 : long i;
978 10949 : for (i = 0; i < k; ++i) polmodular_db_add_level(db, levels[i], inv);
979 5277 : }
980 :
981 : GEN
982 393209 : polmodular_db_for_inv(GEN db, long inv) { return gel(db, (inv==INV_J)? 1: 2); }
983 :
984 : /* TODO: Also cache modpoly mod p for most recent p (avoid repeated
985 : * reductions in, for example, polclass.c:oneroot_of_classpoly(). */
986 : GEN
987 569036 : polmodular_db_getp(GEN db, long L, ulong p)
988 : {
989 569036 : GEN f = gel(db, L);
990 569036 : if (isintzero(f)) pari_err_BUG("polmodular_db_getp");
991 569037 : return ZM_to_Flm(f, p);
992 : }
993 :
994 : /* SECTION: Table of discriminants to use. */
995 : typedef struct {
996 : long GENcode0; /* used when serializing the struct to a t_VECSMALL */
997 : long inv; /* invariant */
998 : long L; /* modpoly level */
999 : long D0; /* fundamental discriminant */
1000 : long D1; /* chosen discriminant */
1001 : long L0; /* first generator norm */
1002 : long L1; /* second generator norm */
1003 : long n1; /* order of L0 in cl(D1) */
1004 : long n2; /* order of L0 in cl(D2) where D2 = L^2 D1 */
1005 : long dl1; /* m such that L0^m = L in cl(D1) */
1006 : long dl2_0; /* These two are (m, n) such that L0^m L1^n = form of norm L^2 in D2 */
1007 : long dl2_1; /* This n is always 1 or 0. */
1008 : /* this part is not serialized */
1009 : long nprimes; /* number of primes needed for D1 */
1010 : long cost; /* cost to enumerate subgroup of cl(L^2D): subgroup size is n2 if L1=0, 2*n2 o.w. */
1011 : long bits;
1012 : ulong *primes;
1013 : ulong *traces;
1014 : } disc_info;
1015 :
1016 : #define MODPOLY_MAX_DCNT 64
1017 :
1018 : /* Flag for last parameter of discriminant_with_classno_at_least.
1019 : * Warning: ignoring the sparse factor makes everything slower by
1020 : * something like (sparse factor)^3. */
1021 : #define USE_SPARSE_FACTOR 0
1022 : #define IGNORE_SPARSE_FACTOR 1
1023 :
1024 : static long
1025 : discriminant_with_classno_at_least(disc_info Ds[MODPOLY_MAX_DCNT], long L,
1026 : long inv, GEN Q, long ignore_sparse);
1027 :
1028 : /* SECTION: evaluation functions for modular polynomials of small level. */
1029 :
1030 : /* Based on phi2_eval_ff() in Sutherland's classpoly programme.
1031 : * Calculates Phi_2(X, j) (mod p) with 6M+7A (4 reductions, not
1032 : * counting those for Phi_2) */
1033 : INLINE GEN
1034 29889809 : Flm_Fl_phi2_evalx(GEN phi2, ulong j, ulong p, ulong pi)
1035 : {
1036 29889809 : GEN res = cgetg(6, t_VECSMALL);
1037 : ulong j2, t1;
1038 :
1039 29811911 : res[1] = 0; /* variable name */
1040 :
1041 29811911 : j2 = Fl_sqr_pre(j, p, pi);
1042 29863936 : t1 = Fl_add(j, coeff(phi2, 3, 1), p);
1043 29851300 : t1 = Fl_addmul2(j, j2, t1, coeff(phi2, 2, 1), p, pi);
1044 29950520 : res[2] = Fl_add(t1, coeff(phi2, 1, 1), p);
1045 :
1046 29917771 : t1 = Fl_addmul2(j, j2, coeff(phi2, 3, 2), coeff(phi2, 2, 2), p, pi);
1047 29987105 : res[3] = Fl_add(t1, coeff(phi2, 2, 1), p);
1048 :
1049 29946713 : t1 = Fl_mul_pre(j, coeff(phi2, 3, 2), p, pi);
1050 29937449 : t1 = Fl_add(t1, coeff(phi2, 3, 1), p);
1051 29904243 : res[4] = Fl_sub(t1, j2, p);
1052 :
1053 29879082 : res[5] = 1;
1054 29879082 : return res;
1055 : }
1056 :
1057 : /* Based on phi3_eval_ff() in Sutherland's classpoly programme.
1058 : * Calculates Phi_3(X, j) (mod p) with 13M+13A (6 reductions, not
1059 : * counting those for Phi_3) */
1060 : INLINE GEN
1061 4215793 : Flm_Fl_phi3_evalx(GEN phi3, ulong j, ulong p, ulong pi)
1062 : {
1063 4215793 : GEN res = cgetg(7, t_VECSMALL);
1064 : ulong j2, j3, t1;
1065 :
1066 4209415 : res[1] = 0; /* variable name */
1067 :
1068 4209415 : j2 = Fl_sqr_pre(j, p, pi);
1069 4215452 : j3 = Fl_mul_pre(j, j2, p, pi);
1070 :
1071 4216390 : t1 = Fl_add(j, coeff(phi3, 4, 1), p);
1072 4216575 : t1 = Fl_addmul3(j, j2, j3, t1, coeff(phi3, 3, 1), coeff(phi3, 2, 1), p, pi);
1073 4227376 : res[2] = Fl_add(t1, coeff(phi3, 1, 1), p);
1074 :
1075 4223804 : t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 2),
1076 4223804 : coeff(phi3, 3, 2), coeff(phi3, 2, 2), p, pi);
1077 4228192 : res[3] = Fl_add(t1, coeff(phi3, 2, 1), p);
1078 :
1079 4224688 : t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 3),
1080 4224688 : coeff(phi3, 3, 3), coeff(phi3, 3, 2), p, pi);
1081 4228660 : res[4] = Fl_add(t1, coeff(phi3, 3, 1), p);
1082 :
1083 4225409 : t1 = Fl_addmul2(j, j2, coeff(phi3, 4, 3), coeff(phi3, 4, 2), p, pi);
1084 4228016 : t1 = Fl_add(t1, coeff(phi3, 4, 1), p);
1085 4224419 : res[5] = Fl_sub(t1, j3, p);
1086 :
1087 4220665 : res[6] = 1;
1088 4220665 : return res;
1089 : }
1090 :
1091 : /* Based on phi5_eval_ff() in Sutherland's classpoly programme.
1092 : * Calculates Phi_5(X, j) (mod p) with 33M+31A (10 reductions, not
1093 : * counting those for Phi_5) */
1094 : INLINE GEN
1095 5307958 : Flm_Fl_phi5_evalx(GEN phi5, ulong j, ulong p, ulong pi)
1096 : {
1097 5307958 : GEN res = cgetg(9, t_VECSMALL);
1098 : ulong j2, j3, j4, j5, t1;
1099 :
1100 5301275 : res[1] = 0; /* variable name */
1101 :
1102 5301275 : j2 = Fl_sqr_pre(j, p, pi);
1103 5307221 : j3 = Fl_mul_pre(j, j2, p, pi);
1104 5307924 : j4 = Fl_sqr_pre(j2, p, pi);
1105 5307633 : j5 = Fl_mul_pre(j, j4, p, pi);
1106 :
1107 5309991 : t1 = Fl_add(j, coeff(phi5, 6, 1), p);
1108 5310278 : t1 = Fl_addmul5(j, j2, j3, j4, j5, t1,
1109 5310278 : coeff(phi5, 5, 1), coeff(phi5, 4, 1),
1110 5310278 : coeff(phi5, 3, 1), coeff(phi5, 2, 1),
1111 : p, pi);
1112 5319262 : res[2] = Fl_add(t1, coeff(phi5, 1, 1), p);
1113 :
1114 5315163 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1115 5315163 : coeff(phi5, 6, 2), coeff(phi5, 5, 2),
1116 5315163 : coeff(phi5, 4, 2), coeff(phi5, 3, 2), coeff(phi5, 2, 2),
1117 : p, pi);
1118 5320194 : res[3] = Fl_add(t1, coeff(phi5, 2, 1), p);
1119 :
1120 5316036 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1121 5316036 : coeff(phi5, 6, 3), coeff(phi5, 5, 3),
1122 5316036 : coeff(phi5, 4, 3), coeff(phi5, 3, 3), coeff(phi5, 3, 2),
1123 : p, pi);
1124 5319718 : res[4] = Fl_add(t1, coeff(phi5, 3, 1), p);
1125 :
1126 5316706 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1127 5316706 : coeff(phi5, 6, 4), coeff(phi5, 5, 4),
1128 5316706 : coeff(phi5, 4, 4), coeff(phi5, 4, 3), coeff(phi5, 4, 2),
1129 : p, pi);
1130 5321319 : res[5] = Fl_add(t1, coeff(phi5, 4, 1), p);
1131 :
1132 5317321 : t1 = Fl_addmul5(j, j2, j3, j4, j5,
1133 5317321 : coeff(phi5, 6, 5), coeff(phi5, 5, 5),
1134 5317321 : coeff(phi5, 5, 4), coeff(phi5, 5, 3), coeff(phi5, 5, 2),
1135 : p, pi);
1136 5322305 : res[6] = Fl_add(t1, coeff(phi5, 5, 1), p);
1137 :
1138 5319465 : t1 = Fl_addmul4(j, j2, j3, j4,
1139 5319465 : coeff(phi5, 6, 5), coeff(phi5, 6, 4),
1140 5319465 : coeff(phi5, 6, 3), coeff(phi5, 6, 2),
1141 : p, pi);
1142 5323445 : t1 = Fl_add(t1, coeff(phi5, 6, 1), p);
1143 5320104 : res[7] = Fl_sub(t1, j5, p);
1144 :
1145 5316956 : res[8] = 1;
1146 5316956 : return res;
1147 : }
1148 :
1149 : GEN
1150 46443822 : Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi)
1151 : {
1152 46443822 : switch (L) {
1153 29902628 : case 2: return Flm_Fl_phi2_evalx(phi, j, p, pi);
1154 4214265 : case 3: return Flm_Fl_phi3_evalx(phi, j, p, pi);
1155 5306801 : case 5: return Flm_Fl_phi5_evalx(phi, j, p, pi);
1156 7020128 : default: { /* not GC clean, but gc_upto-safe */
1157 7020128 : GEN j_powers = Fl_powers_pre(j, L + 1, p, pi);
1158 7103833 : return Flm_Flc_mul_pre_Flx(phi, j_powers, p, pi, 0);
1159 : }
1160 : }
1161 : }
1162 :
1163 : /* SECTION: Velu's formula for the codmain curve (Fl case). */
1164 :
1165 : INLINE ulong
1166 1854428 : Fl_mul4(ulong x, ulong p)
1167 1854428 : { return Fl_double(Fl_double(x, p), p); }
1168 :
1169 : INLINE ulong
1170 98975 : Fl_mul5(ulong x, ulong p)
1171 98975 : { return Fl_add(x, Fl_mul4(x, p), p); }
1172 :
1173 : INLINE ulong
1174 927289 : Fl_mul8(ulong x, ulong p)
1175 927289 : { return Fl_double(Fl_mul4(x, p), p); }
1176 :
1177 : INLINE ulong
1178 828385 : Fl_mul6(ulong x, ulong p)
1179 828385 : { return Fl_sub(Fl_mul8(x, p), Fl_double(x, p), p); }
1180 :
1181 : INLINE ulong
1182 98974 : Fl_mul7(ulong x, ulong p)
1183 98974 : { return Fl_sub(Fl_mul8(x, p), x, p); }
1184 :
1185 : /* Given an elliptic curve E = [a4, a6] over F_p and a nonzero point
1186 : * pt on E, return the quotient E' = E/<P> = [a4_img, a6_img] */
1187 : static void
1188 98989 : Fle_quotient_from_kernel_generator(
1189 : ulong *a4_img, ulong *a6_img, ulong a4, ulong a6, GEN pt, ulong p, ulong pi)
1190 : {
1191 98989 : pari_sp av = avma;
1192 98989 : ulong t = 0, w = 0;
1193 : GEN Q;
1194 : ulong xQ, yQ, tQ, uQ;
1195 :
1196 98989 : Q = gcopy(pt);
1197 : /* Note that, as L is odd, say L = 2n + 1, we necessarily have
1198 : * [(L - 1)/2]P = [n]P = [n - L]P = -[n + 1]P = -[(L + 1)/2]P. This is
1199 : * what the condition Q[1] != xQ tests, so the loop will execute n times. */
1200 : do {
1201 828268 : xQ = uel(Q, 1);
1202 828268 : yQ = uel(Q, 2);
1203 : /* tQ = 6 xQ^2 + b2 xQ + b4
1204 : * = 6 xQ^2 + 2 a4 (since b2 = 0 and b4 = 2 a4) */
1205 828268 : tQ = Fl_add(Fl_mul6(Fl_sqr_pre(xQ, p, pi), p), Fl_double(a4, p), p);
1206 828269 : uQ = Fl_add(Fl_mul4(Fl_sqr_pre(yQ, p, pi), p),
1207 : Fl_mul_pre(tQ, xQ, p, pi), p);
1208 :
1209 828286 : t = Fl_add(t, tQ, p);
1210 828249 : w = Fl_add(w, uQ, p);
1211 828213 : Q = gc_upto(av, Fle_add(pt, Q, a4, p));
1212 828257 : } while (uel(Q, 1) != xQ);
1213 :
1214 98976 : set_avma(av);
1215 : /* a4_img = a4 - 5 * t */
1216 98974 : *a4_img = Fl_sub(a4, Fl_mul5(t, p), p);
1217 : /* a6_img = a6 - b2 * t - 7 * w = a6 - 7 * w (since a1 = a2 = 0 ==> b2 = 0) */
1218 98974 : *a6_img = Fl_sub(a6, Fl_mul7(w, p), p);
1219 98973 : }
1220 :
1221 : /* SECTION: Calculation of modular polynomials. */
1222 :
1223 : /* Given an elliptic curve [a4, a6] over FF_p, try to find a
1224 : * nontrivial L-torsion point on the curve by considering n times a
1225 : * random point; val controls the maximum L-valuation expected of n
1226 : * times a random point */
1227 : static GEN
1228 144772 : find_L_tors_point(
1229 : ulong *ival,
1230 : ulong a4, ulong a6, ulong p, ulong pi,
1231 : ulong n, ulong L, ulong val)
1232 : {
1233 144772 : pari_sp av = avma;
1234 : ulong i;
1235 : GEN P, Q;
1236 : do {
1237 146233 : Q = random_Flj_pre(a4, a6, p, pi);
1238 146229 : P = Flj_mulu_pre(Q, n, a4, p, pi);
1239 146236 : } while (P[3] == 0);
1240 :
1241 281151 : for (i = 0; i < val; ++i) {
1242 235359 : Q = Flj_mulu_pre(P, L, a4, p, pi);
1243 235361 : if (Q[3] == 0) break;
1244 136376 : P = Q;
1245 : }
1246 144777 : if (ival) *ival = i;
1247 144777 : return gc_GEN(av, P);
1248 : }
1249 :
1250 : static GEN
1251 90290 : select_curve_with_L_tors_point(
1252 : ulong *a4, ulong *a6,
1253 : ulong L, ulong j, ulong n, ulong card, ulong val,
1254 : norm_eqn_t ne)
1255 : {
1256 90290 : pari_sp av = avma;
1257 : ulong A4, A4t, A6, A6t;
1258 90290 : ulong p = ne->p, pi = ne->pi;
1259 : GEN P;
1260 90290 : if (card % L != 0) {
1261 0 : pari_err_BUG("select_curve_with_L_tors_point: "
1262 : "Cardinality not divisible by L");
1263 : }
1264 :
1265 90290 : Fl_ellj_to_a4a6(j, p, &A4, &A6);
1266 90285 : Fl_elltwist_disc(A4, A6, ne->T, p, &A4t, &A6t);
1267 :
1268 : /* Either E = [a4, a6] or its twist has cardinality divisible by L
1269 : * because of the choice of p and t earlier on. We find out which
1270 : * by attempting to find a point of order L on each. See bot p16 of
1271 : * Sutherland 2012. */
1272 45795 : while (1) {
1273 : ulong i;
1274 136078 : P = find_L_tors_point(&i, A4, A6, p, pi, n, L, val);
1275 136083 : if (i < val)
1276 90287 : break;
1277 45796 : set_avma(av);
1278 45795 : lswap(A4, A4t);
1279 45795 : lswap(A6, A6t);
1280 : }
1281 90287 : *a4 = A4;
1282 90287 : *a6 = A6; return gc_GEN(av, P);
1283 : }
1284 :
1285 : /* Return 1 if the L-Sylow subgroup of the curve [a4, a6] (mod p) is
1286 : * cyclic, return 0 if it is not cyclic with "high" probability (I
1287 : * guess around 1/L^3 chance it is still cyclic when we return 0).
1288 : *
1289 : * Based on Sutherland's velu.c:velu_verify_Sylow_cyclic() in classpoly-1.0.1 */
1290 : INLINE long
1291 50485 : verify_L_sylow_is_cyclic(long e, ulong a4, ulong a6, ulong p, ulong pi)
1292 : {
1293 : /* Number of times to try to find a point with maximal order in the
1294 : * L-Sylow subgroup. */
1295 : enum { N_RETRIES = 3 };
1296 50485 : pari_sp av = avma;
1297 50485 : long i, res = 0;
1298 : GEN P;
1299 81237 : for (i = 0; i < N_RETRIES; ++i) {
1300 72539 : P = random_Flj_pre(a4, a6, p, pi);
1301 72548 : P = Flj_mulu_pre(P, e, a4, p, pi);
1302 72549 : if (P[3] != 0) { res = 1; break; }
1303 : }
1304 50495 : return gc_long(av,res);
1305 : }
1306 :
1307 : static ulong
1308 90286 : find_noniso_L_isogenous_curve(
1309 : ulong L, ulong n,
1310 : norm_eqn_t ne, long e, ulong val, ulong a4, ulong a6, GEN init_pt, long verify)
1311 : {
1312 : pari_sp ltop, av;
1313 90286 : ulong p = ne->p, pi = ne->pi, j_res = 0;
1314 90286 : GEN pt = init_pt;
1315 90286 : ltop = av = avma;
1316 8697 : while (1) {
1317 : /* c. Use Velu to calculate L-isogenous curve E' = E/<P> */
1318 : ulong a4_img, a6_img;
1319 98983 : ulong z2 = Fl_sqr_pre(pt[3], p, pi);
1320 98992 : pt = mkvecsmall2(Fl_div(pt[1], z2, p),
1321 98991 : Fl_div(pt[2], Fl_mul_pre(z2, pt[3], p, pi), p));
1322 98989 : Fle_quotient_from_kernel_generator(&a4_img, &a6_img,
1323 : a4, a6, pt, p, pi);
1324 :
1325 : /* d. If j(E') = j_res has a different endo ring to j(E), then
1326 : * return j(E'). Otherwise, go to b. */
1327 98973 : if (!verify || verify_L_sylow_is_cyclic(e, a4_img, a6_img, p, pi)) {
1328 90284 : j_res = Fl_ellj_pre(a4_img, a6_img, p, pi);
1329 90292 : break;
1330 : }
1331 :
1332 : /* b. Generate random point P on E of order L */
1333 8698 : set_avma(av);
1334 8698 : pt = find_L_tors_point(NULL, a4, a6, p, pi, n, L, val);
1335 : }
1336 90292 : return gc_ulong(ltop, j_res);
1337 : }
1338 :
1339 : /* Given a prime L and a j-invariant j (mod p), return the j-invariant
1340 : * of a curve which has a different endomorphism ring to j and is
1341 : * L-isogenous to j */
1342 : INLINE ulong
1343 90290 : compute_L_isogenous_curve(
1344 : ulong L, ulong n, norm_eqn_t ne,
1345 : ulong j, ulong card, ulong val, long verify)
1346 : {
1347 : ulong a4, a6;
1348 : long e;
1349 : GEN pt;
1350 :
1351 90290 : if (ne->p < 5 || j == 0 || j == 1728 % ne->p)
1352 0 : pari_err_BUG("compute_L_isogenous_curve");
1353 90290 : pt = select_curve_with_L_tors_point(&a4, &a6, L, j, n, card, val, ne);
1354 90286 : e = card / L;
1355 90286 : if (e * L != card) pari_err_BUG("compute_L_isogenous_curve");
1356 :
1357 90286 : return find_noniso_L_isogenous_curve(L, n, ne, e, val, a4, a6, pt, verify);
1358 : }
1359 :
1360 : INLINE GEN
1361 41799 : get_Lsqr_cycle(const disc_info *dinfo)
1362 : {
1363 41799 : long i, n1 = dinfo->n1, L = dinfo->L;
1364 41799 : GEN cyc = cgetg(L, t_VECSMALL);
1365 41799 : cyc[1] = 0;
1366 351999 : for (i = 2; i <= L / 2; ++i) cyc[i] = cyc[i - 1] + n1;
1367 41799 : if ( ! dinfo->L1) {
1368 116377 : for ( ; i < L; ++i) cyc[i] = cyc[i - 1] + n1;
1369 : } else {
1370 28021 : cyc[L - 1] = 2 * dinfo->n2 - n1 / 2;
1371 249400 : for (i = L - 2; i > L / 2; --i) cyc[i] = cyc[i + 1] - n1;
1372 : }
1373 41799 : return cyc;
1374 : }
1375 :
1376 : INLINE void
1377 618778 : update_Lsqr_cycle(GEN cyc, const disc_info *dinfo)
1378 : {
1379 618778 : long i, L = dinfo->L;
1380 17633987 : for (i = 1; i < L; ++i) ++cyc[i];
1381 618778 : if (dinfo->L1 && cyc[L - 1] == 2 * dinfo->n2) {
1382 26400 : long n1 = dinfo->n1;
1383 246838 : for (i = L / 2 + 1; i < L; ++i) cyc[i] -= n1;
1384 : }
1385 618778 : }
1386 :
1387 : static ulong
1388 41787 : oneroot_of_classpoly(GEN hilb, GEN factu, norm_eqn_t ne, GEN jdb)
1389 : {
1390 41787 : pari_sp av = avma;
1391 41787 : ulong j0, p = ne->p, pi = ne->pi;
1392 41787 : long i, nfactors = lg(gel(factu, 1)) - 1;
1393 41787 : GEN hilbp = ZX_to_Flx(hilb, p);
1394 :
1395 : /* TODO: Work out how to use hilb with better invariant */
1396 41776 : j0 = Flx_oneroot_split_pre(hilbp, p, pi);
1397 41795 : if (j0 == p) {
1398 0 : pari_err_BUG("oneroot_of_classpoly: "
1399 : "Didn't find a root of the class polynomial");
1400 : }
1401 43356 : for (i = 1; i <= nfactors; ++i) {
1402 1561 : long L = gel(factu, 1)[i];
1403 1561 : long val = gel(factu, 2)[i];
1404 1561 : GEN phi = polmodular_db_getp(jdb, L, p);
1405 1560 : val += z_lval(ne->v, L);
1406 1560 : j0 = descend_volcano(phi, j0, p, pi, 0, L, val, val);
1407 1561 : set_avma(av);
1408 : }
1409 41795 : return gc_ulong(av, j0);
1410 : }
1411 :
1412 : /* TODO: Precompute the GEN structs and link them to dinfo */
1413 : INLINE GEN
1414 3104 : make_pcp_surface(const disc_info *dinfo)
1415 : {
1416 3104 : GEN L = mkvecsmall(dinfo->L0);
1417 3104 : GEN n = mkvecsmall(dinfo->n1);
1418 3104 : GEN o = mkvecsmall(dinfo->n1);
1419 3104 : return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, 1, dinfo->n1));
1420 : }
1421 :
1422 : INLINE GEN
1423 3104 : make_pcp_floor(const disc_info *dinfo)
1424 : {
1425 3104 : long k = dinfo->L1 ? 2 : 1;
1426 : GEN L, n, o;
1427 3104 : if (k==1)
1428 : {
1429 1453 : L = mkvecsmall(dinfo->L0);
1430 1453 : n = mkvecsmall(dinfo->n2);
1431 1453 : o = mkvecsmall(dinfo->n2);
1432 : } else
1433 : {
1434 1651 : L = mkvecsmall2(dinfo->L0, dinfo->L1);
1435 1651 : n = mkvecsmall2(dinfo->n2, 2);
1436 1651 : o = mkvecsmall2(dinfo->n2, 2);
1437 : }
1438 3104 : return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, k, dinfo->n2*k));
1439 : }
1440 :
1441 : INLINE GEN
1442 41792 : enum_volcano_surface(norm_eqn_t ne, ulong j0, GEN fdb, GEN G)
1443 : {
1444 41792 : pari_sp av = avma;
1445 41792 : return gc_upto(av, enum_roots(j0, ne, fdb, G, NULL));
1446 : }
1447 :
1448 : INLINE GEN
1449 41797 : enum_volcano_floor(long L, norm_eqn_t ne, ulong j0_pr, GEN fdb, GEN G)
1450 : {
1451 41797 : pari_sp av = avma;
1452 : /* L^2 D is the discriminant for the order R = Z + L OO. */
1453 41797 : long DR = L * L * ne->D;
1454 41797 : long R_cond = L * ne->u; /* conductor(DR); */
1455 41797 : long w = R_cond * ne->v;
1456 : /* TODO: Calculate these once and for all in polmodular0_ZM(). */
1457 : norm_eqn_t eqn;
1458 41797 : memcpy(eqn, ne, sizeof *ne);
1459 41797 : eqn->D = DR;
1460 41797 : eqn->u = R_cond;
1461 41797 : eqn->v = w;
1462 41797 : return gc_upto(av, enum_roots(j0_pr, eqn, fdb, G, NULL));
1463 : }
1464 :
1465 : INLINE void
1466 20110 : carray_reverse_inplace(long *arr, long n)
1467 : {
1468 20110 : long lim = n>>1, i;
1469 20110 : --n;
1470 208290 : for (i = 0; i < lim; i++) lswap(arr[i], arr[n - i]);
1471 20110 : }
1472 :
1473 : INLINE void
1474 660599 : append_neighbours(GEN rts, GEN surface_js, long njs, long L, long m, long i)
1475 : {
1476 660599 : long r_idx = (((i - 1) + m) % njs) + 1; /* (i + m) % njs */
1477 660599 : long l_idx = umodsu((i - 1) - m, njs) + 1; /* (i - m) % njs */
1478 660579 : rts[L] = surface_js[l_idx];
1479 660579 : rts[L + 1] = surface_js[r_idx];
1480 660579 : }
1481 :
1482 : INLINE GEN
1483 44126 : roots_to_coeffs(GEN rts, ulong p, long L)
1484 : {
1485 44126 : long i, k, lrts= lg(rts);
1486 44126 : GEN M = cgetg(L+2+1, t_MAT);
1487 960955 : for (i = 1; i <= L+2; ++i)
1488 916826 : gel(M, i) = cgetg(lrts, t_VECSMALL);
1489 729881 : for (i = 1; i < lrts; ++i) {
1490 685821 : pari_sp av = avma;
1491 685821 : GEN modpol = Flv_roots_to_pol(gel(rts, i), p, 0);
1492 21843455 : for (k = 1; k <= L + 2; ++k) mael(M, k, i) = modpol[k + 1];
1493 685608 : set_avma(av);
1494 : }
1495 44060 : return M;
1496 : }
1497 :
1498 : /* NB: Assumes indices are offset at 0, not at 1 like in GENs;
1499 : * i.e. indices[i] will pick out v[indices[i] + 1] from v. */
1500 : INLINE void
1501 660594 : vecsmall_pick(GEN res, GEN v, GEN indices)
1502 : {
1503 : long i;
1504 18379939 : for (i = 1; i < lg(indices); ++i) res[i] = v[indices[i] + 1];
1505 660594 : }
1506 :
1507 : /* First element of surface_js must lie above the first element of floor_js.
1508 : * Reverse surface_js if it is not oriented in the same direction as floor_js */
1509 : INLINE GEN
1510 41798 : root_matrix(long L, const disc_info *dinfo, long njinvs, GEN surface_js,
1511 : GEN floor_js, ulong n, ulong card, ulong val, norm_eqn_t ne)
1512 : {
1513 : pari_sp av;
1514 41798 : long i, m = dinfo->dl1, njs = lg(surface_js) - 1, inv = dinfo->inv, rev;
1515 41798 : GEN rt_mat = zero_Flm_copy(L + 1, njinvs), rts, cyc;
1516 41799 : ulong p = ne->p, pi = ne->pi, j;
1517 41799 : av = avma;
1518 :
1519 41799 : i = 1;
1520 41799 : cyc = get_Lsqr_cycle(dinfo);
1521 41799 : rts = gel(rt_mat, i);
1522 41799 : vecsmall_pick(rts, floor_js, cyc);
1523 41799 : append_neighbours(rts, surface_js, njs, L, m, i);
1524 :
1525 41799 : i = 2;
1526 41799 : update_Lsqr_cycle(cyc, dinfo);
1527 41799 : rts = gel(rt_mat, i);
1528 41799 : vecsmall_pick(rts, floor_js, cyc);
1529 :
1530 : /* Fix orientation if necessary */
1531 41799 : if (modinv_is_double_eta(inv)) {
1532 : /* TODO: There is potential for refactoring between this,
1533 : * double_eta_initial_js and modfn_preimage. */
1534 6697 : pari_sp av0 = avma;
1535 6697 : GEN F = double_eta_Fl(inv, p);
1536 6697 : pari_sp av = avma;
1537 6697 : ulong r1 = double_eta_power(inv, uel(rts, 1), p, pi);
1538 6697 : GEN r, f = Flx_double_eta_jpoly(F, r1, p, pi);
1539 6697 : if ((j = Flx_oneroot_pre(f, p, pi)) == p) pari_err_BUG("root_matrix");
1540 6697 : j = compute_L_isogenous_curve(L, n, ne, j, card, val, 0);
1541 6697 : set_avma(av);
1542 6697 : r1 = double_eta_power(inv, uel(surface_js, i), p, pi);
1543 6697 : f = Flx_double_eta_jpoly(F, r1, p, pi);
1544 6697 : r = Flx_roots_pre(f, p, pi);
1545 6697 : if (lg(r) != 3) pari_err_BUG("root_matrix");
1546 6697 : rev = (j != uel(r, 1)) && (j != uel(r, 2));
1547 6697 : set_avma(av0);
1548 : } else {
1549 : ulong j1pr, j1;
1550 35102 : j1pr = modfn_preimage(uel(rts, 1), p, pi, dinfo->inv);
1551 35102 : j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
1552 35101 : rev = j1 != modfn_preimage(uel(surface_js, i), p, pi, dinfo->inv);
1553 : }
1554 41798 : if (rev)
1555 20110 : carray_reverse_inplace(surface_js + 2, njs - 1);
1556 41798 : append_neighbours(rts, surface_js, njs, L, m, i);
1557 :
1558 618785 : for (i = 3; i <= njinvs; ++i) {
1559 576988 : update_Lsqr_cycle(cyc, dinfo);
1560 577011 : rts = gel(rt_mat, i);
1561 577011 : vecsmall_pick(rts, floor_js, cyc);
1562 577012 : append_neighbours(rts, surface_js, njs, L, m, i);
1563 : }
1564 41797 : set_avma(av); return rt_mat;
1565 : }
1566 :
1567 : INLINE void
1568 44453 : interpolate_coeffs(GEN phi_modp, ulong p, GEN j_invs, GEN coeff_mat)
1569 : {
1570 44453 : pari_sp av = avma;
1571 : long i;
1572 44453 : GEN pols = Flv_Flm_polint(j_invs, coeff_mat, p, 0);
1573 963361 : for (i = 1; i < lg(pols); ++i) {
1574 918907 : GEN pol = gel(pols, i);
1575 918907 : long k, maxk = lg(pol);
1576 20672094 : for (k = 2; k < maxk; ++k) coeff(phi_modp, k - 1, i) = pol[k];
1577 : }
1578 44454 : set_avma(av);
1579 44456 : }
1580 :
1581 : INLINE long
1582 336717 : Flv_lastnonzero(GEN v)
1583 : {
1584 : long i;
1585 26648650 : for (i = lg(v) - 1; i > 0; --i)
1586 26647979 : if (v[i]) break;
1587 336717 : return i;
1588 : }
1589 :
1590 : /* Assuming the matrix of coefficients in phi corresponds to polynomials
1591 : * phi_k^* satisfying Y^c phi_k^*(Y^s) for c in {0, 1, ..., s} satisfying
1592 : * c + Lk = L + 1 (mod s), change phi so that the coefficients are for the
1593 : * polynomials Y^c phi_k^*(Y^s) (s is the sparsity factor) */
1594 : INLINE void
1595 9971 : inflate_polys(GEN phi, long L, long s)
1596 : {
1597 9971 : long k, deg = L + 1;
1598 : long maxr;
1599 9971 : maxr = nbrows(phi);
1600 346700 : for (k = 0; k <= deg; ) {
1601 336729 : long i, c = umodsu(L * (1 - k) + 1, s);
1602 : /* TODO: We actually know that the last nonzero element of gel(phi, k)
1603 : * can't be later than index n+1, where n is about (L + 1)/s. */
1604 336719 : ++k;
1605 5483380 : for (i = Flv_lastnonzero(gel(phi, k)); i > 0; --i) {
1606 5146661 : long r = c + (i - 1) * s + 1;
1607 5146661 : if (r > maxr) { coeff(phi, i, k) = 0; continue; }
1608 5076165 : if (r != i) {
1609 4973575 : coeff(phi, r, k) = coeff(phi, i, k);
1610 4973575 : coeff(phi, i, k) = 0;
1611 : }
1612 : }
1613 : }
1614 9971 : }
1615 :
1616 : INLINE void
1617 39845 : Flv_powu_inplace_pre(GEN v, ulong n, ulong p, ulong pi)
1618 : {
1619 : long i;
1620 333363 : for (i = 1; i < lg(v); ++i) v[i] = Fl_powu_pre(v[i], n, p, pi);
1621 39845 : }
1622 :
1623 : INLINE void
1624 9971 : normalise_coeffs(GEN coeffs, GEN js, long L, long s, ulong p, ulong pi)
1625 : {
1626 9971 : pari_sp av = avma;
1627 : long k;
1628 : GEN pows, modinv_js;
1629 :
1630 : /* NB: In fact it would be correct to return the coefficients "as is" when
1631 : * s = 1, but we make that an error anyway since this function should never
1632 : * be called with s = 1. */
1633 9971 : if (s <= 1) pari_err_BUG("normalise_coeffs");
1634 :
1635 : /* pows[i + 1] contains 1 / js[i + 1]^i for i = 0, ..., s - 1. */
1636 9971 : pows = cgetg(s + 1, t_VEC);
1637 9971 : gel(pows, 1) = const_vecsmall(lg(js) - 1, 1);
1638 9971 : modinv_js = Flv_inv_pre(js, p, pi);
1639 9971 : gel(pows, 2) = modinv_js;
1640 37668 : for (k = 3; k <= s; ++k) {
1641 27697 : gel(pows, k) = gcopy(modinv_js);
1642 27697 : Flv_powu_inplace_pre(gel(pows, k), k - 1, p, pi);
1643 : }
1644 :
1645 : /* For each column of coefficients coeffs[k] = [a0 .. an],
1646 : * replace ai by ai / js[i]^c.
1647 : * Said in another way, normalise each row i of coeffs by
1648 : * dividing through by js[i - 1]^c (where c depends on i). */
1649 346867 : for (k = 1; k < lg(coeffs); ++k) {
1650 336726 : long i, c = umodsu(L * (1 - (k - 1)) + 1, s);
1651 336725 : GEN col = gel(coeffs, k), C = gel(pows, c + 1);
1652 5845580 : for (i = 1; i < lg(col); ++i)
1653 5508684 : col[i] = Fl_mul_pre(col[i], C[i], p, pi);
1654 : }
1655 10141 : set_avma(av);
1656 9971 : }
1657 :
1658 : INLINE void
1659 6697 : double_eta_initial_js(
1660 : ulong *x0, ulong *x0pr, ulong j0, ulong j0pr, norm_eqn_t ne,
1661 : long inv, ulong L, ulong n, ulong card, ulong val)
1662 : {
1663 6697 : pari_sp av0 = avma;
1664 6697 : ulong p = ne->p, pi = ne->pi, s2 = ne->s2;
1665 6697 : GEN F = double_eta_Fl(inv, p);
1666 6697 : pari_sp av = avma;
1667 : ulong j1pr, j1, r, t;
1668 : GEN f, g;
1669 :
1670 6697 : *x0pr = modinv_double_eta_from_j(F, inv, j0pr, p, pi, s2);
1671 6697 : t = double_eta_power(inv, *x0pr, p, pi);
1672 6697 : f = Flx_div_by_X_x(Flx_double_eta_jpoly(F, t, p, pi), j0pr, p, &r);
1673 6697 : if (r) pari_err_BUG("double_eta_initial_js");
1674 6697 : j1pr = Flx_deg1_root(f, p);
1675 6697 : set_avma(av);
1676 :
1677 6697 : j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
1678 6697 : f = Flx_double_eta_xpoly(F, j0, p, pi);
1679 6697 : g = Flx_double_eta_xpoly(F, j1, p, pi);
1680 : /* x0 is the unique common root of f and g */
1681 6697 : *x0 = Flx_deg1_root(Flx_gcd(f, g, p), p);
1682 6697 : set_avma(av0);
1683 :
1684 6697 : if ( ! double_eta_root(inv, x0, *x0, p, pi, s2))
1685 0 : pari_err_BUG("double_eta_initial_js");
1686 6696 : }
1687 :
1688 : /* This is Sutherland 2012, Algorithm 2.1, p16. */
1689 : static GEN
1690 41783 : polmodular_split_p_Flm(ulong L, GEN hilb, GEN factu, norm_eqn_t ne, GEN db,
1691 : GEN G_surface, GEN G_floor, const disc_info *dinfo)
1692 : {
1693 : ulong j0, j0_rt, j0pr, j0pr_rt;
1694 41783 : ulong n, card, val, p = ne->p, pi = ne->pi;
1695 41783 : long inv = dinfo->inv, s = modinv_sparse_factor(inv);
1696 41782 : long nj_selected = ceil((L + 1)/(double)s) + 1;
1697 : GEN surface_js, floor_js, rts, phi_modp, jdb, fdb;
1698 41782 : long switched_signs = 0;
1699 :
1700 41782 : jdb = polmodular_db_for_inv(db, INV_J);
1701 41785 : fdb = polmodular_db_for_inv(db, inv);
1702 :
1703 : /* Precomputation */
1704 41785 : card = p + 1 - ne->t;
1705 41785 : val = u_lvalrem(card, L, &n); /* n = card / L^{v_L(card)} */
1706 :
1707 41786 : j0 = oneroot_of_classpoly(hilb, factu, ne, jdb);
1708 41796 : j0pr = compute_L_isogenous_curve(L, n, ne, j0, card, val, 1);
1709 41796 : if (modinv_is_double_eta(inv)) {
1710 6697 : double_eta_initial_js(&j0_rt, &j0pr_rt, j0, j0pr, ne, inv, L, n, card, val);
1711 : } else {
1712 35099 : j0_rt = modfn_root(j0, ne, inv);
1713 35098 : j0pr_rt = modfn_root(j0pr, ne, inv);
1714 : }
1715 41792 : surface_js = enum_volcano_surface(ne, j0_rt, fdb, G_surface);
1716 41797 : floor_js = enum_volcano_floor(L, ne, j0pr_rt, fdb, G_floor);
1717 41798 : rts = root_matrix(L, dinfo, nj_selected, surface_js, floor_js,
1718 : n, card, val, ne);
1719 2329 : do {
1720 44126 : pari_sp btop = avma;
1721 : long i;
1722 : GEN coeffs, surf;
1723 :
1724 44126 : coeffs = roots_to_coeffs(rts, p, L);
1725 44118 : surf = vecsmall_shorten(surface_js, nj_selected);
1726 44120 : if (s > 1) {
1727 9971 : normalise_coeffs(coeffs, surf, L, s, p, pi);
1728 9971 : Flv_powu_inplace_pre(surf, s, p, pi);
1729 : }
1730 44120 : phi_modp = zero_Flm_copy(L + 2, L + 2);
1731 44123 : interpolate_coeffs(phi_modp, p, surf, coeffs);
1732 44127 : if (s > 1) inflate_polys(phi_modp, L, s);
1733 :
1734 : /* TODO: Calculate just this coefficient of X^L Y^L, so we can do this
1735 : * test, then calculate the other coefficients; at the moment we are
1736 : * sometimes doing all the roots-to-coeffs, normalisation and interpolation
1737 : * work twice. */
1738 44127 : if (ucoeff(phi_modp, L + 1, L + 1) == p - 1) break;
1739 :
1740 2329 : if (switched_signs) pari_err_BUG("polmodular_split_p_Flm");
1741 :
1742 2329 : set_avma(btop);
1743 27893 : for (i = 1; i < lg(rts); ++i) {
1744 25564 : surface_js[i] = Fl_neg(surface_js[i], p);
1745 25564 : coeff(rts, L, i) = Fl_neg(coeff(rts, L, i), p);
1746 25564 : coeff(rts, L + 1, i) = Fl_neg(coeff(rts, L + 1, i), p);
1747 : }
1748 2329 : switched_signs = 1;
1749 : } while (1);
1750 41798 : dbg_printf(4)(" Phi_%lu(X, Y) (mod %lu) = %Ps\n", L, p, phi_modp);
1751 :
1752 41798 : return phi_modp;
1753 : }
1754 :
1755 : INLINE void
1756 2464 : Flv_deriv_pre_inplace(GEN v, long deg, ulong p, ulong pi)
1757 : {
1758 2464 : long i, ln = lg(v), d = deg % p;
1759 57202 : for (i = ln - 1; i > 1; --i, --d) v[i] = Fl_mul_pre(v[i - 1], d, p, pi);
1760 2464 : v[1] = 0;
1761 2464 : }
1762 :
1763 : INLINE GEN
1764 2674 : eval_modpoly_modp(GEN Tp, GEN j_powers, ulong p, ulong pi, int compute_derivs)
1765 : {
1766 2674 : long L = lg(j_powers) - 3;
1767 2674 : GEN j_pows_p = ZV_to_Flv(j_powers, p);
1768 2674 : GEN tmp = cgetg(2 + 2 * compute_derivs, t_VEC);
1769 : /* We wrap the result in this t_VEC Tp to trick the
1770 : * ZM_*_CRT() functions into thinking it's a matrix. */
1771 2673 : gel(tmp, 1) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1772 2674 : if (compute_derivs) {
1773 1232 : Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
1774 1232 : gel(tmp, 2) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1775 1232 : Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
1776 1232 : gel(tmp, 3) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
1777 : }
1778 2674 : return tmp;
1779 : }
1780 :
1781 : /* Parallel interface */
1782 : GEN
1783 41791 : polmodular_worker(GEN tp, ulong L, GEN hilb, GEN factu, GEN vne, GEN vinfo,
1784 : long derivs, GEN j_powers, GEN G_surface, GEN G_floor,
1785 : GEN fdb)
1786 : {
1787 41791 : pari_sp av = avma;
1788 : norm_eqn_t ne;
1789 41791 : long D = vne[1], u = vne[2];
1790 41791 : ulong vL, t = tp[1], p = tp[2];
1791 : GEN Tp;
1792 :
1793 41791 : if (! uissquareall((4 * p - t * t) / -D, &vL))
1794 0 : pari_err_BUG("polmodular_worker");
1795 41793 : norm_eqn_set(ne, D, t, u, vL, NULL, p); /* L | vL */
1796 41780 : Tp = polmodular_split_p_Flm(L, hilb, factu, ne, fdb,
1797 : G_surface, G_floor, (const disc_info*)vinfo);
1798 41798 : if (!isintzero(j_powers))
1799 2674 : Tp = eval_modpoly_modp(Tp, j_powers, ne->p, ne->pi, derivs);
1800 41798 : return gc_upto(av, Tp);
1801 : }
1802 :
1803 : static GEN
1804 24806 : sympol_to_ZM(GEN phi, long L)
1805 : {
1806 24806 : pari_sp av = avma;
1807 24806 : GEN res = zeromatcopy(L + 2, L + 2);
1808 24806 : long i, j, c = 1;
1809 108531 : for (i = 1; i <= L + 1; ++i)
1810 277410 : for (j = 1; j <= i; ++j, ++c)
1811 193685 : gcoeff(res, i, j) = gcoeff(res, j, i) = gel(phi, c);
1812 24806 : gcoeff(res, L + 2, 1) = gcoeff(res, 1, L + 2) = gen_1;
1813 24806 : return gc_GEN(av, res);
1814 : }
1815 :
1816 : static GEN polmodular_small_ZM(long L, long inv, GEN *db);
1817 :
1818 : INLINE long
1819 28158 : modinv_max_internal_level(long inv)
1820 : {
1821 28158 : switch (inv) {
1822 25355 : case INV_J: return 5;
1823 252 : case INV_G2: return 2;
1824 443 : case INV_F:
1825 : case INV_F2:
1826 : case INV_F4:
1827 443 : case INV_F8: return 5;
1828 210 : case INV_W2W5:
1829 210 : case INV_W2W5E2: return 7;
1830 497 : case INV_W2W3:
1831 : case INV_W2W3E2:
1832 : case INV_W3W3:
1833 497 : case INV_W3W7: return 5;
1834 63 : case INV_W3W3E2:return 2;
1835 680 : case INV_F3:
1836 : case INV_W2W7:
1837 : case INV_W2W7E2:
1838 680 : case INV_W2W13: return 3;
1839 658 : case INV_W3W5:
1840 : case INV_W5W7:
1841 : case INV_W3W13:
1842 : case INV_ATKIN3:
1843 : case INV_ATKIN5:
1844 : case INV_ATKIN7:
1845 : case INV_ATKIN11:
1846 : case INV_ATKIN13:
1847 : case INV_ATKIN17:
1848 : case INV_ATKIN19:
1849 : case INV_ATKIN23:
1850 658 : case INV_ATKIN29: return 2;
1851 : }
1852 : pari_err_BUG("modinv_max_internal_level"); return LONG_MAX;/*LCOV_EXCL_LINE*/
1853 : }
1854 : static void
1855 24 : db_add_levels(GEN *db, GEN P, long inv)
1856 24 : { polmodular_db_add_levels(db, zv_to_longptr(P), lg(P)-1, inv); }
1857 :
1858 : GEN
1859 28039 : polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db)
1860 : {
1861 28039 : pari_sp ltop = avma;
1862 28039 : long k, d, Dcnt, nprimes = 0;
1863 : GEN modpoly, plist, tp, j_powers;
1864 : disc_info Ds[MODPOLY_MAX_DCNT];
1865 28039 : long lvl = modinv_level(inv);
1866 28039 : if (ugcd(L, lvl) != 1)
1867 7 : pari_err_DOMAIN("polmodular0_ZM", "invariant",
1868 : "incompatible with", stoi(L), stoi(lvl));
1869 :
1870 28032 : dbg_printf(1)("Calculating modular polynomial of level %lu for invariant %d\n", L, inv);
1871 28032 : if (L <= modinv_max_internal_level(inv)) return polmodular_small_ZM(L,inv,db);
1872 :
1873 3086 : Dcnt = discriminant_with_classno_at_least(Ds, L, inv, Q, USE_SPARSE_FACTOR);
1874 6190 : for (d = 0; d < Dcnt; d++) nprimes += Ds[d].nprimes;
1875 3086 : modpoly = cgetg(nprimes+1, t_VEC);
1876 3086 : plist = cgetg(nprimes+1, t_VECSMALL);
1877 3086 : tp = mkvec(mkvecsmall2(0,0));
1878 3086 : j_powers = gen_0;
1879 3086 : if (J) {
1880 63 : compute_derivs = !!compute_derivs;
1881 63 : j_powers = Fp_powers(J, L+1, Q);
1882 : }
1883 6190 : for (d = 0, k = 1; d < Dcnt; d++)
1884 : {
1885 3104 : disc_info *dinfo = &Ds[d];
1886 : struct pari_mt pt;
1887 3104 : const long D = dinfo->D1, DK = dinfo->D0;
1888 3104 : const ulong cond = usqrt(D / DK);
1889 3104 : long i, pending = 0;
1890 3104 : GEN worker, hilb, factu = factoru(cond);
1891 :
1892 3104 : polmodular_db_add_level(db, dinfo->L0, inv);
1893 3104 : if (dinfo->L1) polmodular_db_add_level(db, dinfo->L1, inv);
1894 3104 : dbg_printf(1)("Selected discriminant D = %ld = %ld^2 * %ld.\n", D,cond,DK);
1895 3104 : hilb = polclass0(DK, INV_J, 0, db);
1896 3104 : if (cond > 1) db_add_levels(db, gel(factu,1), INV_J);
1897 3104 : dbg_printf(1)("D = %ld, L0 = %lu, L1 = %lu, ", dinfo->D1, dinfo->L0, dinfo->L1);
1898 3104 : dbg_printf(1)("n1 = %lu, n2 = %lu, dl1 = %lu, dl2_0 = %lu, dl2_1 = %lu\n",
1899 : dinfo->n1, dinfo->n2, dinfo->dl1, dinfo->dl2_0, dinfo->dl2_1);
1900 3104 : dbg_printf(0)("Calculating modular polynomial of level %lu:", L);
1901 :
1902 3104 : worker = snm_closure(is_entry("_polmodular_worker"),
1903 : mkvecn(10, utoi(L), hilb, factu, mkvecsmall2(D, cond),
1904 : (GEN)dinfo, stoi(compute_derivs), j_powers,
1905 : make_pcp_surface(dinfo),
1906 : make_pcp_floor(dinfo), *db));
1907 3104 : mt_queue_start_lim(&pt, worker, dinfo->nprimes);
1908 49049 : for (i = 0; i < dinfo->nprimes || pending; i++)
1909 : {
1910 : long workid;
1911 : GEN done;
1912 45945 : if (i < dinfo->nprimes)
1913 : {
1914 41799 : mael(tp, 1, 1) = dinfo->traces[i];
1915 41799 : mael(tp, 1, 2) = dinfo->primes[i];
1916 : }
1917 45945 : mt_queue_submit(&pt, i, i < dinfo->nprimes? tp: NULL);
1918 45945 : done = mt_queue_get(&pt, &workid, &pending);
1919 45945 : if (done)
1920 : {
1921 41799 : plist[k] = dinfo->primes[workid];
1922 41799 : gel(modpoly, k) = done; k++;
1923 41799 : dbg_printf(0)(" %ld%%", k*100/nprimes);
1924 : }
1925 : }
1926 3104 : dbg_printf(0)(" done\n");
1927 3104 : mt_queue_end(&pt);
1928 3104 : killblock((GEN)dinfo->primes);
1929 : }
1930 3086 : modpoly = nmV_chinese_center(modpoly, plist, NULL);
1931 3086 : if (J) modpoly = FpM_red(modpoly, Q);
1932 3086 : return gc_upto(ltop, modpoly);
1933 : }
1934 :
1935 : GEN
1936 19266 : polmodular_ZM(long L, long inv)
1937 : {
1938 : GEN db, Phi;
1939 :
1940 19266 : if (L < 2)
1941 7 : pari_err_DOMAIN("polmodular_ZM", "L", "<", gen_2, stoi(L));
1942 :
1943 : /* TODO: Handle nonprime L. Algorithm 1.1 and Corollary 3.4 in Sutherland,
1944 : * "Class polynomials for nonholomorphic modular functions" */
1945 19259 : if (! uisprime(L)) pari_err_IMPL("composite level");
1946 :
1947 19252 : db = polmodular_db_init(inv);
1948 19252 : Phi = polmodular0_ZM(L, inv, NULL, NULL, 0, &db);
1949 19245 : gunclone_deep(db); return Phi;
1950 : }
1951 :
1952 : GEN
1953 19182 : polmodular_ZXX(long L, long inv, long vx, long vy)
1954 : {
1955 19182 : pari_sp av = avma;
1956 19182 : GEN phi = polmodular_ZM(L, inv);
1957 :
1958 19161 : if (vx < 0) vx = 0;
1959 19161 : if (vy < 0) vy = 1;
1960 19161 : if (varncmp(vx, vy) >= 0)
1961 14 : pari_err_PRIORITY("polmodular_ZXX", pol_x(vx), "<=", vy);
1962 19147 : return gc_GEN(av, RgM_to_RgXX(phi, vx, vy));
1963 : }
1964 :
1965 : INLINE GEN
1966 56 : FpV_deriv(GEN v, long deg, GEN P)
1967 : {
1968 56 : long i, ln = lg(v);
1969 56 : GEN dv = cgetg(ln, t_VEC);
1970 392 : for (i = ln-1; i > 1; i--, deg--) gel(dv, i) = Fp_mulu(gel(v, i-1), deg, P);
1971 56 : gel(dv, 1) = gen_0; return dv;
1972 : }
1973 :
1974 : GEN
1975 126 : Fp_polmodular_evalx(long L, long inv, GEN J, GEN P, long v, int compute_derivs)
1976 : {
1977 126 : pari_sp av = avma;
1978 : GEN db, phi;
1979 :
1980 126 : if (L <= modinv_max_internal_level(inv)) {
1981 : GEN tmp;
1982 63 : GEN phi = RgM_to_FpM(polmodular_ZM(L, inv), P);
1983 63 : GEN j_powers = Fp_powers(J, L + 1, P);
1984 63 : GEN modpol = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1985 63 : if (compute_derivs) {
1986 28 : tmp = cgetg(4, t_VEC);
1987 28 : gel(tmp, 1) = modpol;
1988 28 : j_powers = FpV_deriv(j_powers, L + 1, P);
1989 28 : gel(tmp, 2) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1990 28 : j_powers = FpV_deriv(j_powers, L + 1, P);
1991 28 : gel(tmp, 3) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
1992 : } else
1993 35 : tmp = modpol;
1994 63 : return gc_GEN(av, tmp);
1995 : }
1996 :
1997 63 : db = polmodular_db_init(inv);
1998 63 : phi = polmodular0_ZM(L, inv, J, P, compute_derivs, &db);
1999 63 : phi = RgM_to_RgXV(phi, v);
2000 63 : gunclone_deep(db);
2001 63 : return gc_GEN(av, compute_derivs? phi: gel(phi, 1));
2002 : }
2003 :
2004 : GEN
2005 651 : polmodular(long L, long inv, GEN x, long v, long compute_derivs)
2006 : {
2007 651 : pari_sp av = avma;
2008 : long tx;
2009 651 : GEN J = NULL, P = NULL, res = NULL, one = NULL;
2010 :
2011 651 : check_modinv(inv);
2012 644 : if (!x || gequalX(x)) {
2013 504 : long xv = 0;
2014 504 : if (x) xv = varn(x);
2015 504 : if (compute_derivs) pari_err_FLAG("polmodular");
2016 497 : return polmodular_ZXX(L, inv, xv, v);
2017 : }
2018 :
2019 140 : tx = typ(x);
2020 140 : if (tx == t_INTMOD) {
2021 63 : J = gel(x, 2);
2022 63 : P = gel(x, 1);
2023 63 : one = mkintmod(gen_1, P);
2024 77 : } else if (tx == t_FFELT) {
2025 70 : J = FF_to_FpXQ_i(x);
2026 70 : if (degpol(J) > 0)
2027 7 : pari_err_DOMAIN("polmodular", "x", "not in prime subfield ", gen_0, x);
2028 63 : J = constant_coeff(J);
2029 63 : P = FF_p_i(x);
2030 63 : one = FF_1(x);
2031 : } else
2032 7 : pari_err_TYPE("polmodular", x);
2033 :
2034 126 : if (v < 0) v = 1;
2035 126 : res = Fp_polmodular_evalx(L, inv, J, P, v, compute_derivs);
2036 126 : return gc_upto(av, gmul(res, one));
2037 : }
2038 :
2039 : /* SECTION: Modular polynomials of level <= MAX_INTERNAL_MODPOLY_LEVEL. */
2040 :
2041 : /* These functions return a vector of coefficients of classical modular
2042 : * polynomials Phi_L(X,Y) of small level L. The number of such coefficients is
2043 : * (L+1)(L+2)/2 since Phi is symmetric. We omit the common coefficient of
2044 : * X^{L+1} and Y^{L+1} since it is always 1. Use sympol_to_ZM() to get the
2045 : * corresponding desymmetrised matrix of coefficients */
2046 :
2047 : /* Phi2, the modular polynomial of level 2:
2048 : *
2049 : * X^3 + X^2 * (-Y^2 + 1488*Y - 162000)
2050 : * + X * (1488*Y^2 + 40773375*Y + 8748000000)
2051 : * + Y^3 - 162000*Y^2 + 8748000000*Y - 157464000000000
2052 : *
2053 : * [[3, 0, 1],
2054 : * [2, 2, -1],
2055 : * [2, 1, 1488],
2056 : * [2, 0, -162000],
2057 : * [1, 1, 40773375],
2058 : * [1, 0, 8748000000],
2059 : * [0, 0, -157464000000000]], */
2060 : static GEN
2061 20015 : phi2_ZV(void)
2062 : {
2063 20015 : GEN phi2 = cgetg(7, t_VEC);
2064 20015 : gel(phi2, 1) = uu32toi(36662, 1908994048);
2065 20015 : setsigne(gel(phi2, 1), -1);
2066 20015 : gel(phi2, 2) = uu32toi(2, 158065408);
2067 20015 : gel(phi2, 3) = stoi(40773375);
2068 20015 : gel(phi2, 4) = stoi(-162000);
2069 20015 : gel(phi2, 5) = stoi(1488);
2070 20015 : gel(phi2, 6) = gen_m1;
2071 20015 : return phi2;
2072 : }
2073 :
2074 : /* L = 3
2075 : *
2076 : * [4, 0, 1],
2077 : * [3, 3, -1],
2078 : * [3, 2, 2232],
2079 : * [3, 1, -1069956],
2080 : * [3, 0, 36864000],
2081 : * [2, 2, 2587918086],
2082 : * [2, 1, 8900222976000],
2083 : * [2, 0, 452984832000000],
2084 : * [1, 1, -770845966336000000],
2085 : * [1, 0, 1855425871872000000000]
2086 : * [0, 0, 0]
2087 : *
2088 : * 1855425871872000000000 = 2^32 * (100 * 2^32 + 2503270400) */
2089 : static GEN
2090 1910 : phi3_ZV(void)
2091 : {
2092 1910 : GEN phi3 = cgetg(11, t_VEC);
2093 1910 : pari_sp av = avma;
2094 1910 : gel(phi3, 1) = gen_0;
2095 1910 : gel(phi3, 2) = gc_upto(av, shifti(uu32toi(100, 2503270400UL), 32));
2096 1910 : gel(phi3, 3) = uu32toi(179476562, 2147483648UL);
2097 1910 : setsigne(gel(phi3, 3), -1);
2098 1910 : gel(phi3, 4) = uu32toi(105468, 3221225472UL);
2099 1910 : gel(phi3, 5) = uu32toi(2072, 1050738688);
2100 1910 : gel(phi3, 6) = utoi(2587918086UL);
2101 1910 : gel(phi3, 7) = stoi(36864000);
2102 1910 : gel(phi3, 8) = stoi(-1069956);
2103 1910 : gel(phi3, 9) = stoi(2232);
2104 1910 : gel(phi3, 10) = gen_m1;
2105 1910 : return phi3;
2106 : }
2107 :
2108 : static GEN
2109 1880 : phi5_ZV(void)
2110 : {
2111 1880 : GEN phi5 = cgetg(22, t_VEC);
2112 1880 : gel(phi5, 1) = mkintn(5, 0x18c2cc9cUL, 0x484382b2UL, 0xdc000000UL, 0x0UL, 0x0UL);
2113 1880 : gel(phi5, 2) = mkintn(5, 0x2638fUL, 0x2ff02690UL, 0x68026000UL, 0x0UL, 0x0UL);
2114 1880 : gel(phi5, 3) = mkintn(5, 0x308UL, 0xac9d9a4UL, 0xe0fdab12UL, 0xc0000000UL, 0x0UL);
2115 1880 : setsigne(gel(phi5, 3), -1);
2116 1880 : gel(phi5, 4) = mkintn(5, 0x13UL, 0xaae09f9dUL, 0x1b5ef872UL, 0x30000000UL, 0x0UL);
2117 1880 : gel(phi5, 5) = mkintn(4, 0x1b802fa9UL, 0x77ba0653UL, 0xd2f78000UL, 0x0UL);
2118 1880 : gel(phi5, 6) = mkintn(4, 0xfbfdUL, 0x278e4756UL, 0xdf08a7c4UL, 0x40000000UL);
2119 1880 : gel(phi5, 7) = mkintn(4, 0x35f922UL, 0x62ccea6fUL, 0x153d0000UL, 0x0UL);
2120 1880 : gel(phi5, 8) = mkintn(4, 0x97dUL, 0x29203fafUL, 0xc3036909UL, 0x80000000UL);
2121 1880 : setsigne(gel(phi5, 8), -1);
2122 1880 : gel(phi5, 9) = mkintn(3, 0x56e9e892UL, 0xd7781867UL, 0xf2ea0000UL);
2123 1880 : gel(phi5, 10) = mkintn(3, 0x5d6dUL, 0xe0a58f4eUL, 0x9ee68c14UL);
2124 1880 : setsigne(gel(phi5, 10), -1);
2125 1880 : gel(phi5, 11) = mkintn(3, 0x1100dUL, 0x85cea769UL, 0x40000000UL);
2126 1880 : gel(phi5, 12) = mkintn(3, 0x1b38UL, 0x43cf461fUL, 0x3a900000UL);
2127 1880 : gel(phi5, 13) = mkintn(3, 0x14UL, 0xc45a616eUL, 0x4801680fUL);
2128 1880 : gel(phi5, 14) = uu32toi(0x17f4350UL, 0x493ca3e0UL);
2129 1880 : gel(phi5, 15) = uu32toi(0x183UL, 0xe54ce1f8UL);
2130 1880 : gel(phi5, 16) = uu32toi(0x1c9UL, 0x18860000UL);
2131 1880 : gel(phi5, 17) = uu32toi(0x39UL, 0x6f7a2206UL);
2132 1880 : setsigne(gel(phi5, 17), -1);
2133 1880 : gel(phi5, 18) = stoi(2028551200);
2134 1880 : gel(phi5, 19) = stoi(-4550940);
2135 1880 : gel(phi5, 20) = stoi(3720);
2136 1880 : gel(phi5, 21) = gen_m1;
2137 1880 : return phi5;
2138 : }
2139 :
2140 : static GEN
2141 189 : phi5_f_ZV(void)
2142 : {
2143 189 : GEN phi = zerovec(21);
2144 189 : gel(phi, 3) = stoi(4);
2145 189 : gel(phi, 21) = gen_m1;
2146 189 : return phi;
2147 : }
2148 :
2149 : static GEN
2150 14 : phi3_f3_ZV(void)
2151 : {
2152 14 : GEN phi = zerovec(10);
2153 14 : gel(phi, 3) = stoi(8);
2154 14 : gel(phi, 10) = gen_m1;
2155 14 : return phi;
2156 : }
2157 :
2158 : static GEN
2159 98 : phi2_g2_ZV(void)
2160 98 : { return mkvec6s(-54000,0,495,0,0,-1); }
2161 :
2162 : static GEN
2163 56 : phi5_w2w3_ZV(void)
2164 : {
2165 56 : GEN phi = zerovec(21);
2166 56 : gel(phi, 3) = gen_m1;
2167 56 : gel(phi, 10) = stoi(5);
2168 56 : gel(phi, 21) = gen_m1;
2169 56 : return phi;
2170 : }
2171 :
2172 : static GEN
2173 91 : phi7_w2w5_ZV(void)
2174 : {
2175 91 : GEN phi = zerovec(36);
2176 91 : gel(phi, 3) = gen_m1;
2177 91 : gel(phi, 15) = stoi(56);
2178 91 : gel(phi, 19) = stoi(42);
2179 91 : gel(phi, 24) = stoi(21);
2180 91 : gel(phi, 30) = stoi(7);
2181 91 : gel(phi, 36) = gen_m1;
2182 91 : return phi;
2183 : }
2184 :
2185 : static GEN
2186 63 : phi5_w3w3_ZV(void)
2187 : {
2188 63 : GEN phi = zerovec(21);
2189 63 : gel(phi, 3) = stoi(9);
2190 63 : gel(phi, 6) = stoi(-15);
2191 63 : gel(phi, 15) = stoi(5);
2192 63 : gel(phi, 21) = gen_m1;
2193 63 : return phi;
2194 : }
2195 :
2196 : static GEN
2197 182 : phi3_w2w7_ZV(void)
2198 : {
2199 182 : GEN phi = zerovec(10);
2200 182 : gel(phi, 3) = gen_m1;
2201 182 : gel(phi, 6) = stoi(3);
2202 182 : gel(phi, 10) = gen_m1;
2203 182 : return phi;
2204 : }
2205 :
2206 : static GEN
2207 35 : phi2_w3w5_ZV(void)
2208 35 : { return mkvec6s(0,0,1,0,0,-1); }
2209 :
2210 : static GEN
2211 49 : phi5_w3w7_ZV(void)
2212 : {
2213 49 : GEN phi = zerovec(21);
2214 49 : gel(phi, 3) = gen_m1;
2215 49 : gel(phi, 6) = stoi(10);
2216 49 : gel(phi, 8) = stoi(5);
2217 49 : gel(phi, 10) = stoi(35);
2218 49 : gel(phi, 13) = stoi(20);
2219 49 : gel(phi, 15) = stoi(10);
2220 49 : gel(phi, 17) = stoi(5);
2221 49 : gel(phi, 19) = stoi(5);
2222 49 : gel(phi, 21) = gen_m1;
2223 49 : return phi;
2224 : }
2225 :
2226 : static GEN
2227 35 : phi3_w2w13_ZV(void)
2228 : {
2229 35 : GEN phi = zerovec(10);
2230 35 : gel(phi, 3) = gen_m1;
2231 35 : gel(phi, 6) = stoi(3);
2232 35 : gel(phi, 8) = stoi(3);
2233 35 : gel(phi, 10) = gen_m1;
2234 35 : return phi;
2235 : }
2236 :
2237 : static GEN
2238 21 : phi2_w3w3e2_ZV(void)
2239 21 : { return mkvec6s(0,0,3,0,0,-1); }
2240 :
2241 : static GEN
2242 70 : phi2_w5w7_ZV(void)
2243 70 : { return mkvec6s(0,0,1,0,2,-1); }
2244 :
2245 : static GEN
2246 14 : phi2_w3w13_ZV(void)
2247 14 : { return mkvec6s(0,0,-1,0,2,-1); }
2248 :
2249 : static GEN
2250 7 : phi2_atkin3_ZV(void)
2251 7 : { return mkvec6s(28166076,741474,17343,1566,0,-1); }
2252 :
2253 : static GEN
2254 14 : phi2_atkin5_ZV(void)
2255 14 : { return mkvec6s(323456,24244,1519,268,0,-1); }
2256 :
2257 : static GEN
2258 7 : phi2_atkin7_ZV(void)
2259 7 : { return mkvec6s(27100,3810,407,102,0,-1); }
2260 :
2261 : static GEN
2262 0 : phi2_atkin11_ZV(void)
2263 0 : { return mkvec6s(1600,470,91,34,0,-1); }
2264 :
2265 : static GEN
2266 0 : phi2_atkin13_ZV(void)
2267 0 : { return mkvec6s(656,240,55,24,0,-1); }
2268 :
2269 : static GEN
2270 0 : phi2_atkin17_ZV(void)
2271 0 : { return mkvec6s(156,86,27,14,0,-1); }
2272 :
2273 : static GEN
2274 14 : phi2_atkin19_ZV(void)
2275 14 : { return mkvec6s(100,60,19,12,0,-1); }
2276 :
2277 : static GEN
2278 21 : phi2_atkin23_ZV(void)
2279 21 : { return mkvec6s(2,6,9,4,2,-1); }
2280 :
2281 : static GEN
2282 21 : phi2_atkin29_ZV(void)
2283 21 : { return mkvec6s(0,0,3,2,2,-1); }
2284 :
2285 : INLINE long
2286 140 : modinv_parent(long inv)
2287 : {
2288 140 : switch (inv) {
2289 42 : case INV_F2:
2290 : case INV_F4:
2291 42 : case INV_F8: return INV_F;
2292 14 : case INV_W2W3E2: return INV_W2W3;
2293 21 : case INV_W2W5E2: return INV_W2W5;
2294 63 : case INV_W2W7E2: return INV_W2W7;
2295 0 : case INV_W3W3E2: return INV_W3W3;
2296 : default: pari_err_BUG("modinv_parent"); return -1;/*LCOV_EXCL_LINE*/
2297 : }
2298 : }
2299 :
2300 : /* TODO: Think of a better name than "parent power"; sheesh. */
2301 : INLINE long
2302 140 : modinv_parent_power(long inv)
2303 : {
2304 140 : switch (inv) {
2305 14 : case INV_F4: return 4;
2306 14 : case INV_F8: return 8;
2307 112 : case INV_F2:
2308 : case INV_W2W3E2:
2309 : case INV_W2W5E2:
2310 : case INV_W2W7E2:
2311 112 : case INV_W3W3E2: return 2;
2312 : default: pari_err_BUG("modinv_parent_power"); return -1;/*LCOV_EXCL_LINE*/
2313 : }
2314 : }
2315 :
2316 : static GEN
2317 140 : polmodular0_powerup_ZM(long L, long inv, GEN *db)
2318 : {
2319 140 : pari_sp ltop = avma, av;
2320 : long s, D, nprimes, N;
2321 : GEN mp, pol, P, H;
2322 140 : long parent = modinv_parent(inv);
2323 140 : long e = modinv_parent_power(inv);
2324 : disc_info Ds[MODPOLY_MAX_DCNT];
2325 : /* FIXME: We throw away the table of fundamental discriminants here. */
2326 140 : long nDs = discriminant_with_classno_at_least(Ds, L, inv, NULL, IGNORE_SPARSE_FACTOR);
2327 140 : if (nDs != 1) pari_err_BUG("polmodular0_powerup_ZM");
2328 140 : D = Ds[0].D1;
2329 140 : nprimes = Ds[0].nprimes + 1;
2330 140 : mp = polmodular0_ZM(L, parent, NULL, NULL, 0, db);
2331 140 : H = polclass0(D, parent, 0, db);
2332 :
2333 140 : N = L + 2;
2334 140 : if (degpol(H) < N) pari_err_BUG("polmodular0_powerup_ZM");
2335 :
2336 140 : av = avma;
2337 140 : pol = ZM_init_CRT(zero_Flm_copy(N, L + 2), 1);
2338 140 : P = gen_1;
2339 469 : for (s = 1; s < nprimes; ++s) {
2340 : pari_sp av1, av2;
2341 329 : ulong p = Ds[0].primes[s-1], pi = get_Fl_red(p);
2342 : long i;
2343 : GEN Hrts, js, Hp, Phip, coeff_mat, phi_modp;
2344 :
2345 329 : phi_modp = zero_Flm_copy(N, L + 2);
2346 329 : av1 = avma;
2347 329 : Hp = ZX_to_Flx(H, p);
2348 329 : Hrts = Flx_roots_pre(Hp, p, pi);
2349 329 : if (lg(Hrts)-1 < N) pari_err_BUG("polmodular0_powerup_ZM");
2350 329 : js = cgetg(N + 1, t_VECSMALL);
2351 2506 : for (i = 1; i <= N; ++i)
2352 2177 : uel(js, i) = Fl_powu_pre(uel(Hrts, i), e, p, pi);
2353 :
2354 329 : Phip = ZM_to_Flm(mp, p);
2355 329 : coeff_mat = zero_Flm_copy(N, L + 2);
2356 329 : av2 = avma;
2357 2506 : for (i = 1; i <= N; ++i) {
2358 : long k;
2359 : GEN phi_at_ji, mprts;
2360 :
2361 2177 : phi_at_ji = Flm_Fl_polmodular_evalx(Phip, L, uel(Hrts, i), p, pi);
2362 2177 : mprts = Flx_roots_pre(phi_at_ji, p, pi);
2363 2177 : if (lg(mprts) != L + 2) pari_err_BUG("polmodular0_powerup_ZM");
2364 :
2365 2177 : Flv_powu_inplace_pre(mprts, e, p, pi);
2366 2177 : phi_at_ji = Flv_roots_to_pol(mprts, p, 0);
2367 :
2368 17290 : for (k = 1; k <= L + 2; ++k)
2369 15113 : ucoeff(coeff_mat, i, k) = uel(phi_at_ji, k + 1);
2370 2177 : set_avma(av2);
2371 : }
2372 :
2373 329 : interpolate_coeffs(phi_modp, p, js, coeff_mat);
2374 329 : set_avma(av1);
2375 :
2376 329 : (void) ZM_incremental_CRT(&pol, phi_modp, &P, p);
2377 329 : if (gc_needed(av, 2)) (void)gc_all(av, 2, &pol, &P);
2378 : }
2379 140 : killblock((GEN)Ds[0].primes); return gc_upto(ltop, pol);
2380 : }
2381 :
2382 : /* Returns the modular polynomial with the smallest level for the given
2383 : * invariant, except if inv is INV_J, in which case return the modular
2384 : * polynomial of level L in {2,3,5}. NULL is returned if the modular
2385 : * polynomial can be calculated using polmodular0_powerup_ZM. */
2386 : INLINE GEN
2387 24946 : internal_db(long L, long inv)
2388 : {
2389 24946 : switch (inv) {
2390 23805 : case INV_J: switch (L) {
2391 20015 : case 2: return phi2_ZV();
2392 1910 : case 3: return phi3_ZV();
2393 1880 : case 5: return phi5_ZV();
2394 0 : default: break;
2395 : }
2396 189 : case INV_F: return phi5_f_ZV();
2397 14 : case INV_F2: return NULL;
2398 14 : case INV_F3: return phi3_f3_ZV();
2399 14 : case INV_F4: return NULL;
2400 98 : case INV_G2: return phi2_g2_ZV();
2401 56 : case INV_W2W3: return phi5_w2w3_ZV();
2402 14 : case INV_F8: return NULL;
2403 63 : case INV_W3W3: return phi5_w3w3_ZV();
2404 91 : case INV_W2W5: return phi7_w2w5_ZV();
2405 182 : case INV_W2W7: return phi3_w2w7_ZV();
2406 35 : case INV_W3W5: return phi2_w3w5_ZV();
2407 49 : case INV_W3W7: return phi5_w3w7_ZV();
2408 14 : case INV_W2W3E2: return NULL;
2409 21 : case INV_W2W5E2: return NULL;
2410 35 : case INV_W2W13: return phi3_w2w13_ZV();
2411 63 : case INV_W2W7E2: return NULL;
2412 21 : case INV_W3W3E2: return phi2_w3w3e2_ZV();
2413 70 : case INV_W5W7: return phi2_w5w7_ZV();
2414 14 : case INV_W3W13: return phi2_w3w13_ZV();
2415 7 : case INV_ATKIN3: return phi2_atkin3_ZV();
2416 14 : case INV_ATKIN5: return phi2_atkin5_ZV();
2417 7 : case INV_ATKIN7: return phi2_atkin7_ZV();
2418 0 : case INV_ATKIN11: return phi2_atkin11_ZV();
2419 0 : case INV_ATKIN13: return phi2_atkin13_ZV();
2420 0 : case INV_ATKIN17: return phi2_atkin17_ZV();
2421 14 : case INV_ATKIN19: return phi2_atkin19_ZV();
2422 21 : case INV_ATKIN23: return phi2_atkin23_ZV();
2423 21 : case INV_ATKIN29: return phi2_atkin29_ZV();
2424 : }
2425 0 : pari_err_BUG("internal_db");
2426 : return NULL;/*LCOV_EXCL_LINE*/
2427 : }
2428 :
2429 : /* NB: Should only be called if L <= modinv_max_internal_level(inv) */
2430 : static GEN
2431 24946 : polmodular_small_ZM(long L, long inv, GEN *db)
2432 : {
2433 24946 : GEN f = internal_db(L, inv);
2434 24946 : if (!f) return polmodular0_powerup_ZM(L, inv, db);
2435 24806 : return sympol_to_ZM(f, L);
2436 : }
2437 :
2438 : /* Each function phi_w?w?_j() returns a vector V containing two
2439 : * vectors u and v, and a scalar k, which together represent the
2440 : * bivariate polnomial
2441 : *
2442 : * phi(X, Y) = \sum_i u[i] X^i + Y \sum_i v[i] X^i + Y^2 X^k
2443 : */
2444 : static GEN
2445 1060 : phi_w2w3_j(void)
2446 : {
2447 : GEN phi, phi0, phi1;
2448 1060 : phi = cgetg(4, t_VEC);
2449 :
2450 1060 : phi0 = cgetg(14, t_VEC);
2451 1060 : gel(phi0, 1) = gen_1;
2452 1060 : gel(phi0, 2) = utoineg(0x3cUL);
2453 1060 : gel(phi0, 3) = utoi(0x702UL);
2454 1060 : gel(phi0, 4) = utoineg(0x797cUL);
2455 1060 : gel(phi0, 5) = utoi(0x5046fUL);
2456 1060 : gel(phi0, 6) = utoineg(0x1be0b8UL);
2457 1060 : gel(phi0, 7) = utoi(0x28ef9cUL);
2458 1060 : gel(phi0, 8) = utoi(0x15e2968UL);
2459 1060 : gel(phi0, 9) = utoi(0x1b8136fUL);
2460 1060 : gel(phi0, 10) = utoi(0xa67674UL);
2461 1060 : gel(phi0, 11) = utoi(0x23982UL);
2462 1060 : gel(phi0, 12) = utoi(0x294UL);
2463 1060 : gel(phi0, 13) = gen_1;
2464 :
2465 1060 : phi1 = cgetg(13, t_VEC);
2466 1060 : gel(phi1, 1) = gen_0;
2467 1060 : gel(phi1, 2) = gen_0;
2468 1060 : gel(phi1, 3) = gen_m1;
2469 1060 : gel(phi1, 4) = utoi(0x23UL);
2470 1060 : gel(phi1, 5) = utoineg(0xaeUL);
2471 1060 : gel(phi1, 6) = utoineg(0x5b8UL);
2472 1060 : gel(phi1, 7) = utoi(0x12d7UL);
2473 1060 : gel(phi1, 8) = utoineg(0x7c86UL);
2474 1060 : gel(phi1, 9) = utoi(0x37c8UL);
2475 1060 : gel(phi1, 10) = utoineg(0x69cUL);
2476 1060 : gel(phi1, 11) = utoi(0x48UL);
2477 1060 : gel(phi1, 12) = gen_m1;
2478 :
2479 1060 : gel(phi, 1) = phi0;
2480 1060 : gel(phi, 2) = phi1;
2481 1060 : gel(phi, 3) = utoi(5); return phi;
2482 : }
2483 :
2484 : static GEN
2485 3608 : phi_w3w3_j(void)
2486 : {
2487 : GEN phi, phi0, phi1;
2488 3608 : phi = cgetg(4, t_VEC);
2489 :
2490 3608 : phi0 = cgetg(14, t_VEC);
2491 3608 : gel(phi0, 1) = utoi(0x2d9UL);
2492 3608 : gel(phi0, 2) = utoi(0x4fbcUL);
2493 3608 : gel(phi0, 3) = utoi(0x5828aUL);
2494 3608 : gel(phi0, 4) = utoi(0x3a7a3cUL);
2495 3608 : gel(phi0, 5) = utoi(0x1bd8edfUL);
2496 3608 : gel(phi0, 6) = utoi(0x8348838UL);
2497 3608 : gel(phi0, 7) = utoi(0x1983f8acUL);
2498 3608 : gel(phi0, 8) = utoi(0x14e4e098UL);
2499 3608 : gel(phi0, 9) = utoi(0x69ed1a7UL);
2500 3608 : gel(phi0, 10) = utoi(0xc3828cUL);
2501 3608 : gel(phi0, 11) = utoi(0x2696aUL);
2502 3608 : gel(phi0, 12) = utoi(0x2acUL);
2503 3608 : gel(phi0, 13) = gen_1;
2504 :
2505 3608 : phi1 = cgetg(13, t_VEC);
2506 3608 : gel(phi1, 1) = gen_0;
2507 3608 : gel(phi1, 2) = utoineg(0x1bUL);
2508 3608 : gel(phi1, 3) = utoineg(0x5d6UL);
2509 3608 : gel(phi1, 4) = utoineg(0x1c7bUL);
2510 3608 : gel(phi1, 5) = utoi(0x7980UL);
2511 3608 : gel(phi1, 6) = utoi(0x12168UL);
2512 3608 : gel(phi1, 7) = utoineg(0x3528UL);
2513 3608 : gel(phi1, 8) = utoineg(0x6174UL);
2514 3608 : gel(phi1, 9) = utoi(0x2208UL);
2515 3608 : gel(phi1, 10) = utoineg(0x41dUL);
2516 3608 : gel(phi1, 11) = utoi(0x36UL);
2517 3608 : gel(phi1, 12) = gen_m1;
2518 :
2519 3608 : gel(phi, 1) = phi0;
2520 3608 : gel(phi, 2) = phi1;
2521 3608 : gel(phi, 3) = gen_2; return phi;
2522 : }
2523 :
2524 : static GEN
2525 2927 : phi_w2w5_j(void)
2526 : {
2527 : GEN phi, phi0, phi1;
2528 2927 : phi = cgetg(4, t_VEC);
2529 :
2530 2927 : phi0 = cgetg(20, t_VEC);
2531 2927 : gel(phi0, 1) = gen_1;
2532 2927 : gel(phi0, 2) = utoineg(0x2aUL);
2533 2927 : gel(phi0, 3) = utoi(0x549UL);
2534 2927 : gel(phi0, 4) = utoineg(0x6530UL);
2535 2927 : gel(phi0, 5) = utoi(0x60504UL);
2536 2927 : gel(phi0, 6) = utoineg(0x3cbbc8UL);
2537 2927 : gel(phi0, 7) = utoi(0x1d1ee74UL);
2538 2927 : gel(phi0, 8) = utoineg(0x7ef9ab0UL);
2539 2927 : gel(phi0, 9) = utoi(0x12b888beUL);
2540 2927 : gel(phi0, 10) = utoineg(0x15fa174cUL);
2541 2927 : gel(phi0, 11) = utoi(0x615d9feUL);
2542 2927 : gel(phi0, 12) = utoi(0xbeca070UL);
2543 2927 : gel(phi0, 13) = utoineg(0x88de74cUL);
2544 2927 : gel(phi0, 14) = utoineg(0x2b3a268UL);
2545 2927 : gel(phi0, 15) = utoi(0x24b3244UL);
2546 2927 : gel(phi0, 16) = utoi(0xb56270UL);
2547 2927 : gel(phi0, 17) = utoi(0x25989UL);
2548 2927 : gel(phi0, 18) = utoi(0x2a6UL);
2549 2927 : gel(phi0, 19) = gen_1;
2550 :
2551 2927 : phi1 = cgetg(19, t_VEC);
2552 2927 : gel(phi1, 1) = gen_0;
2553 2927 : gel(phi1, 2) = gen_0;
2554 2927 : gel(phi1, 3) = gen_m1;
2555 2927 : gel(phi1, 4) = utoi(0x1eUL);
2556 2927 : gel(phi1, 5) = utoineg(0xffUL);
2557 2927 : gel(phi1, 6) = utoi(0x243UL);
2558 2927 : gel(phi1, 7) = utoineg(0xf3UL);
2559 2927 : gel(phi1, 8) = utoineg(0x5c4UL);
2560 2927 : gel(phi1, 9) = utoi(0x107bUL);
2561 2927 : gel(phi1, 10) = utoineg(0x11b2fUL);
2562 2927 : gel(phi1, 11) = utoi(0x48fa8UL);
2563 2927 : gel(phi1, 12) = utoineg(0x6ff7cUL);
2564 2927 : gel(phi1, 13) = utoi(0x4bf48UL);
2565 2927 : gel(phi1, 14) = utoineg(0x187efUL);
2566 2927 : gel(phi1, 15) = utoi(0x404cUL);
2567 2927 : gel(phi1, 16) = utoineg(0x582UL);
2568 2927 : gel(phi1, 17) = utoi(0x3cUL);
2569 2927 : gel(phi1, 18) = gen_m1;
2570 :
2571 2927 : gel(phi, 1) = phi0;
2572 2927 : gel(phi, 2) = phi1;
2573 2927 : gel(phi, 3) = utoi(7); return phi;
2574 : }
2575 :
2576 : static GEN
2577 6628 : phi_w2w7_j(void)
2578 : {
2579 : GEN phi, phi0, phi1;
2580 6628 : phi = cgetg(4, t_VEC);
2581 :
2582 6628 : phi0 = cgetg(26, t_VEC);
2583 6628 : gel(phi0, 1) = gen_1;
2584 6628 : gel(phi0, 2) = utoineg(0x24UL);
2585 6628 : gel(phi0, 3) = utoi(0x4ceUL);
2586 6628 : gel(phi0, 4) = utoineg(0x5d60UL);
2587 6628 : gel(phi0, 5) = utoi(0x62b05UL);
2588 6628 : gel(phi0, 6) = utoineg(0x47be78UL);
2589 6628 : gel(phi0, 7) = utoi(0x2a3880aUL);
2590 6628 : gel(phi0, 8) = utoineg(0x114bccf4UL);
2591 6628 : gel(phi0, 9) = utoi(0x4b95e79aUL);
2592 6628 : gel(phi0, 10) = utoineg(0xe2cfee1cUL);
2593 6628 : gel(phi0, 11) = uu32toi(0x1UL, 0xe43d1126UL);
2594 6628 : gel(phi0, 12) = uu32toineg(0x2UL, 0xf04dc6f8UL);
2595 6628 : gel(phi0, 13) = uu32toi(0x3UL, 0x5384987dUL);
2596 6628 : gel(phi0, 14) = uu32toineg(0x2UL, 0xa5ccbe18UL);
2597 6628 : gel(phi0, 15) = uu32toi(0x1UL, 0x4c52c8a6UL);
2598 6628 : gel(phi0, 16) = utoineg(0x2643fdecUL);
2599 6628 : gel(phi0, 17) = utoineg(0x49f5ab66UL);
2600 6628 : gel(phi0, 18) = utoi(0x33074d3cUL);
2601 6628 : gel(phi0, 19) = utoineg(0x6a3e376UL);
2602 6628 : gel(phi0, 20) = utoineg(0x675aa58UL);
2603 6628 : gel(phi0, 21) = utoi(0x2674005UL);
2604 6628 : gel(phi0, 22) = utoi(0xba5be0UL);
2605 6628 : gel(phi0, 23) = utoi(0x2644eUL);
2606 6628 : gel(phi0, 24) = utoi(0x2acUL);
2607 6628 : gel(phi0, 25) = gen_1;
2608 :
2609 6628 : phi1 = cgetg(25, t_VEC);
2610 6628 : gel(phi1, 1) = gen_0;
2611 6628 : gel(phi1, 2) = gen_0;
2612 6628 : gel(phi1, 3) = gen_m1;
2613 6628 : gel(phi1, 4) = utoi(0x1cUL);
2614 6628 : gel(phi1, 5) = utoineg(0x10aUL);
2615 6628 : gel(phi1, 6) = utoi(0x3f0UL);
2616 6628 : gel(phi1, 7) = utoineg(0x5d3UL);
2617 6628 : gel(phi1, 8) = utoi(0x3efUL);
2618 6628 : gel(phi1, 9) = utoineg(0x102UL);
2619 6628 : gel(phi1, 10) = utoineg(0x5c8UL);
2620 6628 : gel(phi1, 11) = utoi(0x102fUL);
2621 6628 : gel(phi1, 12) = utoineg(0x13f8aUL);
2622 6628 : gel(phi1, 13) = utoi(0x86538UL);
2623 6628 : gel(phi1, 14) = utoineg(0x1bbd10UL);
2624 6628 : gel(phi1, 15) = utoi(0x3614e8UL);
2625 6628 : gel(phi1, 16) = utoineg(0x42f793UL);
2626 6628 : gel(phi1, 17) = utoi(0x364698UL);
2627 6628 : gel(phi1, 18) = utoineg(0x1c7a10UL);
2628 6628 : gel(phi1, 19) = utoi(0x97cc8UL);
2629 6628 : gel(phi1, 20) = utoineg(0x1fc8aUL);
2630 6628 : gel(phi1, 21) = utoi(0x4210UL);
2631 6628 : gel(phi1, 22) = utoineg(0x524UL);
2632 6628 : gel(phi1, 23) = utoi(0x38UL);
2633 6628 : gel(phi1, 24) = gen_m1;
2634 :
2635 6628 : gel(phi, 1) = phi0;
2636 6628 : gel(phi, 2) = phi1;
2637 6628 : gel(phi, 3) = utoi(9); return phi;
2638 : }
2639 :
2640 : static GEN
2641 2157 : phi_w2w13_j(void)
2642 : {
2643 : GEN phi, phi0, phi1;
2644 2157 : phi = cgetg(4, t_VEC);
2645 :
2646 2157 : phi0 = cgetg(44, t_VEC);
2647 2157 : gel(phi0, 1) = gen_1;
2648 2157 : gel(phi0, 2) = utoineg(0x1eUL);
2649 2157 : gel(phi0, 3) = utoi(0x45fUL);
2650 2157 : gel(phi0, 4) = utoineg(0x5590UL);
2651 2157 : gel(phi0, 5) = utoi(0x64407UL);
2652 2157 : gel(phi0, 6) = utoineg(0x53a792UL);
2653 2157 : gel(phi0, 7) = utoi(0x3b21af3UL);
2654 2157 : gel(phi0, 8) = utoineg(0x20d056d0UL);
2655 2157 : gel(phi0, 9) = utoi(0xe02db4a6UL);
2656 2157 : gel(phi0, 10) = uu32toineg(0x4UL, 0xb23400b0UL);
2657 2157 : gel(phi0, 11) = uu32toi(0x14UL, 0x57fbb906UL);
2658 2157 : gel(phi0, 12) = uu32toineg(0x49UL, 0xcf80c00UL);
2659 2157 : gel(phi0, 13) = uu32toi(0xdeUL, 0x84ff421UL);
2660 2157 : gel(phi0, 14) = uu32toineg(0x244UL, 0xc500c156UL);
2661 2157 : gel(phi0, 15) = uu32toi(0x52cUL, 0x79162979UL);
2662 2157 : gel(phi0, 16) = uu32toineg(0xa64UL, 0x8edc5650UL);
2663 2157 : gel(phi0, 17) = uu32toi(0x1289UL, 0x4225bb41UL);
2664 2157 : gel(phi0, 18) = uu32toineg(0x1d89UL, 0x2a15229aUL);
2665 2157 : gel(phi0, 19) = uu32toi(0x2a3eUL, 0x4539f1ebUL);
2666 2157 : gel(phi0, 20) = uu32toineg(0x366aUL, 0xa5ea1130UL);
2667 2157 : gel(phi0, 21) = uu32toi(0x3f47UL, 0xa19fecb4UL);
2668 2157 : gel(phi0, 22) = uu32toineg(0x4282UL, 0x91a3c4a0UL);
2669 2157 : gel(phi0, 23) = uu32toi(0x3f30UL, 0xbaa305b4UL);
2670 2157 : gel(phi0, 24) = uu32toineg(0x3635UL, 0xd11c2530UL);
2671 2157 : gel(phi0, 25) = uu32toi(0x29e2UL, 0x89df27ebUL);
2672 2157 : gel(phi0, 26) = uu32toineg(0x1d03UL, 0x6509d48aUL);
2673 2156 : gel(phi0, 27) = uu32toi(0x11e2UL, 0x272cc601UL);
2674 2156 : gel(phi0, 28) = uu32toineg(0x9b0UL, 0xacd58ff0UL);
2675 2156 : gel(phi0, 29) = uu32toi(0x485UL, 0x608d7db9UL);
2676 2156 : gel(phi0, 30) = uu32toineg(0x1bfUL, 0xa941546UL);
2677 2157 : gel(phi0, 31) = uu32toi(0x82UL, 0x56e48b21UL);
2678 2157 : gel(phi0, 32) = uu32toineg(0x13UL, 0xc36b2340UL);
2679 2157 : gel(phi0, 33) = uu32toineg(0x5UL, 0x6637257aUL);
2680 2157 : gel(phi0, 34) = uu32toi(0x5UL, 0x40f70bd0UL);
2681 2157 : gel(phi0, 35) = uu32toineg(0x1UL, 0xf70842daUL);
2682 2157 : gel(phi0, 36) = utoi(0x53eea5f0UL);
2683 2157 : gel(phi0, 37) = utoi(0xda17bf3UL);
2684 2157 : gel(phi0, 38) = utoineg(0xaf246c2UL);
2685 2157 : gel(phi0, 39) = utoi(0x278f847UL);
2686 2157 : gel(phi0, 40) = utoi(0xbf5550UL);
2687 2157 : gel(phi0, 41) = utoi(0x26f1fUL);
2688 2157 : gel(phi0, 42) = utoi(0x2b2UL);
2689 2157 : gel(phi0, 43) = gen_1;
2690 :
2691 2157 : phi1 = cgetg(43, t_VEC);
2692 2157 : gel(phi1, 1) = gen_0;
2693 2157 : gel(phi1, 2) = gen_0;
2694 2157 : gel(phi1, 3) = gen_m1;
2695 2157 : gel(phi1, 4) = utoi(0x1aUL);
2696 2157 : gel(phi1, 5) = utoineg(0x111UL);
2697 2157 : gel(phi1, 6) = utoi(0x5e4UL);
2698 2157 : gel(phi1, 7) = utoineg(0x1318UL);
2699 2157 : gel(phi1, 8) = utoi(0x2804UL);
2700 2157 : gel(phi1, 9) = utoineg(0x3cd6UL);
2701 2157 : gel(phi1, 10) = utoi(0x467cUL);
2702 2157 : gel(phi1, 11) = utoineg(0x3cd6UL);
2703 2157 : gel(phi1, 12) = utoi(0x2804UL);
2704 2157 : gel(phi1, 13) = utoineg(0x1318UL);
2705 2157 : gel(phi1, 14) = utoi(0x5e3UL);
2706 2157 : gel(phi1, 15) = utoineg(0x10dUL);
2707 2157 : gel(phi1, 16) = utoineg(0x5ccUL);
2708 2157 : gel(phi1, 17) = utoi(0x100bUL);
2709 2157 : gel(phi1, 18) = utoineg(0x160e1UL);
2710 2157 : gel(phi1, 19) = utoi(0xd2cb0UL);
2711 2157 : gel(phi1, 20) = utoineg(0x4c85fcUL);
2712 2157 : gel(phi1, 21) = utoi(0x137cb98UL);
2713 2157 : gel(phi1, 22) = utoineg(0x3c75568UL);
2714 2157 : gel(phi1, 23) = utoi(0x95c69c8UL);
2715 2157 : gel(phi1, 24) = utoineg(0x131557bcUL);
2716 2157 : gel(phi1, 25) = utoi(0x20aacfd0UL);
2717 2157 : gel(phi1, 26) = utoineg(0x2f9164e6UL);
2718 2157 : gel(phi1, 27) = utoi(0x3b6a5e40UL);
2719 2157 : gel(phi1, 28) = utoineg(0x3ff54344UL);
2720 2157 : gel(phi1, 29) = utoi(0x3b6a9140UL);
2721 2157 : gel(phi1, 30) = utoineg(0x2f927fa6UL);
2722 2157 : gel(phi1, 31) = utoi(0x20ae6450UL);
2723 2157 : gel(phi1, 32) = utoineg(0x131cd87cUL);
2724 2157 : gel(phi1, 33) = utoi(0x967d1e8UL);
2725 2157 : gel(phi1, 34) = utoineg(0x3d48ca8UL);
2726 2157 : gel(phi1, 35) = utoi(0x14333b8UL);
2727 2157 : gel(phi1, 36) = utoineg(0x5406bcUL);
2728 2157 : gel(phi1, 37) = utoi(0x10c130UL);
2729 2157 : gel(phi1, 38) = utoineg(0x27ba1UL);
2730 2157 : gel(phi1, 39) = utoi(0x433cUL);
2731 2157 : gel(phi1, 40) = utoineg(0x4c6UL);
2732 2157 : gel(phi1, 41) = utoi(0x34UL);
2733 2157 : gel(phi1, 42) = gen_m1;
2734 :
2735 2157 : gel(phi, 1) = phi0;
2736 2157 : gel(phi, 2) = phi1;
2737 2157 : gel(phi, 3) = utoi(15); return phi;
2738 : }
2739 :
2740 : static GEN
2741 1160 : phi_w3w5_j(void)
2742 : {
2743 : GEN phi, phi0, phi1;
2744 1160 : phi = cgetg(4, t_VEC);
2745 :
2746 1160 : phi0 = cgetg(26, t_VEC);
2747 1160 : gel(phi0, 1) = gen_1;
2748 1160 : gel(phi0, 2) = utoi(0x18UL);
2749 1160 : gel(phi0, 3) = utoi(0xb4UL);
2750 1160 : gel(phi0, 4) = utoineg(0x178UL);
2751 1160 : gel(phi0, 5) = utoineg(0x2d7eUL);
2752 1160 : gel(phi0, 6) = utoineg(0x89b8UL);
2753 1160 : gel(phi0, 7) = utoi(0x35c24UL);
2754 1160 : gel(phi0, 8) = utoi(0x128a18UL);
2755 1160 : gel(phi0, 9) = utoineg(0x12a911UL);
2756 1160 : gel(phi0, 10) = utoineg(0xcc0190UL);
2757 1160 : gel(phi0, 11) = utoi(0x94368UL);
2758 1160 : gel(phi0, 12) = utoi(0x1439d0UL);
2759 1160 : gel(phi0, 13) = utoi(0x96f931cUL);
2760 1160 : gel(phi0, 14) = utoineg(0x1f59ff0UL);
2761 1160 : gel(phi0, 15) = utoi(0x20e7e8UL);
2762 1160 : gel(phi0, 16) = utoineg(0x25fdf150UL);
2763 1160 : gel(phi0, 17) = utoineg(0x7091511UL);
2764 1160 : gel(phi0, 18) = utoi(0x1ef52f8UL);
2765 1160 : gel(phi0, 19) = utoi(0x341f2de4UL);
2766 1160 : gel(phi0, 20) = utoi(0x25d72c28UL);
2767 1160 : gel(phi0, 21) = utoi(0x95d2082UL);
2768 1160 : gel(phi0, 22) = utoi(0xd2d828UL);
2769 1160 : gel(phi0, 23) = utoi(0x281f4UL);
2770 1160 : gel(phi0, 24) = utoi(0x2b8UL);
2771 1160 : gel(phi0, 25) = gen_1;
2772 :
2773 1160 : phi1 = cgetg(25, t_VEC);
2774 1160 : gel(phi1, 1) = gen_0;
2775 1160 : gel(phi1, 2) = gen_0;
2776 1160 : gel(phi1, 3) = gen_0;
2777 1160 : gel(phi1, 4) = gen_1;
2778 1160 : gel(phi1, 5) = utoi(0xfUL);
2779 1160 : gel(phi1, 6) = utoi(0x2eUL);
2780 1160 : gel(phi1, 7) = utoineg(0x1fUL);
2781 1160 : gel(phi1, 8) = utoineg(0x2dUL);
2782 1160 : gel(phi1, 9) = utoineg(0x5caUL);
2783 1160 : gel(phi1, 10) = utoineg(0x358UL);
2784 1160 : gel(phi1, 11) = utoi(0x2f1cUL);
2785 1160 : gel(phi1, 12) = utoi(0xd8eaUL);
2786 1160 : gel(phi1, 13) = utoineg(0x38c70UL);
2787 1160 : gel(phi1, 14) = utoineg(0x1a964UL);
2788 1160 : gel(phi1, 15) = utoi(0x93512UL);
2789 1160 : gel(phi1, 16) = utoineg(0x58f2UL);
2790 1160 : gel(phi1, 17) = utoineg(0x5af1eUL);
2791 1160 : gel(phi1, 18) = utoi(0x1afb8UL);
2792 1160 : gel(phi1, 19) = utoi(0xc084UL);
2793 1160 : gel(phi1, 20) = utoineg(0x7fcbUL);
2794 1160 : gel(phi1, 21) = utoi(0x1c89UL);
2795 1160 : gel(phi1, 22) = utoineg(0x32aUL);
2796 1160 : gel(phi1, 23) = utoi(0x2dUL);
2797 1160 : gel(phi1, 24) = gen_m1;
2798 :
2799 1160 : gel(phi, 1) = phi0;
2800 1160 : gel(phi, 2) = phi1;
2801 1160 : gel(phi, 3) = utoi(8); return phi;
2802 : }
2803 :
2804 : static GEN
2805 2986 : phi_w3w7_j(void)
2806 : {
2807 : GEN phi, phi0, phi1;
2808 2986 : phi = cgetg(4, t_VEC);
2809 :
2810 2986 : phi0 = cgetg(34, t_VEC);
2811 2986 : gel(phi0, 1) = gen_1;
2812 2986 : gel(phi0, 2) = utoineg(0x14UL);
2813 2986 : gel(phi0, 3) = utoi(0x82UL);
2814 2986 : gel(phi0, 4) = utoi(0x1f8UL);
2815 2986 : gel(phi0, 5) = utoineg(0x2a45UL);
2816 2986 : gel(phi0, 6) = utoi(0x9300UL);
2817 2986 : gel(phi0, 7) = utoi(0x32abeUL);
2818 2986 : gel(phi0, 8) = utoineg(0x19c91cUL);
2819 2986 : gel(phi0, 9) = utoi(0xc1ba9UL);
2820 2986 : gel(phi0, 10) = utoi(0x1788f68UL);
2821 2986 : gel(phi0, 11) = utoineg(0x2b1989cUL);
2822 2986 : gel(phi0, 12) = utoineg(0x7a92408UL);
2823 2986 : gel(phi0, 13) = utoi(0x1238d56eUL);
2824 2986 : gel(phi0, 14) = utoi(0x13dd66a0UL);
2825 2986 : gel(phi0, 15) = utoineg(0x2dbedca8UL);
2826 2986 : gel(phi0, 16) = utoineg(0x34282eb8UL);
2827 2986 : gel(phi0, 17) = utoi(0x2c2a54d2UL);
2828 2986 : gel(phi0, 18) = utoi(0x98db81a8UL);
2829 2986 : gel(phi0, 19) = utoineg(0x4088be8UL);
2830 2986 : gel(phi0, 20) = utoineg(0xe424a220UL);
2831 2986 : gel(phi0, 21) = utoineg(0x67bbb232UL);
2832 2986 : gel(phi0, 22) = utoi(0x7dd8bb98UL);
2833 2986 : gel(phi0, 23) = uu32toi(0x1UL, 0xcaff744UL);
2834 2986 : gel(phi0, 24) = utoineg(0x1d46a378UL);
2835 2986 : gel(phi0, 25) = utoineg(0x82fa50f7UL);
2836 2986 : gel(phi0, 26) = utoineg(0x700ef38cUL);
2837 2986 : gel(phi0, 27) = utoi(0x20aa202eUL);
2838 2986 : gel(phi0, 28) = utoi(0x299b3440UL);
2839 2986 : gel(phi0, 29) = utoi(0xa476c4bUL);
2840 2986 : gel(phi0, 30) = utoi(0xd80558UL);
2841 2986 : gel(phi0, 31) = utoi(0x28a32UL);
2842 2986 : gel(phi0, 32) = utoi(0x2bcUL);
2843 2986 : gel(phi0, 33) = gen_1;
2844 :
2845 2986 : phi1 = cgetg(33, t_VEC);
2846 2986 : gel(phi1, 1) = gen_0;
2847 2986 : gel(phi1, 2) = gen_0;
2848 2986 : gel(phi1, 3) = gen_0;
2849 2986 : gel(phi1, 4) = gen_m1;
2850 2986 : gel(phi1, 5) = utoi(0xeUL);
2851 2986 : gel(phi1, 6) = utoineg(0x31UL);
2852 2986 : gel(phi1, 7) = utoineg(0xeUL);
2853 2986 : gel(phi1, 8) = utoi(0x99UL);
2854 2986 : gel(phi1, 9) = utoineg(0x8UL);
2855 2986 : gel(phi1, 10) = utoineg(0x2eUL);
2856 2986 : gel(phi1, 11) = utoineg(0x5ccUL);
2857 2986 : gel(phi1, 12) = utoi(0x308UL);
2858 2986 : gel(phi1, 13) = utoi(0x2904UL);
2859 2986 : gel(phi1, 14) = utoineg(0x15700UL);
2860 2986 : gel(phi1, 15) = utoineg(0x2b9ecUL);
2861 2986 : gel(phi1, 16) = utoi(0xf0966UL);
2862 2986 : gel(phi1, 17) = utoi(0xb3cc8UL);
2863 2986 : gel(phi1, 18) = utoineg(0x38241cUL);
2864 2986 : gel(phi1, 19) = utoineg(0x8604cUL);
2865 2986 : gel(phi1, 20) = utoi(0x578a64UL);
2866 2986 : gel(phi1, 21) = utoineg(0x11a798UL);
2867 2986 : gel(phi1, 22) = utoineg(0x39c85eUL);
2868 2986 : gel(phi1, 23) = utoi(0x1a5084UL);
2869 2986 : gel(phi1, 24) = utoi(0xcdeb4UL);
2870 2986 : gel(phi1, 25) = utoineg(0xb0364UL);
2871 2986 : gel(phi1, 26) = utoi(0x129d4UL);
2872 2986 : gel(phi1, 27) = utoi(0x126fcUL);
2873 2986 : gel(phi1, 28) = utoineg(0x8649UL);
2874 2986 : gel(phi1, 29) = utoi(0x1aa2UL);
2875 2986 : gel(phi1, 30) = utoineg(0x2dfUL);
2876 2986 : gel(phi1, 31) = utoi(0x2aUL);
2877 2986 : gel(phi1, 32) = gen_m1;
2878 :
2879 2986 : gel(phi, 1) = phi0;
2880 2986 : gel(phi, 2) = phi1;
2881 2986 : gel(phi, 3) = utoi(10); return phi;
2882 : }
2883 :
2884 : static GEN
2885 210 : phi_w3w13_j(void)
2886 : {
2887 : GEN phi, phi0, phi1;
2888 210 : phi = cgetg(4, t_VEC);
2889 :
2890 210 : phi0 = cgetg(58, t_VEC);
2891 210 : gel(phi0, 1) = gen_1;
2892 210 : gel(phi0, 2) = utoineg(0x10UL);
2893 210 : gel(phi0, 3) = utoi(0x58UL);
2894 210 : gel(phi0, 4) = utoi(0x258UL);
2895 210 : gel(phi0, 5) = utoineg(0x270cUL);
2896 210 : gel(phi0, 6) = utoi(0x9c00UL);
2897 210 : gel(phi0, 7) = utoi(0x2b40cUL);
2898 210 : gel(phi0, 8) = utoineg(0x20e250UL);
2899 210 : gel(phi0, 9) = utoi(0x4f46baUL);
2900 210 : gel(phi0, 10) = utoi(0x1869448UL);
2901 210 : gel(phi0, 11) = utoineg(0xa49ab68UL);
2902 210 : gel(phi0, 12) = utoi(0x96c7630UL);
2903 210 : gel(phi0, 13) = utoi(0x4f7e0af6UL);
2904 210 : gel(phi0, 14) = utoineg(0xea093590UL);
2905 210 : gel(phi0, 15) = utoineg(0x6735bc50UL);
2906 210 : gel(phi0, 16) = uu32toi(0x5UL, 0x971a2e08UL);
2907 210 : gel(phi0, 17) = uu32toineg(0x6UL, 0x29c9d965UL);
2908 210 : gel(phi0, 18) = uu32toineg(0xdUL, 0xeb9aa360UL);
2909 210 : gel(phi0, 19) = uu32toi(0x26UL, 0xe9c0584UL);
2910 210 : gel(phi0, 20) = uu32toineg(0x1UL, 0xb0cadce8UL);
2911 210 : gel(phi0, 21) = uu32toineg(0x62UL, 0x73586014UL);
2912 210 : gel(phi0, 22) = uu32toi(0x66UL, 0xaf672e38UL);
2913 210 : gel(phi0, 23) = uu32toi(0x6bUL, 0x93c28cdcUL);
2914 210 : gel(phi0, 24) = uu32toineg(0x11eUL, 0x4f633080UL);
2915 210 : gel(phi0, 25) = uu32toi(0x3cUL, 0xcc42461bUL);
2916 210 : gel(phi0, 26) = uu32toi(0x17bUL, 0xdec0a78UL);
2917 210 : gel(phi0, 27) = uu32toineg(0x166UL, 0x910d8bd0UL);
2918 210 : gel(phi0, 28) = uu32toineg(0xd4UL, 0x47873030UL);
2919 210 : gel(phi0, 29) = uu32toi(0x204UL, 0x811828baUL);
2920 210 : gel(phi0, 30) = uu32toineg(0x50UL, 0x5d713960UL);
2921 210 : gel(phi0, 31) = uu32toineg(0x198UL, 0xa27e42b0UL);
2922 210 : gel(phi0, 32) = uu32toi(0xe1UL, 0x25685138UL);
2923 210 : gel(phi0, 33) = uu32toi(0xe3UL, 0xaa5774bbUL);
2924 210 : gel(phi0, 34) = uu32toineg(0xcfUL, 0x392a9a00UL);
2925 210 : gel(phi0, 35) = uu32toineg(0x81UL, 0xfb334d04UL);
2926 210 : gel(phi0, 36) = uu32toi(0xabUL, 0x59594a68UL);
2927 210 : gel(phi0, 37) = uu32toi(0x42UL, 0x356993acUL);
2928 210 : gel(phi0, 38) = uu32toineg(0x86UL, 0x307ba678UL);
2929 210 : gel(phi0, 39) = uu32toineg(0xbUL, 0x7a9e59dcUL);
2930 210 : gel(phi0, 40) = uu32toi(0x4cUL, 0x27935f20UL);
2931 210 : gel(phi0, 41) = uu32toineg(0x2UL, 0xe0ac9045UL);
2932 210 : gel(phi0, 42) = uu32toineg(0x24UL, 0x14495758UL);
2933 210 : gel(phi0, 43) = utoi(0x20973410UL);
2934 210 : gel(phi0, 44) = uu32toi(0x13UL, 0x99ff4e00UL);
2935 210 : gel(phi0, 45) = uu32toineg(0x1UL, 0xa710d34aUL);
2936 210 : gel(phi0, 46) = uu32toineg(0x7UL, 0xfe5405c0UL);
2937 210 : gel(phi0, 47) = uu32toi(0x1UL, 0xcdee0f8UL);
2938 210 : gel(phi0, 48) = uu32toi(0x2UL, 0x660c92a8UL);
2939 210 : gel(phi0, 49) = utoi(0x3f13a35aUL);
2940 210 : gel(phi0, 50) = utoineg(0xe4eb4ba0UL);
2941 210 : gel(phi0, 51) = utoineg(0x6420f4UL);
2942 210 : gel(phi0, 52) = utoi(0x2c624370UL);
2943 210 : gel(phi0, 53) = utoi(0xb31b814UL);
2944 210 : gel(phi0, 54) = utoi(0xdd3ad8UL);
2945 210 : gel(phi0, 55) = utoi(0x29278UL);
2946 210 : gel(phi0, 56) = utoi(0x2c0UL);
2947 210 : gel(phi0, 57) = gen_1;
2948 :
2949 210 : phi1 = cgetg(57, t_VEC);
2950 210 : gel(phi1, 1) = gen_0;
2951 210 : gel(phi1, 2) = gen_0;
2952 210 : gel(phi1, 3) = gen_0;
2953 210 : gel(phi1, 4) = gen_m1;
2954 210 : gel(phi1, 5) = utoi(0xdUL);
2955 210 : gel(phi1, 6) = utoineg(0x34UL);
2956 210 : gel(phi1, 7) = utoi(0x1aUL);
2957 210 : gel(phi1, 8) = utoi(0xf7UL);
2958 210 : gel(phi1, 9) = utoineg(0x16cUL);
2959 210 : gel(phi1, 10) = utoineg(0xddUL);
2960 210 : gel(phi1, 11) = utoi(0x28aUL);
2961 210 : gel(phi1, 12) = utoineg(0xddUL);
2962 210 : gel(phi1, 13) = utoineg(0x16cUL);
2963 210 : gel(phi1, 14) = utoi(0xf6UL);
2964 210 : gel(phi1, 15) = utoi(0x1dUL);
2965 210 : gel(phi1, 16) = utoineg(0x31UL);
2966 210 : gel(phi1, 17) = utoineg(0x5ceUL);
2967 210 : gel(phi1, 18) = utoi(0x2e4UL);
2968 210 : gel(phi1, 19) = utoi(0x252cUL);
2969 210 : gel(phi1, 20) = utoineg(0x1b34cUL);
2970 210 : gel(phi1, 21) = utoi(0xaf80UL);
2971 210 : gel(phi1, 22) = utoi(0x1cc5f9UL);
2972 210 : gel(phi1, 23) = utoineg(0x3e1aa5UL);
2973 210 : gel(phi1, 24) = utoineg(0x86d17aUL);
2974 210 : gel(phi1, 25) = utoi(0x2427264UL);
2975 210 : gel(phi1, 26) = utoineg(0x691c1fUL);
2976 210 : gel(phi1, 27) = utoineg(0x862ad4eUL);
2977 210 : gel(phi1, 28) = utoi(0xab21e1fUL);
2978 210 : gel(phi1, 29) = utoi(0xbc19ddcUL);
2979 210 : gel(phi1, 30) = utoineg(0x24331db8UL);
2980 210 : gel(phi1, 31) = utoi(0x972c105UL);
2981 210 : gel(phi1, 32) = utoi(0x363d7107UL);
2982 210 : gel(phi1, 33) = utoineg(0x39696450UL);
2983 210 : gel(phi1, 34) = utoineg(0x1bce7c48UL);
2984 210 : gel(phi1, 35) = utoi(0x552ecba0UL);
2985 210 : gel(phi1, 36) = utoineg(0x1c7771b8UL);
2986 210 : gel(phi1, 37) = utoineg(0x393029b8UL);
2987 210 : gel(phi1, 38) = utoi(0x3755be97UL);
2988 210 : gel(phi1, 39) = utoi(0x83402a9UL);
2989 210 : gel(phi1, 40) = utoineg(0x24d5be62UL);
2990 210 : gel(phi1, 41) = utoi(0xdb6d90aUL);
2991 210 : gel(phi1, 42) = utoi(0xa0ef177UL);
2992 210 : gel(phi1, 43) = utoineg(0x99ff162UL);
2993 210 : gel(phi1, 44) = utoi(0xb09e27UL);
2994 210 : gel(phi1, 45) = utoi(0x26a7adcUL);
2995 210 : gel(phi1, 46) = utoineg(0x116e2fcUL);
2996 210 : gel(phi1, 47) = utoineg(0x1383b5UL);
2997 210 : gel(phi1, 48) = utoi(0x35a9e7UL);
2998 210 : gel(phi1, 49) = utoineg(0x1082a0UL);
2999 210 : gel(phi1, 50) = utoineg(0x4696UL);
3000 210 : gel(phi1, 51) = utoi(0x19f98UL);
3001 210 : gel(phi1, 52) = utoineg(0x8bb3UL);
3002 210 : gel(phi1, 53) = utoi(0x18bbUL);
3003 210 : gel(phi1, 54) = utoineg(0x297UL);
3004 210 : gel(phi1, 55) = utoi(0x27UL);
3005 210 : gel(phi1, 56) = gen_m1;
3006 :
3007 210 : gel(phi, 1) = phi0;
3008 210 : gel(phi, 2) = phi1;
3009 210 : gel(phi, 3) = utoi(16); return phi;
3010 : }
3011 :
3012 : static GEN
3013 3331 : phi_w5w7_j(void)
3014 : {
3015 : GEN phi, phi0, phi1;
3016 3331 : phi = cgetg(4, t_VEC);
3017 :
3018 3331 : phi0 = cgetg(50, t_VEC);
3019 3331 : gel(phi0, 1) = gen_1;
3020 3331 : gel(phi0, 2) = utoi(0xcUL);
3021 3331 : gel(phi0, 3) = utoi(0x2aUL);
3022 3331 : gel(phi0, 4) = utoi(0x10UL);
3023 3331 : gel(phi0, 5) = utoineg(0x69UL);
3024 3331 : gel(phi0, 6) = utoineg(0x318UL);
3025 3331 : gel(phi0, 7) = utoineg(0x148aUL);
3026 3331 : gel(phi0, 8) = utoineg(0x17c4UL);
3027 3331 : gel(phi0, 9) = utoi(0x1a73UL);
3028 3331 : gel(phi0, 10) = gen_0;
3029 3331 : gel(phi0, 11) = utoi(0x338a0UL);
3030 3331 : gel(phi0, 12) = utoi(0x61698UL);
3031 3331 : gel(phi0, 13) = utoineg(0x96e8UL);
3032 3331 : gel(phi0, 14) = utoi(0x140910UL);
3033 3331 : gel(phi0, 15) = utoineg(0x45f6b4UL);
3034 3332 : gel(phi0, 16) = utoineg(0x309f50UL);
3035 3332 : gel(phi0, 17) = utoineg(0xef9f8bUL);
3036 3332 : gel(phi0, 18) = utoineg(0x283167cUL);
3037 3332 : gel(phi0, 19) = utoi(0x625e20aUL);
3038 3332 : gel(phi0, 20) = utoineg(0x16186350UL);
3039 3332 : gel(phi0, 21) = utoi(0x46861281UL);
3040 3332 : gel(phi0, 22) = utoineg(0x754b96a0UL);
3041 3332 : gel(phi0, 23) = uu32toi(0x1UL, 0x421ca02aUL);
3042 3332 : gel(phi0, 24) = uu32toineg(0x2UL, 0xdb76a5cUL);
3043 3332 : gel(phi0, 25) = uu32toi(0x4UL, 0xf6afd8eUL);
3044 3332 : gel(phi0, 26) = uu32toineg(0x6UL, 0xaafd3cb4UL);
3045 3332 : gel(phi0, 27) = uu32toi(0x8UL, 0xda2539caUL);
3046 3332 : gel(phi0, 28) = uu32toineg(0xfUL, 0x84343790UL);
3047 3332 : gel(phi0, 29) = uu32toi(0xfUL, 0x914ff421UL);
3048 3332 : gel(phi0, 30) = uu32toineg(0x19UL, 0x3c123950UL);
3049 3332 : gel(phi0, 31) = uu32toi(0x15UL, 0x381f722aUL);
3050 3332 : gel(phi0, 32) = uu32toineg(0x15UL, 0xe01c0c24UL);
3051 3332 : gel(phi0, 33) = uu32toi(0x19UL, 0x3360b375UL);
3052 3332 : gel(phi0, 34) = utoineg(0x59fda9c0UL);
3053 3332 : gel(phi0, 35) = uu32toi(0x20UL, 0xff55024cUL);
3054 3332 : gel(phi0, 36) = uu32toi(0x16UL, 0xcc600800UL);
3055 3332 : gel(phi0, 37) = uu32toi(0x24UL, 0x1879c898UL);
3056 3332 : gel(phi0, 38) = uu32toi(0x1cUL, 0x37f97498UL);
3057 3332 : gel(phi0, 39) = uu32toi(0x19UL, 0x39ec4b60UL);
3058 3332 : gel(phi0, 40) = uu32toi(0x10UL, 0x52c660d0UL);
3059 3332 : gel(phi0, 41) = uu32toi(0x9UL, 0xcab00333UL);
3060 3332 : gel(phi0, 42) = uu32toi(0x4UL, 0x7fe69be4UL);
3061 3332 : gel(phi0, 43) = uu32toi(0x1UL, 0xa0c6f116UL);
3062 3332 : gel(phi0, 44) = utoi(0x69244638UL);
3063 3332 : gel(phi0, 45) = utoi(0xed560f7UL);
3064 3332 : gel(phi0, 46) = utoi(0xe7b660UL);
3065 3332 : gel(phi0, 47) = utoi(0x29d8aUL);
3066 3332 : gel(phi0, 48) = utoi(0x2c4UL);
3067 3332 : gel(phi0, 49) = gen_1;
3068 :
3069 3332 : phi1 = cgetg(49, t_VEC);
3070 3332 : gel(phi1, 1) = gen_0;
3071 3332 : gel(phi1, 2) = gen_0;
3072 3332 : gel(phi1, 3) = gen_0;
3073 3332 : gel(phi1, 4) = gen_0;
3074 3332 : gel(phi1, 5) = gen_0;
3075 3332 : gel(phi1, 6) = gen_1;
3076 3332 : gel(phi1, 7) = utoi(0x7UL);
3077 3332 : gel(phi1, 8) = utoi(0x8UL);
3078 3332 : gel(phi1, 9) = utoineg(0x9UL);
3079 3332 : gel(phi1, 10) = gen_0;
3080 3332 : gel(phi1, 11) = utoineg(0x13UL);
3081 3332 : gel(phi1, 12) = utoineg(0x7UL);
3082 3332 : gel(phi1, 13) = utoineg(0x5ceUL);
3083 3332 : gel(phi1, 14) = utoineg(0xb0UL);
3084 3332 : gel(phi1, 15) = utoi(0x460UL);
3085 3332 : gel(phi1, 16) = utoineg(0x194bUL);
3086 3332 : gel(phi1, 17) = utoi(0x87c3UL);
3087 3332 : gel(phi1, 18) = utoi(0x3cdeUL);
3088 3332 : gel(phi1, 19) = utoineg(0xd683UL);
3089 3332 : gel(phi1, 20) = utoi(0x6099bUL);
3090 3332 : gel(phi1, 21) = utoineg(0x111ea8UL);
3091 3332 : gel(phi1, 22) = utoi(0xfa113UL);
3092 3332 : gel(phi1, 23) = utoineg(0x1a6561UL);
3093 3332 : gel(phi1, 24) = utoineg(0x1e997UL);
3094 3332 : gel(phi1, 25) = utoi(0x214e54UL);
3095 3332 : gel(phi1, 26) = utoineg(0x29c3f4UL);
3096 3332 : gel(phi1, 27) = utoi(0x67e102UL);
3097 3332 : gel(phi1, 28) = utoineg(0x227eaaUL);
3098 3332 : gel(phi1, 29) = utoi(0x191d10UL);
3099 3332 : gel(phi1, 30) = utoi(0x1a9cd5UL);
3100 3332 : gel(phi1, 31) = utoineg(0x58386fUL);
3101 3332 : gel(phi1, 32) = utoi(0x2e49f6UL);
3102 3332 : gel(phi1, 33) = utoineg(0x31194bUL);
3103 3332 : gel(phi1, 34) = utoi(0x9e07aUL);
3104 3332 : gel(phi1, 35) = utoi(0x260d59UL);
3105 3332 : gel(phi1, 36) = utoineg(0x189921UL);
3106 3332 : gel(phi1, 37) = utoi(0xeca4aUL);
3107 3332 : gel(phi1, 38) = utoineg(0xa3d9cUL);
3108 3332 : gel(phi1, 39) = utoineg(0x426daUL);
3109 3332 : gel(phi1, 40) = utoi(0x91875UL);
3110 3332 : gel(phi1, 41) = utoineg(0x3b55bUL);
3111 3332 : gel(phi1, 42) = utoineg(0x56f4UL);
3112 3332 : gel(phi1, 43) = utoi(0xcd1bUL);
3113 3332 : gel(phi1, 44) = utoineg(0x5159UL);
3114 3332 : gel(phi1, 45) = utoi(0x10f4UL);
3115 3332 : gel(phi1, 46) = utoineg(0x20dUL);
3116 3332 : gel(phi1, 47) = utoi(0x23UL);
3117 3332 : gel(phi1, 48) = gen_m1;
3118 :
3119 3332 : gel(phi, 1) = phi0;
3120 3332 : gel(phi, 2) = phi1;
3121 3332 : gel(phi, 3) = utoi(12); return phi;
3122 : }
3123 :
3124 : static GEN
3125 693 : phi_atkin3_j(void)
3126 : {
3127 : GEN phi, phi0, phi1;
3128 693 : phi = cgetg(4, t_VEC);
3129 :
3130 693 : phi0 = cgetg(6, t_VEC);
3131 693 : gel(phi0, 1) = utoi(538141968);
3132 693 : gel(phi0, 2) = utoi(19712160);
3133 693 : gel(phi0, 3) = utoi(193752);
3134 693 : gel(phi0, 4) = utoi(744);
3135 693 : gel(phi0, 5) = gen_1;
3136 :
3137 693 : phi1 = cgetg(5, t_VEC);
3138 693 : gel(phi1, 1) = utoi(24528);
3139 693 : gel(phi1, 2) = utoi(2348);
3140 693 : gel(phi1, 3) = gen_0;
3141 693 : gel(phi1, 4) = gen_m1;
3142 :
3143 693 : gel(phi, 1) = phi0;
3144 693 : gel(phi, 2) = phi1;
3145 693 : gel(phi, 3) = gen_0; return phi;
3146 : }
3147 :
3148 : static GEN
3149 727 : phi_atkin5_j(void)
3150 : {
3151 : GEN phi, phi0, phi1;
3152 727 : phi = cgetg(4, t_VEC);
3153 :
3154 727 : phi0 = cgetg(8, t_VEC);
3155 727 : gel(phi0, 1) = uu32toi(0xd,0x595d1000UL);
3156 727 : gel(phi0, 2) = uu32toi(0x2,0x935de800UL);
3157 727 : gel(phi0, 3) = utoi(756084480);
3158 727 : gel(phi0, 4) = utoi(20990720);
3159 727 : gel(phi0, 5) = utoi(196080);
3160 727 : gel(phi0, 6) = utoi(744);
3161 728 : gel(phi0, 7) = gen_1;
3162 :
3163 728 : phi1 = cgetg(7, t_VEC);
3164 728 : gel(phi1, 1) = utoineg(449408);
3165 728 : gel(phi1, 2) = utoineg(73056);
3166 728 : gel(phi1, 3) = utoi(3800);
3167 727 : gel(phi1, 4) = utoi(670);
3168 726 : gel(phi1, 5) = gen_0;
3169 726 : gel(phi1, 6) = gen_m1;
3170 :
3171 726 : gel(phi, 1) = phi0;
3172 726 : gel(phi, 2) = phi1;
3173 726 : gel(phi, 3) = gen_0; return phi;
3174 : }
3175 :
3176 : static GEN
3177 70 : phi_atkin7_j(void)
3178 : {
3179 : GEN phi, phi0, phi1;
3180 70 : phi = cgetg(4, t_VEC);
3181 :
3182 70 : phi0 = cgetg(10, t_VEC);
3183 70 : gel(phi0, 1) = uu32toi(0x136,0xe07f9221UL);
3184 70 : gel(phi0, 2) = uu32toi(0x9d,0xc4224ba8UL);
3185 70 : gel(phi0, 3) = uu32toi(0x20,0x58246d3cUL);
3186 70 : gel(phi0, 4) = uu32toi(0x3,0x631e2dd8UL);
3187 70 : gel(phi0, 5) = utoi(803037606);
3188 70 : gel(phi0, 6) = utoi(21226520);
3189 70 : gel(phi0, 7) = utoi(196476);
3190 70 : gel(phi0, 8) = utoi(744);
3191 70 : gel(phi0, 9) = gen_1;
3192 :
3193 70 : phi1 = cgetg(9, t_VEC);
3194 70 : gel(phi1, 1) = utoi(2128500);
3195 70 : gel(phi1, 2) = utoi(186955);
3196 70 : gel(phi1, 3) = utoineg(204792);
3197 70 : gel(phi1, 4) = utoineg(31647);
3198 70 : gel(phi1, 5) = utoi(1428);
3199 70 : gel(phi1, 6) = utoi(357);
3200 70 : gel(phi1, 7) = gen_0;
3201 70 : gel(phi1, 8) = gen_m1;
3202 :
3203 70 : gel(phi, 1) = phi0;
3204 70 : gel(phi, 2) = phi1;
3205 70 : gel(phi, 3) = gen_0; return phi;
3206 : }
3207 :
3208 : static GEN
3209 0 : phi_atkin11_j(void)
3210 : {
3211 : GEN phi, phi0, phi1;
3212 0 : phi = cgetg(4, t_VEC);
3213 :
3214 0 : phi0 = cgetg(14, t_VEC);
3215 0 : gel(phi0, 1) = uu32toi(0x351f,0xe3329000);
3216 0 : gel(phi0, 2) = uu32toi(0x5a09,0xb4cae000);
3217 0 : gel(phi0, 3) = uu32toi(0x4386,0xeec9c800);
3218 0 : gel(phi0, 4) = uu32toi(0x1d6c,0x110f8800);
3219 0 : gel(phi0, 5) = uu32toi(0x836,0xd0d89f00);
3220 0 : gel(phi0, 6) = uu32toi(0x186,0xd34d0c00);
3221 0 : gel(phi0, 7) = uu32toi(0x30,0x8f70b700);
3222 0 : gel(phi0, 8) = uu32toi(0x3,0xedd91100);
3223 0 : gel(phi0, 9) = utoi(830467440);
3224 0 : gel(phi0, 10) = utoi(21354080);
3225 0 : gel(phi0, 11) = utoi(196680);
3226 0 : gel(phi0, 12) = utoi(744);
3227 0 : gel(phi0, 13) = gen_1;
3228 :
3229 0 : phi1 = cgetg(13, t_VEC);
3230 0 : gel(phi1, 1) = utoineg(8720000);
3231 0 : gel(phi1, 2) = utoineg(19849600);
3232 0 : gel(phi1, 3) = utoineg(8252640);
3233 0 : gel(phi1, 4) = utoi(1867712);
3234 0 : gel(phi1, 5) = utoi(1675784);
3235 0 : gel(phi1, 6) = utoi(184184);
3236 0 : gel(phi1, 7) = utoineg(57442);
3237 0 : gel(phi1, 8) = utoineg(11440);
3238 0 : gel(phi1, 9) = utoi(506);
3239 0 : gel(phi1, 10) = utoi(187);
3240 0 : gel(phi1, 11) = gen_0;
3241 0 : gel(phi1, 12) = gen_m1;
3242 :
3243 0 : gel(phi, 1) = phi0;
3244 0 : gel(phi, 2) = phi1;
3245 0 : gel(phi, 3) = gen_0; return phi;
3246 : }
3247 :
3248 : static GEN
3249 1119 : phi_atkin13_j(void)
3250 : {
3251 : GEN phi, phi0, phi1;
3252 1119 : phi = cgetg(4, t_VEC);
3253 :
3254 1119 : phi0 = cgetg(16, t_VEC);
3255 1119 : gel(phi0, 1) = uu32toi(0x8954,0x40000000);
3256 1120 : gel(phi0, 2) = uu32toi(0x169eb,0x5e000000);
3257 1120 : gel(phi0, 3) = uu32toi(0x1ae7f,0x36e00000);
3258 1120 : gel(phi0, 4) = uu32toi(0x13107,0x840d8000);
3259 1120 : gel(phi0, 5) = uu32toi(0x8f0a,0xa4ccb800);
3260 1120 : gel(phi0, 6) = uu32toi(0x2e9f,0x7cfb8de0);
3261 1120 : gel(phi0, 7) = uu32toi(0xac8,0xedcc81b1);
3262 1120 : gel(phi0, 8) = uu32toi(0x1c6,0x36bee68);
3263 1120 : gel(phi0, 9) = uu32toi(0x34,0x377ed40c);
3264 1120 : gel(phi0, 10) = uu32toi(0x4,0xa132b38);
3265 1120 : gel(phi0, 11) = utoi(835688022);
3266 1120 : gel(phi0, 12) = utoi(21377304);
3267 1120 : gel(phi0, 13) = utoi(196716);
3268 1120 : gel(phi0, 14) = utoi(744);
3269 1120 : gel(phi0, 15) = gen_1;
3270 :
3271 1120 : phi1 = cgetg(15, t_VEC);
3272 1120 : gel(phi1, 1) = utoi(24576000);
3273 1120 : gel(phi1, 2) = utoi(32384000);
3274 1120 : gel(phi1, 3) = utoineg(5859360);
3275 1120 : gel(phi1, 4) = utoineg(23669490);
3276 1120 : gel(phi1, 5) = utoineg(9614956);
3277 1120 : gel(phi1, 6) = utoi(700323);
3278 1120 : gel(phi1, 7) = utoi(1161420);
3279 1120 : gel(phi1, 8) = utoi(149786);
3280 1120 : gel(phi1, 9) = utoineg(37596);
3281 1120 : gel(phi1, 10) = utoineg(8502);
3282 1120 : gel(phi1, 11) = utoi(364);
3283 1120 : gel(phi1, 12) = utoi(156);
3284 1120 : gel(phi1, 13) = gen_0;
3285 1120 : gel(phi1, 14) = gen_m1;
3286 :
3287 1120 : gel(phi, 1) = phi0;
3288 1120 : gel(phi, 2) = phi1;
3289 1120 : gel(phi, 3) = gen_0; return phi;
3290 : }
3291 :
3292 : static GEN
3293 1119 : phi_atkin17_j(void)
3294 : {
3295 : GEN phi, phi0, phi1;
3296 1119 : phi = cgetg(4, t_VEC);
3297 :
3298 1119 : phi0 = cgetg(20, t_VEC);
3299 1119 : gel(phi0, 1) = uu32toi(0x1657c,0x54a85640);
3300 1119 : gel(phi0, 2) = uu32toi(0x700a8,0xf0f3e240);
3301 1119 : gel(phi0, 3) = uu32toi(0x104ffa,0x16a394f0);
3302 1120 : gel(phi0, 4) = uu32toi(0x176924,0x252cada0);
3303 1120 : gel(phi0, 5) = uu32toi(0x172465,0xa95c437c);
3304 1120 : gel(phi0, 6) = uu32toi(0x10afa6,0x44a03d44);
3305 1120 : gel(phi0, 7) = uu32toi(0x90fff,0xc76052b1);
3306 1120 : gel(phi0, 8) = uu32toi(0x3c625,0x26e00dfc);
3307 1120 : gel(phi0, 9) = uu32toi(0x136f3,0xc7587fe);
3308 1120 : gel(phi0, 10) = uu32toi(0x4d55,0x39993e90);
3309 1120 : gel(phi0, 11) = uu32toi(0xebe,0x56879c1f);
3310 1120 : gel(phi0, 12) = uu32toi(0x21e,0x4cf30138);
3311 1120 : gel(phi0, 13) = uu32toi(0x39,0x6108ad0);
3312 1120 : gel(phi0, 14) = uu32toi(0x4,0x2dd68d04);
3313 1120 : gel(phi0, 15) = utoi(842077983);
3314 1120 : gel(phi0, 16) = utoi(21404972);
3315 1120 : gel(phi0, 17) = utoi(196758);
3316 1120 : gel(phi0, 18) = utoi(744);
3317 1120 : gel(phi0, 19) = gen_1;
3318 :
3319 1120 : phi1 = cgetg(19, t_VEC);
3320 1120 : gel(phi1, 1) = utoineg(25608112);
3321 1120 : gel(phi1, 2) = utoineg(128884056);
3322 1120 : gel(phi1, 3) = utoineg(169635044);
3323 1120 : gel(phi1, 4) = utoineg(18738794);
3324 1120 : gel(phi1, 5) = utoi(125706976);
3325 1120 : gel(phi1, 6) = utoi(98725154);
3326 1120 : gel(phi1, 7) = utoi(13049914);
3327 1120 : gel(phi1, 8) = utoineg(16023299);
3328 1120 : gel(phi1, 9) = utoineg(7118240);
3329 1120 : gel(phi1, 10) = utoi(70737);
3330 1120 : gel(phi1, 11) = utoi(630836);
3331 1120 : gel(phi1, 12) = utoi(91766);
3332 1120 : gel(phi1, 13) = utoineg(20808);
3333 1120 : gel(phi1, 14) = utoineg(5338);
3334 1120 : gel(phi1, 15) = utoi(238);
3335 1120 : gel(phi1, 16) = utoi(119);
3336 1120 : gel(phi1, 17) = gen_0;
3337 1120 : gel(phi1, 18) = gen_m1;
3338 :
3339 1120 : gel(phi, 1) = phi0;
3340 1120 : gel(phi, 2) = phi1;
3341 1120 : gel(phi, 3) = gen_0; return phi;
3342 : }
3343 :
3344 : static GEN
3345 1073 : phi_atkin19_j(void)
3346 : {
3347 : GEN phi, phi0, phi1;
3348 1073 : phi = cgetg(4, t_VEC);
3349 :
3350 1073 : phi0 = cgetg(22, t_VEC);
3351 1073 : gel(phi0, 1) = uu32toi(0x8954,0x40000000);
3352 1073 : gel(phi0, 2) = uu32toi(0x3f55f,0xd4000000);
3353 1073 : gel(phi0, 3) = uu32toi(0xd919c,0xfec00000);
3354 1073 : gel(phi0, 4) = uu32toi(0x1caf6f,0x559c0000);
3355 1073 : gel(phi0, 5) = uu32toi(0x29e098,0x33660000);
3356 1073 : gel(phi0, 6) = uu32toi(0x2ccab4,0x9d840000);
3357 1073 : gel(phi0, 7) = uu32toi(0x2456c7,0x80a1b000);
3358 1073 : gel(phi0, 8) = uu32toi(0x16d60a,0xd745d000);
3359 1073 : gel(phi0, 9) = uu32toi(0xb4073,0xd4d99000);
3360 1073 : gel(phi0, 10) = uu32toi(0x45efb,0xfafc9940);
3361 1073 : gel(phi0, 11) = uu32toi(0x156b5,0xc5077760);
3362 1073 : gel(phi0, 12) = uu32toi(0x524a,0x36e3a250);
3363 1073 : gel(phi0, 13) = uu32toi(0xf4f,0x2f2d5961);
3364 1073 : gel(phi0, 14) = uu32toi(0x229,0xdaeee798);
3365 1073 : gel(phi0, 15) = uu32toi(0x39,0x9e6319bc);
3366 1073 : gel(phi0, 16) = uu32toi(0x4,0x322f8d88);
3367 1073 : gel(phi0, 17) = utoi(842900838);
3368 1073 : gel(phi0, 18) = utoi(21408744);
3369 1073 : gel(phi0, 19) = utoi(196764);
3370 1073 : gel(phi0, 20) = utoi(744);
3371 1073 : gel(phi0, 21) = gen_1;
3372 :
3373 1073 : phi1 = cgetg(21, t_VEC);
3374 1073 : gel(phi1, 1) = utoi(24576000);
3375 1073 : gel(phi1, 2) = utoi(90675200);
3376 1073 : gel(phi1, 3) = utoi(51363840);
3377 1073 : gel(phi1, 4) = utoineg(196605312);
3378 1073 : gel(phi1, 5) = utoineg(358921248);
3379 1073 : gel(phi1, 6) = utoineg(190349904);
3380 1073 : gel(phi1, 7) = utoi(54954270);
3381 1073 : gel(phi1, 8) = utoi(101838024);
3382 1073 : gel(phi1, 9) = utoi(30202704);
3383 1073 : gel(phi1, 10) = utoineg(9356265);
3384 1073 : gel(phi1, 11) = utoineg(6935646);
3385 1073 : gel(phi1, 12) = utoineg(444030);
3386 1073 : gel(phi1, 13) = utoi(519042);
3387 1073 : gel(phi1, 14) = utoi(97983);
3388 1073 : gel(phi1, 15) = utoineg(16416);
3389 1073 : gel(phi1, 16) = utoineg(5073);
3390 1073 : gel(phi1, 17) = utoi(190);
3391 1073 : gel(phi1, 18) = utoi(114);
3392 1073 : gel(phi1, 19) = gen_0;
3393 1073 : gel(phi1, 20) = gen_m1;
3394 :
3395 1073 : gel(phi, 1) = phi0;
3396 1073 : gel(phi, 2) = phi1;
3397 1073 : gel(phi, 3) = gen_0; return phi;
3398 : }
3399 :
3400 : static GEN
3401 1883 : phi_atkin23_j(void)
3402 : {
3403 : GEN phi, phi0, phi1;
3404 1883 : phi = cgetg(4, t_VEC);
3405 :
3406 1883 : phi0 = cgetg(26, t_VEC);
3407 1883 : gel(phi0, 1) = utoi(1073741824);
3408 1883 : gel(phi0, 2) = uu32toi(0x3,0xf0000000);
3409 1883 : gel(phi0, 3) = uu32toi(0x1e,0x30000000);
3410 1883 : gel(phi0, 4) = uu32toi(0x95,0x97000000);
3411 1883 : gel(phi0, 5) = uu32toi(0x218,0xa3000000);
3412 1883 : gel(phi0, 6) = uu32toi(0x5c7,0x5f700000);
3413 1883 : gel(phi0, 7) = uu32toi(0xcaf,0xfac0000);
3414 1883 : gel(phi0, 8) = uu32toi(0x16aa,0x3900000);
3415 1883 : gel(phi0, 9) = uu32toi(0x216f,0x69d20000);
3416 1883 : gel(phi0, 10) = uu32toi(0x2911,0x5ada0000);
3417 1883 : gel(phi0, 11) = uu32toi(0x2a2c,0x744d0000);
3418 1883 : gel(phi0, 12) = uu32toi(0x243b,0xc40d8000);
3419 1883 : gel(phi0, 13) = uu32toi(0x19fa,0x68c53000);
3420 1883 : gel(phi0, 14) = uu32toi(0xf74,0x41e0c000);
3421 1883 : gel(phi0, 15) = uu32toi(0x78e,0xa9057000);
3422 1883 : gel(phi0, 16) = uu32toi(0x2ff,0x6f4f000);
3423 1883 : gel(phi0, 17) = uu32toi(0xf1,0xb1e5a000);
3424 1883 : gel(phi0, 18) = uu32toi(0x3a,0xd0793f00);
3425 1883 : gel(phi0, 19) = uu32toi(0xa,0x97960840);
3426 1883 : gel(phi0, 20) = uu32toi(0x1,0x52727000);
3427 1883 : gel(phi0, 21) = utoi(441081120);
3428 1883 : gel(phi0, 22) = utoi(17282016);
3429 1883 : gel(phi0, 23) = utoi(179952);
3430 1883 : gel(phi0, 24) = utoi(720);
3431 1883 : gel(phi0, 25) = gen_1;
3432 :
3433 1883 : phi1 = cgetg(25, t_VEC);
3434 1883 : gel(phi1, 1) = utoi(65536);
3435 1883 : gel(phi1, 2) = utoi(516096);
3436 1883 : gel(phi1, 3) = utoi(1648640);
3437 1883 : gel(phi1, 4) = utoi(2213888);
3438 1883 : gel(phi1, 5) = utoineg(1554432);
3439 1883 : gel(phi1, 6) = utoineg(11787776);
3440 1883 : gel(phi1, 7) = utoineg(21906304);
3441 1883 : gel(phi1, 8) = utoineg(19783680);
3442 1883 : gel(phi1, 9) = utoineg(3833824);
3443 1883 : gel(phi1, 10) = utoi(11002464);
3444 1883 : gel(phi1, 11) = utoi(11625488);
3445 1883 : gel(phi1, 12) = utoi(2882544);
3446 1883 : gel(phi1, 13) = utoineg(2689666);
3447 1883 : gel(phi1, 14) = utoineg(1978368);
3448 1883 : gel(phi1, 15) = utoi(19136);
3449 1883 : gel(phi1, 16) = utoi(393024);
3450 1883 : gel(phi1, 17) = utoi(53084);
3451 1883 : gel(phi1, 18) = utoineg(46644);
3452 1883 : gel(phi1, 19) = utoineg(5681);
3453 1883 : gel(phi1, 20) = utoi(3864);
3454 1883 : gel(phi1, 21) = gen_0;
3455 1883 : gel(phi1, 22) = utoineg(161);
3456 1883 : gel(phi1, 23) = utoi(23);
3457 1883 : gel(phi1, 24) = gen_m1;
3458 :
3459 1883 : gel(phi, 1) = phi0;
3460 1883 : gel(phi, 2) = phi1;
3461 1883 : gel(phi, 3) = gen_0; return phi;
3462 : }
3463 :
3464 : static GEN
3465 3858 : phi_atkin29_j(void)
3466 : {
3467 : GEN phi, phi0, phi1;
3468 3858 : phi = cgetg(4, t_VEC);
3469 :
3470 3858 : phi0 = cgetg(32, t_VEC);
3471 3858 : gel(phi0, 1) = utoi(11390625);
3472 3858 : gel(phi0, 2) = utoi(41006250);
3473 3858 : gel(phi0, 3) = utoi(118918125);
3474 3858 : gel(phi0, 4) = utoi(73993500);
3475 3859 : gel(phi0, 5) = utoineg(591595650);
3476 3859 : gel(phi0, 6) = utoineg(2067026040);
3477 3858 : gel(phi0, 7) = utoineg(3310173216);
3478 3858 : gel(phi0, 8) = utoi(1339615908);
3479 3858 : gel(phi0, 9) = uu32toi(0x4,0x1bdea49);
3480 3858 : gel(phi0, 10) = uu32toi(0x7,0x4588df8a);
3481 3858 : gel(phi0, 11) = uu32toi(0x2,0x76591fcf);
3482 3859 : gel(phi0, 12) = uu32toineg(0x10,0xa19368b8);
3483 3858 : gel(phi0, 13) = uu32toineg(0x25,0x583f669);
3484 3858 : gel(phi0, 14) = uu32toineg(0x12,0x2b9ec67e);
3485 3858 : gel(phi0, 15) = uu32toi(0x31,0x939eef85);
3486 3858 : gel(phi0, 16) = uu32toi(0x5b,0x174f9444);
3487 3858 : gel(phi0, 17) = uu32toi(0x23,0xe0a92fdd);
3488 3859 : gel(phi0, 18) = uu32toineg(0x40,0xed23b2fe);
3489 3859 : gel(phi0, 19) = uu32toineg(0x65,0x35e74a61);
3490 3859 : gel(phi0, 20) = uu32toineg(0x31,0xc9fb3f18);
3491 3859 : gel(phi0, 21) = uu32toi(0x12,0x72304077);
3492 3859 : gel(phi0, 22) = uu32toi(0x2c,0xf570520a);
3493 3859 : gel(phi0, 23) = uu32toi(0x21,0xef31d011);
3494 3859 : gel(phi0, 24) = uu32toi(0xf,0x2daf2ec4);
3495 3859 : gel(phi0, 25) = uu32toi(0x4,0x598183a8);
3496 3859 : gel(phi0, 26) = utoi(3339922344);
3497 3859 : gel(phi0, 27) = utoi(340795182);
3498 3859 : gel(phi0, 28) = utoi(16216684);
3499 3859 : gel(phi0, 29) = utoi(175653);
3500 3859 : gel(phi0, 30) = utoi(714);
3501 3859 : gel(phi0, 31) = gen_1;
3502 :
3503 3859 : phi1 = cgetg(31, t_VEC);
3504 3859 : gel(phi1, 1) = utoi(6750);
3505 3859 : gel(phi1, 2) = utoi(12150);
3506 3859 : gel(phi1, 3) = utoineg(281880);
3507 3859 : gel(phi1, 4) = utoineg(570024);
3508 3859 : gel(phi1, 5) = utoi(1754181);
3509 3859 : gel(phi1, 6) = utoi(5229135);
3510 3859 : gel(phi1, 7) = utoineg(2357613);
3511 3859 : gel(phi1, 8) = utoineg(19103721);
3512 3859 : gel(phi1, 9) = utoineg(9708910);
3513 3859 : gel(phi1, 10) = utoi(31795426);
3514 3859 : gel(phi1, 11) = utoi(38397537);
3515 3859 : gel(phi1, 12) = utoineg(19207947);
3516 3859 : gel(phi1, 13) = utoineg(54103270);
3517 3859 : gel(phi1, 14) = utoineg(9216142);
3518 3859 : gel(phi1, 15) = utoi(37142939);
3519 3859 : gel(phi1, 16) = utoi(18871083);
3520 3859 : gel(phi1, 17) = utoineg(14041394);
3521 3859 : gel(phi1, 18) = utoineg(10954634);
3522 3859 : gel(phi1, 19) = utoi(3592085);
3523 3859 : gel(phi1, 20) = utoi(3427365);
3524 3859 : gel(phi1, 21) = utoineg(853818);
3525 3859 : gel(phi1, 22) = utoineg(622398);
3526 3859 : gel(phi1, 23) = utoi(189399);
3527 3859 : gel(phi1, 24) = utoi(53679);
3528 3859 : gel(phi1, 25) = utoineg(26680);
3529 3859 : gel(phi1, 26) = utoi(580);
3530 3859 : gel(phi1, 27) = utoi(1421);
3531 3859 : gel(phi1, 28) = utoineg(319);
3532 3859 : gel(phi1, 29) = utoi(29);
3533 3859 : gel(phi1, 30) = gen_m1;
3534 :
3535 3859 : gel(phi, 1) = phi0;
3536 3859 : gel(phi, 2) = phi1;
3537 3859 : gel(phi, 3) = gen_0; return phi;
3538 : }
3539 :
3540 : GEN
3541 34609 : double_eta_raw(long inv)
3542 : {
3543 34609 : switch (inv) {
3544 1060 : case INV_W2W3:
3545 1060 : case INV_W2W3E2: return phi_w2w3_j();
3546 3608 : case INV_W3W3:
3547 3608 : case INV_W3W3E2: return phi_w3w3_j();
3548 2927 : case INV_W2W5:
3549 2927 : case INV_W2W5E2: return phi_w2w5_j();
3550 6628 : case INV_W2W7:
3551 6628 : case INV_W2W7E2: return phi_w2w7_j();
3552 1160 : case INV_W3W5: return phi_w3w5_j();
3553 2986 : case INV_W3W7: return phi_w3w7_j();
3554 2157 : case INV_W2W13: return phi_w2w13_j();
3555 210 : case INV_W3W13: return phi_w3w13_j();
3556 3331 : case INV_W5W7: return phi_w5w7_j();
3557 693 : case INV_ATKIN3: return phi_atkin3_j();
3558 727 : case INV_ATKIN5: return phi_atkin5_j();
3559 70 : case INV_ATKIN7: return phi_atkin7_j();
3560 0 : case INV_ATKIN11: return phi_atkin11_j();
3561 1119 : case INV_ATKIN13: return phi_atkin13_j();
3562 1119 : case INV_ATKIN17: return phi_atkin17_j();
3563 1073 : case INV_ATKIN19: return phi_atkin19_j();
3564 1883 : case INV_ATKIN23: return phi_atkin23_j();
3565 3858 : case INV_ATKIN29: return phi_atkin29_j();
3566 : default: pari_err_BUG("double_eta_raw"); return NULL;/*LCOV_EXCL_LINE*/
3567 : }
3568 : }
3569 :
3570 : /* SECTION: Select discriminant for given modpoly level. */
3571 :
3572 : /* require an L1, useful for multi-threading */
3573 : #define MODPOLY_USE_L1 1
3574 : /* no bound on L1 other than the fixed bound MAX_L1 - needed to
3575 : * handle small L for certain invariants (but not for j) */
3576 : #define MODPOLY_NO_MAX_L1 2
3577 : /* don't use any auxilliary primes - needed to handle small L for
3578 : * certain invariants (but not for j) */
3579 : #define MODPOLY_NO_AUX_L 4
3580 : #define MODPOLY_IGNORE_SPARSE_FACTOR 8
3581 :
3582 : INLINE double
3583 3226 : modpoly_height_bound(long L, long inv)
3584 : {
3585 : double nbits, nbits2;
3586 : double c;
3587 : long hf;
3588 :
3589 : /* proven bound (in bits), derived from: 6l*log(l)+16*l+13*sqrt(l)*log(l) */
3590 3226 : nbits = 6.0*L*log2(L)+16/M_LN2*L+8.0*sqrt((double)L)*log2(L);
3591 : /* alternative proven bound (in bits), derived from: 6l*log(l)+17*l */
3592 3226 : nbits2 = 6.0*L*log2(L)+17/M_LN2*L;
3593 3226 : if ( nbits2 < nbits ) nbits = nbits2;
3594 3226 : hf = modinv_height_factor(inv);
3595 3226 : if (hf > 1) {
3596 : /* IMPORTANT: when dividing by the height factor, we only want to reduce
3597 : terms related to the bound on j (the roots of Phi_l(X,y)), not terms arising
3598 : from binomial coefficients. These arise in lemmas 2 and 3 of the height
3599 : bound paper, terms of (log 2)*L and 2.085*(L+1) which we convert here to
3600 : binary logs */
3601 : /* Massive overestimate: if you care about speed, determine a good height
3602 : * bound empirically as done for INV_F below */
3603 1802 : nbits2 = nbits - 4.01*L -3.0;
3604 1802 : nbits = nbits2/hf + 4.01*L + 3.0;
3605 : }
3606 3226 : if (inv == INV_F) {
3607 142 : if (L < 30) c = 45;
3608 35 : else if (L < 100) c = 36;
3609 21 : else if (L < 300) c = 32;
3610 7 : else if (L < 600) c = 26;
3611 0 : else if (L < 1200) c = 24;
3612 0 : else if (L < 2400) c = 22;
3613 0 : else c = 20;
3614 142 : nbits = (6.0*L*log2(L) + c*L)/hf;
3615 : }
3616 3226 : return nbits;
3617 : }
3618 :
3619 : /* small enough to write the factorization of a smooth in a BIL bit integer */
3620 : #define SMOOTH_PRIMES ((BITS_IN_LONG >> 1) - 1)
3621 :
3622 : #define MAX_ATKIN 255
3623 :
3624 : #define MAX_L1 255
3625 :
3626 : typedef struct D_entry_struct {
3627 : ulong m;
3628 : long D, h;
3629 : } D_entry;
3630 :
3631 : /* Returns a form that generates the classes of norm p^2 in cl(p^2D)
3632 : * (i.e. one with order p-1), where p is an odd prime that splits in D
3633 : * and does not divide its conductor (but this is not verified) */
3634 : INLINE GEN
3635 86991 : qform_primeform2(long p, long D)
3636 : {
3637 86991 : GEN a = sqru(p), Dp2 = mulis(a, D), M = Z_factor(utoipos(p - 1));
3638 86991 : pari_sp av = avma;
3639 : long k;
3640 :
3641 176246 : for (k = D & 1; k <= p; k += 2)
3642 : {
3643 176246 : long ord, c = (k * k - D) / 4;
3644 : GEN Q, q;
3645 :
3646 176246 : if (!(c % p)) continue;
3647 152847 : q = mkqfis(a, k * p, c, Dp2); Q = qfi_red(q);
3648 : /* TODO: How do we know that Q has order dividing p - 1? If we don't, then
3649 : * the call to gen_order should be replaced with a call to something with
3650 : * fastorder semantics (i.e. return 0 if ord(Q) \ndiv M). */
3651 152847 : ord = itos(qfi_order(Q, M));
3652 152847 : if (ord == p - 1) {
3653 : /* TODO: This check that gen_order returned the correct result should be
3654 : * removed when gen_order is replaced with fastorder semantics. */
3655 86991 : if (qfb_equal1(gpowgs(Q, p - 1))) return q;
3656 0 : break;
3657 : }
3658 65856 : set_avma(av);
3659 : }
3660 0 : return NULL;
3661 : }
3662 :
3663 : /* Let n = #cl(D); return x such that [L0]^x = [L] in cl(D), or -1 if x was
3664 : * not found */
3665 : INLINE long
3666 211978 : primeform_discrete_log(long L0, long L, long n, long D)
3667 : {
3668 211978 : pari_sp av = avma;
3669 211978 : GEN X, Q, R, DD = stoi(D);
3670 211978 : Q = primeform_u(DD, L0);
3671 211978 : R = primeform_u(DD, L);
3672 211978 : X = qfi_Shanks(R, Q, n);
3673 211978 : return gc_long(av, X? itos(X): -1);
3674 : }
3675 :
3676 : /* Return the norm of a class group generator appropriate for a discriminant
3677 : * that will be used to calculate the modular polynomial of level L and
3678 : * invariant inv. Don't consider norms less than initial_L0 */
3679 : static long
3680 3226 : select_L0(long L, long inv, long initial_L0)
3681 : {
3682 3226 : long L0, modinv_N = modinv_level(inv);
3683 :
3684 3226 : if (modinv_N % L == 0) pari_err_BUG("select_L0");
3685 :
3686 : /* TODO: Clean up these anomolous L0 choices */
3687 :
3688 : /* I've no idea why the discriminant-finding code fails with L0=5
3689 : * when L=19 and L=29, nor why L0=7 and L0=11 don't work for L=19
3690 : * either, nor why this happens for the otherwise unrelated
3691 : * invariants Weber-f and (2,3) double-eta. */
3692 :
3693 3226 : if (inv == INV_F || inv == INV_F2 || inv == INV_F4 || inv == INV_F8
3694 2972 : || inv == INV_W2W3 || inv == INV_W2W3E2
3695 2909 : || inv == INV_W3W3) {
3696 422 : if (L == 19) return 13;
3697 372 : else if (L == 29) return 7;
3698 : }
3699 3169 : if ((inv == INV_W2W5) && (L == 19)) return 13;
3700 3155 : if ((inv == INV_W2W5E2)
3701 49 : && (L == 7 || L == 19)) return 13;
3702 3134 : if ((inv == INV_W2W7 || inv == INV_W2W7E2)
3703 358 : && L == 11) return 13;
3704 3106 : if (inv == INV_W3W5) {
3705 63 : if (L == 7) return 13;
3706 56 : else if (L == 17) return 7;
3707 : }
3708 3099 : if (inv == INV_W3W7) {
3709 161 : if (L == 29 || L == 101) return 11;
3710 133 : if (L == 11 || L == 19) return 13;
3711 : }
3712 :
3713 : /* L0 = smallest small prime different from L that doesn't divide modinv_N */
3714 3036 : for (L0 = unextprime(initial_L0 + 1);
3715 4754 : L0 == L || modinv_N % L0 == 0;
3716 1718 : L0 = unextprime(L0 + 1))
3717 : ;
3718 3036 : return L0;
3719 : }
3720 :
3721 : /* Return the order of [L]^n in cl(D), where #cl(D) = ord. */
3722 : INLINE long
3723 1116787 : primeform_exp_order(long L, long n, long D, long ord)
3724 : {
3725 1116787 : pari_sp av = avma;
3726 1116787 : GEN Q = gpowgs(primeform_u(stoi(D), L), n);
3727 1116787 : long m = itos(qfi_order(Q, Z_factor(stoi(ord))));
3728 1116787 : return gc_long(av,m);
3729 : }
3730 :
3731 : /* If an ideal of norm modinv_deg is equivalent to an ideal of norm L0, we
3732 : * have an orientation ambiguity that we need to avoid. Note that we need to
3733 : * check all the possibilities (up to 8), but we can cheaply check inverses
3734 : * (so at most 2) */
3735 : static long
3736 48746 : orientation_ambiguity(long D1, long L0, long modinv_p1, long modinv_p2, long modinv_N)
3737 : {
3738 48746 : pari_sp av = avma;
3739 48746 : long ambiguity = 0;
3740 48746 : GEN Q1 = red_primeform(D1, modinv_p1), Q2 = NULL;
3741 :
3742 48746 : if (modinv_p2 > 1)
3743 : {
3744 33983 : if (modinv_p1 == modinv_p2) Q1 = qfbsqr(Q1);
3745 : else
3746 : {
3747 27453 : GEN P2 = red_primeform(D1, modinv_p2);
3748 27453 : GEN Q = qfbsqr(P2), R = qfbsqr(Q1);
3749 : /* check that p1^2 != p2^{+/-2}, since this leads to
3750 : * ambiguities when converting j's to f's */
3751 27453 : if (equalii(gel(Q,1), gel(R,1)) && absequalii(gel(Q,2), gel(R,2)))
3752 : {
3753 0 : dbg_printf(3)("Bad D=%ld, a^2=b^2 problem between modinv_p1=%ld and modinv_p2=%ld\n",
3754 : D1, modinv_p1, modinv_p2);
3755 0 : ambiguity = 1;
3756 : }
3757 : else
3758 : { /* generate both p1*p2 and p1*p2^{-1} */
3759 27453 : Q2 = qfbcomp(Q1, P2);
3760 27453 : P2 = ginv(P2);
3761 27453 : Q1 = qfbcomp(Q1, P2);
3762 : }
3763 : }
3764 : }
3765 48746 : if (!ambiguity)
3766 : {
3767 48746 : GEN P = qfbsqr(red_primeform(D1, L0));
3768 48746 : if (equalii(gel(P,1), gel(Q1,1))
3769 47611 : || (modinv_p2 > 1 && modinv_p1 != modinv_p2
3770 26521 : && equalii(gel(P,1), gel(Q2,1)))) {
3771 1648 : dbg_printf(3)("Bad D=%ld, a=b^{+/-2} problem between modinv_N=%ld and L0=%ld\n",
3772 : D1, modinv_N, L0);
3773 1648 : ambiguity = 1;
3774 : }
3775 : }
3776 48746 : return gc_long(av, ambiguity);
3777 : }
3778 :
3779 : static long
3780 813798 : check_generators(
3781 : long *n1_, long *m_,
3782 : long D, long h, long n, long subgrp_sz, long L0, long L1)
3783 : {
3784 813798 : long n1, m = primeform_exp_order(L0, n, D, h);
3785 813798 : if (m_) *m_ = m;
3786 813798 : n1 = n * m;
3787 813798 : if (!n1) pari_err_BUG("check_generators");
3788 813798 : *n1_ = n1;
3789 813798 : if (n1 < subgrp_sz/2 || ( ! L1 && n1 < subgrp_sz)) {
3790 34044 : dbg_printf(3)("Bad D1=%ld with n1=%ld, h1=%ld, L1=%ld: "
3791 : "L0 and L1 don't span subgroup of size d in cl(D1)\n",
3792 : D, n, h, L1);
3793 34044 : return 0;
3794 : }
3795 779754 : if (n1 < subgrp_sz && ! (n1 & 1)) {
3796 : int res;
3797 : /* check whether L1 is generated by L0, use the fact that it has order 2 */
3798 22697 : pari_sp av = avma;
3799 22697 : GEN D1 = stoi(D);
3800 22697 : GEN Q = gpowgs(primeform_u(D1, L0), n1 / 2);
3801 22697 : res = gequal(Q, qfi_red(primeform_u(D1, L1)));
3802 22697 : set_avma(av);
3803 22697 : if (res) {
3804 6607 : dbg_printf(3)("Bad D1=%ld, with n1=%ld, h1=%ld, L1=%ld: "
3805 : "L1 generated by L0 in cl(D1)\n", D, n, h, L1);
3806 6607 : return 0;
3807 : }
3808 : }
3809 773147 : return 1;
3810 : }
3811 :
3812 : /* Calculate solutions (p, t) to the norm equation
3813 : * 4 p = t^2 - v^2 L^2 D (*)
3814 : * corresponding to the descriminant described by Dinfo.
3815 : *
3816 : * INPUT:
3817 : * - max: length of primes and traces
3818 : * - xprimes: p to exclude from primes (if they arise)
3819 : * - xcnt: length of xprimes
3820 : * - minbits: sum of log2(p) must be larger than this
3821 : * - Dinfo: discriminant, invariant and L for which we seek solutions to (*)
3822 : *
3823 : * OUTPUT:
3824 : * - primes: array of p in (*)
3825 : * - traces: array of t in (*)
3826 : * - totbits: sum of log2(p) for p in primes.
3827 : *
3828 : * RETURN:
3829 : * - the number of primes and traces found (these are always the same).
3830 : *
3831 : * NOTE: primes and traces are both NULL or both non-NULL.
3832 : * xprimes can be zero, in which case it is treated as empty. */
3833 : static long
3834 12649 : modpoly_pickD_primes(
3835 : ulong *primes, ulong *traces, long max, ulong *xprimes, long xcnt,
3836 : long *totbits, long minbits, disc_info *Dinfo)
3837 : {
3838 : double bits;
3839 : long D, m, n, vcnt, pfilter, one_prime, inv;
3840 : ulong maxp;
3841 : ulong a1, a2, v, t, p, a1_start, a1_delta, L0, L1, L, absD;
3842 12649 : ulong FF_BITS = BITS_IN_LONG - 2; /* BITS_IN_LONG - NAIL_BITS */
3843 :
3844 12649 : D = Dinfo->D1; absD = -D;
3845 12649 : L0 = Dinfo->L0;
3846 12649 : L1 = Dinfo->L1;
3847 12649 : L = Dinfo->L;
3848 12649 : inv = Dinfo->inv;
3849 :
3850 : /* make sure pfilter and D don't preclude the possibility of p=(t^2-v^2D)/4 being prime */
3851 12649 : pfilter = modinv_pfilter(inv);
3852 12649 : if ((pfilter & IQ_FILTER_1MOD3) && ! (D % 3)) return 0;
3853 12614 : if ((pfilter & IQ_FILTER_1MOD4) && ! (D & 0xF)) return 0;
3854 :
3855 : /* Naively estimate the number of primes satisfying 4p=t^2-L^2D with
3856 : * t=2 mod L and pfilter. This is roughly
3857 : * #{t: t^2 < max p and t=2 mod L} / pi(max p) * filter_density,
3858 : * where filter_density is 1, 2, or 4 depending on pfilter. If this quantity
3859 : * is already more than twice the number of bits we need, assume that,
3860 : * barring some obstruction, we should have no problem getting enough primes.
3861 : * In this case we just verify we can get one prime (which should always be
3862 : * true, assuming we chose D properly). */
3863 12614 : one_prime = 0;
3864 12614 : *totbits = 0;
3865 12614 : if (max <= 1 && ! one_prime) {
3866 9368 : p = ((pfilter & IQ_FILTER_1MOD3) ? 2 : 1) * ((pfilter & IQ_FILTER_1MOD4) ? 2 : 1);
3867 9368 : one_prime = (1UL << ((FF_BITS+1)/2)) * (log2(L*L*(-D))-1)
3868 9368 : > p*L*minbits*FF_BITS*M_LN2;
3869 9368 : if (one_prime) *totbits = minbits+1; /* lie */
3870 : }
3871 :
3872 12614 : m = n = 0;
3873 12614 : bits = 0.0;
3874 12614 : maxp = 0;
3875 31941 : for (v = 1; v < 100 && bits < minbits; v++) {
3876 : /* Don't allow v dividing the conductor. */
3877 28478 : if (ugcd(absD, v) != 1) continue;
3878 : /* Avoid v dividing the level. */
3879 28172 : if (v > 2 && modinv_is_double_eta(inv) && ugcd(modinv_level(inv), v) != 1)
3880 953 : continue;
3881 : /* can't get odd p with D=1 mod 8 unless v is even */
3882 27219 : if ((v & 1) && (D & 7) == 1) continue;
3883 : /* disallow 4 | v for L0=2 (removing this restriction is costly) */
3884 13466 : if (L0 == 2 && !(v & 3)) continue;
3885 : /* can't get p=3mod4 if v^2D is 0 mod 16 */
3886 13088 : if ((pfilter & IQ_FILTER_1MOD4) && !((v*v*D) & 0xF)) continue;
3887 13005 : if ((pfilter & IQ_FILTER_1MOD3) && !(v%3) ) continue;
3888 : /* avoid L0-volcanos with nonzero height */
3889 12951 : if (L0 != 2 && ! (v % L0)) continue;
3890 : /* ditto for L1 */
3891 12930 : if (L1 && !(v % L1)) continue;
3892 12930 : vcnt = 0;
3893 12930 : if ((v*v*absD)/4 > (1L<<FF_BITS)/(L*L)) break;
3894 12847 : if (both_odd(v,D)) {
3895 0 : a1_start = 1;
3896 0 : a1_delta = 2;
3897 : } else {
3898 12847 : a1_start = ((v*v*D) & 7)? 2: 0;
3899 12847 : a1_delta = 4;
3900 : }
3901 687616 : for (a1 = a1_start; bits < minbits; a1 += a1_delta) {
3902 684167 : a2 = (a1*a1 + v*v*absD) >> 2;
3903 684167 : if (!(a2 % L)) continue;
3904 588268 : t = a1*L + 2;
3905 588268 : p = a2*L*L + t - 1;
3906 : /* double check calculation just in case of overflow or other weirdness */
3907 588268 : if (!odd(p) || t*t + v*v*L*L*absD != 4*p)
3908 0 : pari_err_BUG("modpoly_pickD_primes");
3909 588268 : if (p > (1UL<<FF_BITS)) break;
3910 587938 : if (xprimes) {
3911 373800 : while (m < xcnt && xprimes[m] < p) m++;
3912 373374 : if (m < xcnt && p == xprimes[m]) {
3913 0 : dbg_printf(1)("skipping duplicate prime %ld\n", p);
3914 0 : continue;
3915 : }
3916 : }
3917 587938 : if (!modinv_good_prime(inv, p) || !uisprime(p)) continue;
3918 66223 : if (primes) {
3919 42152 : if (n >= max) goto done;
3920 : /* TODO: Implement test to filter primes that lead to
3921 : * L-valuation != 2 */
3922 42152 : primes[n] = p;
3923 42152 : traces[n] = t;
3924 : }
3925 66223 : n++;
3926 66223 : vcnt++;
3927 66223 : bits += log2(p);
3928 66223 : if (p > maxp) maxp = p;
3929 66223 : if (one_prime) goto done;
3930 : }
3931 3779 : if (vcnt)
3932 3776 : dbg_printf(3)("%ld primes with v=%ld, maxp=%ld (%.2f bits)\n",
3933 : vcnt, v, maxp, log2(maxp));
3934 : }
3935 3463 : done:
3936 12614 : if (!n) {
3937 9 : dbg_printf(3)("check_primes failed completely for D=%ld\n", D);
3938 9 : return 0;
3939 : }
3940 12605 : dbg_printf(3)("D=%ld: Found %ld primes totalling %0.2f of %ld bits\n",
3941 : D, n, bits, minbits);
3942 12605 : if (!*totbits) *totbits = (long)bits;
3943 12605 : return n;
3944 : }
3945 :
3946 : #define MAX_VOLCANO_FLOOR_SIZE 100000000
3947 :
3948 : static long
3949 3228 : calc_primes_for_discriminants(disc_info Ds[], long Dcnt, long L, long minbits)
3950 : {
3951 3228 : pari_sp av = avma;
3952 : long i, j, k, m, n, D1, pcnt, totbits;
3953 : ulong *primes, *Dprimes, *Dtraces;
3954 :
3955 : /* D1 is the discriminant with smallest absolute value among those we found */
3956 3228 : D1 = Ds[0].D1;
3957 9359 : for (i = 1; i < Dcnt; i++)
3958 6131 : if (Ds[i].D1 > D1) D1 = Ds[i].D1;
3959 :
3960 : /* n is an upper bound on the number of primes we might get. */
3961 3228 : n = ceil(minbits / (log2(L * L * (-D1)) - 2)) + 1;
3962 3228 : primes = (ulong *) stack_malloc(n * sizeof(*primes));
3963 3228 : Dprimes = (ulong *) stack_malloc(n * sizeof(*Dprimes));
3964 3228 : Dtraces = (ulong *) stack_malloc(n * sizeof(*Dtraces));
3965 3246 : for (i = 0, totbits = 0, pcnt = 0; i < Dcnt && totbits < minbits; i++)
3966 : {
3967 3246 : long np = modpoly_pickD_primes(Dprimes, Dtraces, n, primes, pcnt,
3968 3246 : &Ds[i].bits, minbits - totbits, Ds + i);
3969 3246 : ulong *T = (ulong *)newblock(2*np);
3970 3246 : Ds[i].nprimes = np;
3971 3246 : Ds[i].primes = T; memcpy(T , Dprimes, np * sizeof(*Dprimes));
3972 3246 : Ds[i].traces = T+np; memcpy(T+np, Dtraces, np * sizeof(*Dtraces));
3973 :
3974 3246 : totbits += Ds[i].bits;
3975 3246 : pcnt += np;
3976 :
3977 3246 : if (totbits >= minbits || i == Dcnt - 1) { Dcnt = i + 1; break; }
3978 : /* merge lists */
3979 589 : for (j = pcnt - np - 1, k = np - 1, m = pcnt - 1; m >= 0; m--) {
3980 571 : if (k >= 0) {
3981 546 : if (j >= 0 && primes[j] > Dprimes[k])
3982 301 : primes[m] = primes[j--];
3983 : else
3984 245 : primes[m] = Dprimes[k--];
3985 : } else {
3986 25 : primes[m] = primes[j--];
3987 : }
3988 : }
3989 : }
3990 3228 : if (totbits < minbits) {
3991 2 : dbg_printf(1)("Only obtained %ld of %ld bits using %ld discriminants\n",
3992 : totbits, minbits, Dcnt);
3993 4 : for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
3994 2 : Dcnt = 0;
3995 : }
3996 3228 : return gc_long(av, Dcnt);
3997 : }
3998 :
3999 : /* Select discriminant(s) to use when calculating the modular
4000 : * polynomial of level L and invariant inv.
4001 : *
4002 : * INPUT:
4003 : * - L: level of modular polynomial (must be odd)
4004 : * - inv: invariant of modular polynomial
4005 : * - L0: result of select_L0(L, inv)
4006 : * - minbits: height of modular polynomial
4007 : * - flags: see below
4008 : * - tab: result of scanD0(L0)
4009 : * - tablen: length of tab
4010 : *
4011 : * OUTPUT:
4012 : * - Ds: the selected discriminant(s)
4013 : *
4014 : * RETURN:
4015 : * - the number of Ds found
4016 : *
4017 : * The flags parameter is constructed by ORing zero or more of the
4018 : * following values:
4019 : * - MODPOLY_USE_L1: force use of second class group generator
4020 : * - MODPOLY_NO_AUX_L: don't use auxillary class group elements
4021 : * - MODPOLY_IGNORE_SPARSE_FACTOR: obtain D for which h(D) > L + 1
4022 : * rather than h(D) > (L + 1)/s */
4023 : static long
4024 3228 : modpoly_pickD(disc_info Ds[MODPOLY_MAX_DCNT], long L, long inv,
4025 : long L0, long max_L1, long minbits, long flags, D_entry *tab, long tablen)
4026 : {
4027 3228 : pari_sp ltop = avma, btop;
4028 : disc_info Dinfo;
4029 : pari_timer T;
4030 : long modinv_p1, modinv_p2; /* const after next line */
4031 3228 : const long modinv_deg = modinv_degree(&modinv_p1, &modinv_p2, inv);
4032 3228 : const long pfilter = modinv_pfilter(inv), modinv_N = modinv_level(inv);
4033 : long i, k, use_L1, Dcnt, D0_i, d, cost, enum_cost, best_cost, totbits;
4034 3228 : const double L_bits = log2(L);
4035 :
4036 3228 : if (!odd(L)) pari_err_BUG("modpoly_pickD");
4037 :
4038 3228 : timer_start(&T);
4039 3228 : if (flags & MODPOLY_IGNORE_SPARSE_FACTOR) d = L+2;
4040 3088 : else d = ceildivuu(L+1, modinv_sparse_factor(inv)) + 1;
4041 :
4042 : /* Now set level to 0 unless we will need to compute N-isogenies */
4043 3228 : dbg_printf(1)("Using L0=%ld for L=%ld, d=%ld, modinv_N=%ld, modinv_deg=%ld\n",
4044 : L0, L, d, modinv_N, modinv_deg);
4045 :
4046 : /* We use L1 if (L0|L) == 1 or if we are forced to by flags. */
4047 3228 : use_L1 = (kross(L0,L) > 0 || (flags & MODPOLY_USE_L1));
4048 :
4049 3228 : Dcnt = best_cost = totbits = 0;
4050 3228 : dbg_printf(3)("use_L1=%ld\n", use_L1);
4051 3228 : dbg_printf(3)("minbits = %ld\n", minbits);
4052 :
4053 : /* Iterate over the fundamental discriminants for L0 */
4054 1980307 : for (D0_i = 0; D0_i < tablen; D0_i++)
4055 : {
4056 1977079 : D_entry D0_entry = tab[D0_i];
4057 1977079 : long m, n0, h0, deg, L1, H_cost, twofactor, D0 = D0_entry.D;
4058 : double D0_bits;
4059 3059479 : if (! modinv_good_disc(inv, D0)) continue;
4060 1301161 : dbg_printf(3)("D0=%ld\n", D0);
4061 : /* don't allow either modinv_p1 or modinv_p2 to ramify */
4062 1301161 : if (kross(D0, L) < 1
4063 587223 : || (modinv_p1 > 1 && kross(D0, modinv_p1) < 1)
4064 579892 : || (modinv_p2 > 1 && kross(D0, modinv_p2) < 1)) {
4065 731694 : dbg_printf(3)("Bad D0=%ld due to nonsplit L or ramified level\n", D0);
4066 731694 : continue;
4067 : }
4068 569467 : deg = D0_entry.h; /* class poly degree */
4069 569467 : h0 = ((D0_entry.m & 2) ? 2*deg : deg); /* class number */
4070 : /* (D0_entry.m & 1) is 1 if ord(L0) < h0 (hence = h0/2),
4071 : * is 0 if ord(L0) = h0 */
4072 569467 : n0 = h0 / ((D0_entry.m & 1) + 1); /* = ord(L0) */
4073 :
4074 : /* Look for L1: for each smooth prime p */
4075 569467 : L1 = 0;
4076 13708894 : for (i = 1 ; i <= SMOOTH_PRIMES; i++)
4077 : {
4078 13260255 : long p = (long)pari_PRIMES[i];
4079 13260255 : if (p <= L0) continue;
4080 : /* If 1 + (D0 | p) = 1, i.e. p | D0 */
4081 12512908 : if (((D0_entry.m >> (2*i)) & 3) == 1) {
4082 : /* XXX: Why (p | L) = -1? Presumably so (L^2 v^2 D0 | p) = -1? */
4083 413945 : if (p <= max_L1 && modinv_N % p && kross(p,L) < 0) { L1 = p; break; }
4084 : }
4085 : }
4086 569467 : if (i > SMOOTH_PRIMES && (n0 < h0 || use_L1))
4087 : { /* Didn't find suitable L1 though we need one */
4088 266478 : dbg_printf(3)("Bad D0=%ld because there is no good L1\n", D0);
4089 266478 : continue;
4090 : }
4091 302989 : dbg_printf(3)("Good D0=%ld with L1=%ld, n0=%ld, h0=%ld, d=%ld\n",
4092 : D0, L1, n0, h0, d);
4093 :
4094 : /* We're finished if we have sufficiently many discriminants that satisfy
4095 : * the cost requirement */
4096 302989 : if (totbits > minbits && best_cost && h0*(L-1) > 3*best_cost) break;
4097 :
4098 302989 : D0_bits = log2(-D0);
4099 : /* If L^2 D0 is too big to fit in a BIL bit integer, skip D0. */
4100 302989 : if (D0_bits + 2 * L_bits > (BITS_IN_LONG - 1)) continue;
4101 :
4102 : /* m is the order of L0^n0 in L^2 D0? */
4103 302989 : m = primeform_exp_order(L0, n0, L * L * D0, n0 * (L-1));
4104 302989 : if (m < (L-1)/2) {
4105 84228 : dbg_printf(3)("Bad D0=%ld because %ld is less than (L-1)/2=%ld\n",
4106 0 : D0, m, (L - 1)/2);
4107 84228 : continue;
4108 : }
4109 : /* Heuristic. Doesn't end up contributing much. */
4110 218761 : H_cost = 2 * deg * deg;
4111 :
4112 : /* 0xc = 0b1100, so D0_entry.m & 0xc == 1 + (D0 | 2) */
4113 218761 : if ((D0 & 7) == 5) /* D0 = 5 (mod 8) */
4114 6065 : twofactor = ((D0_entry.m & 0xc) ? 1 : 3);
4115 : else
4116 212696 : twofactor = 0;
4117 :
4118 218761 : btop = avma;
4119 : /* For each small prime... */
4120 770017 : for (i = 0; i <= SMOOTH_PRIMES; i++) {
4121 : long h1, h2, D1, D2, n1, n2, dl1, dl20, dl21, p, q, j;
4122 : double p_bits;
4123 769912 : set_avma(btop);
4124 : /* i = 0 corresponds to 1, which we do not want to skip! (i.e. DK = D) */
4125 769912 : if (i) {
4126 1091450 : if (modinv_odd_conductor(inv) && i == 1) continue;
4127 540836 : p = (long)pari_PRIMES[i];
4128 : /* Don't allow large factors in the conductor. */
4129 659537 : if (p > max_L1) break;
4130 440881 : if (p == L0 || p == L1 || p == L || p == modinv_p1 || p == modinv_p2)
4131 152824 : continue;
4132 288057 : p_bits = log2(p);
4133 : /* h1 is the class number of D1 = q^2 D0, where q = p^j (j defined in the loop below) */
4134 288057 : h1 = h0 * (p - ((D0_entry.m >> (2*i)) & 0x3) + 1);
4135 : /* q is the smallest power of p such that h1 >= d ~ "L + 1". */
4136 291527 : for (j = 1, q = p; h1 < d; j++, q *= p, h1 *= p)
4137 : ;
4138 288057 : D1 = q * q * D0;
4139 : /* can't have D1 = 0 mod 16 and hope to get any primes congruent to 3 mod 4 */
4140 288057 : if ((pfilter & IQ_FILTER_1MOD4) && !(D1 & 0xF)) continue;
4141 : } else {
4142 : /* i = 0, corresponds to "p = 1". */
4143 218761 : h1 = h0;
4144 218761 : D1 = D0;
4145 218761 : p = q = j = 1;
4146 218761 : p_bits = 0;
4147 : }
4148 : /* include a factor of 4 if D1 is 5 mod 8 */
4149 : /* XXX: No idea why he does this. */
4150 506748 : if (twofactor && (q & 1)) {
4151 15418 : if (modinv_odd_conductor(inv)) continue;
4152 119 : D1 *= 4;
4153 119 : h1 *= twofactor;
4154 : }
4155 : /* heuristic early abort; we may miss good D1's, but this saves time */
4156 491449 : if (totbits > minbits && best_cost && h1*(L-1) > 2.2*best_cost) continue;
4157 :
4158 : /* log2(D0 * (p^j)^2 * L^2 * twofactor) > (BIL - 1) -- params too big. */
4159 969115 : if (D0_bits + 2*j*p_bits + 2*L_bits
4160 483670 : + (twofactor && (q & 1) ? 2.0 : 0.0) > (BITS_IN_LONG-1)) continue;
4161 :
4162 481895 : if (! check_generators(&n1, NULL, D1, h1, n0, d, L0, L1)) continue;
4163 :
4164 460278 : if (n1 >= h1) dl1 = -1; /* fill it in later */
4165 208758 : else if ((dl1 = primeform_discrete_log(L0, L, n1, D1)) < 0) continue;
4166 333551 : dbg_printf(3)("Good D0=%ld, D1=%ld with q=%ld, L1=%ld, n1=%ld, h1=%ld\n",
4167 : D0, D1, q, L1, n1, h1);
4168 333551 : if (modinv_deg && orientation_ambiguity(D1, L0, modinv_p1, modinv_p2, modinv_N))
4169 1648 : continue;
4170 :
4171 331903 : D2 = L * L * D1;
4172 331903 : h2 = h1 * (L-1);
4173 : /* m is the order of L0^n1 in cl(D2) */
4174 331903 : if (!check_generators(&n2, &m, D2, h2, n1, d*(L-1), L0, L1)) continue;
4175 :
4176 : /* This restriction on m is not necessary, but simplifies life later */
4177 312869 : if (m < (L-1)/2 || (!L1 && m < L-1)) {
4178 150613 : dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4179 : "order of L0^n1 in cl(D2) is too small\n", D2, D1, D0, n2, h2, L1);
4180 150613 : continue;
4181 : }
4182 162256 : dl20 = n1;
4183 162256 : dl21 = 0;
4184 162256 : if (m < L-1) {
4185 86991 : GEN Q1 = qform_primeform2(L, D1), Q2, X;
4186 86991 : if (!Q1) pari_err_BUG("modpoly_pickD");
4187 86991 : Q2 = primeform_u(stoi(D2), L1);
4188 86991 : Q2 = qfbcomp(Q1, Q2); /* we know this element has order L-1 */
4189 86991 : Q1 = primeform_u(stoi(D2), L0);
4190 86991 : k = ((n2 & 1) ? 2*n2 : n2)/(L-1);
4191 86991 : Q1 = gpowgs(Q1, k);
4192 86991 : X = qfi_Shanks(Q2, Q1, L-1);
4193 86991 : if (!X) {
4194 14094 : dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4195 : "form of norm L^2 not generated by L0 and L1\n",
4196 : D2, D1, D0, n2, h2, L1);
4197 14094 : continue;
4198 : }
4199 72897 : dl20 = itos(X) * k;
4200 72897 : dl21 = 1;
4201 : }
4202 148162 : if (! (m < L-1 || n2 < d*(L-1)) && n1 >= d && ! use_L1)
4203 74771 : L1 = 0; /* we don't need L1 */
4204 :
4205 148162 : if (!L1 && use_L1) {
4206 0 : dbg_printf(3)("not using D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
4207 : "because we don't need L1 but must use it\n",
4208 : D2, D1, D0, n2, h2, L1);
4209 0 : continue;
4210 : }
4211 : /* don't allow zero dl21 with L1 for the moment, since
4212 : * modpoly doesn't handle it - we may change this in the future */
4213 148162 : if (L1 && ! dl21) continue;
4214 147668 : dbg_printf(3)("Good D0=%ld, D1=%ld, D2=%ld with s=%ld^%ld, L1=%ld, dl2=%ld, n2=%ld, h2=%ld\n",
4215 : D0, D1, D2, p, j, L1, dl20, n2, h2);
4216 :
4217 : /* This estimate is heuristic and fiddling with the
4218 : * parameters 5 and 0.25 can change things quite a bit. */
4219 147668 : enum_cost = n2 * (5 * L0 * L0 + 0.25 * L1 * L1);
4220 147668 : cost = enum_cost + H_cost;
4221 147668 : if (best_cost && cost > 2.2*best_cost) break;
4222 37684 : if (best_cost && cost >= 0.99*best_cost) continue;
4223 :
4224 9403 : Dinfo.GENcode0 = evaltyp(t_VECSMALL)|_evallg(13);
4225 9403 : Dinfo.inv = inv;
4226 9403 : Dinfo.L = L;
4227 9403 : Dinfo.D0 = D0;
4228 9403 : Dinfo.D1 = D1;
4229 9403 : Dinfo.L0 = L0;
4230 9403 : Dinfo.L1 = L1;
4231 9403 : Dinfo.n1 = n1;
4232 9403 : Dinfo.n2 = n2;
4233 9403 : Dinfo.dl1 = dl1;
4234 9403 : Dinfo.dl2_0 = dl20;
4235 9403 : Dinfo.dl2_1 = dl21;
4236 9403 : Dinfo.cost = cost;
4237 :
4238 9403 : if (!modpoly_pickD_primes(NULL, NULL, 0, NULL, 0, &Dinfo.bits, minbits, &Dinfo))
4239 44 : continue;
4240 9359 : dbg_printf(2)("Best D2=%ld, D1=%ld, D0=%ld with s=%ld^%ld, L1=%ld, "
4241 : "n1=%ld, n2=%ld, cost ratio %.2f, bits=%ld\n",
4242 : D2, D1, D0, p, j, L1, n1, n2,
4243 0 : (double)cost/(d*(L-1)), Dinfo.bits);
4244 : /* Insert Dinfo into the Ds array. Ds is sorted by ascending cost. */
4245 50474 : for (j = 0; j < Dcnt; j++)
4246 47233 : if (Dinfo.cost < Ds[j].cost) break;
4247 9359 : if (n2 > MAX_VOLCANO_FLOOR_SIZE && n2*(L1 ? 2 : 1) > 1.2* (d*(L-1)) ) {
4248 0 : dbg_printf(3)("Not using D1=%ld, D2=%ld for space reasons\n", D1, D2);
4249 0 : continue;
4250 : }
4251 9359 : if (j == Dcnt && Dcnt == MODPOLY_MAX_DCNT)
4252 0 : continue;
4253 9359 : totbits += Dinfo.bits;
4254 9359 : if (Dcnt == MODPOLY_MAX_DCNT) totbits -= Ds[Dcnt-1].bits;
4255 9359 : if (Dcnt < MODPOLY_MAX_DCNT) Dcnt++;
4256 9359 : if (n2 > MAX_VOLCANO_FLOOR_SIZE)
4257 0 : dbg_printf(3)("totbits=%ld, minbits=%ld\n", totbits, minbits);
4258 21673 : for (k = Dcnt-1; k > j; k--) Ds[k] = Ds[k-1];
4259 9359 : Ds[k] = Dinfo;
4260 9359 : best_cost = (totbits > minbits)? Ds[Dcnt-1].cost: 0;
4261 : /* if we were able to use D1 with s = 1, there is no point in
4262 : * using any larger D1 for the same D0 */
4263 9359 : if (!i) break;
4264 : } /* END FOR over small primes */
4265 : } /* END WHILE over D0's */
4266 3228 : dbg_printf(2)(" checked %ld of %ld fundamental discriminants to find suitable "
4267 : "discriminant (Dcnt = %ld)\n", D0_i, tablen, Dcnt);
4268 3228 : if ( ! Dcnt) {
4269 0 : dbg_printf(1)("failed completely for L=%ld\n", L);
4270 0 : return 0;
4271 : }
4272 :
4273 3228 : Dcnt = calc_primes_for_discriminants(Ds, Dcnt, L, minbits);
4274 :
4275 : /* fill in any missing dl1's */
4276 6472 : for (i = 0 ; i < Dcnt; i++)
4277 3244 : if (Ds[i].dl1 < 0 &&
4278 3220 : (Ds[i].dl1 = primeform_discrete_log(L0, L, Ds[i].n1, Ds[i].D1)) < 0)
4279 0 : pari_err_BUG("modpoly_pickD");
4280 3228 : if (DEBUGLEVEL > 1+3) {
4281 0 : err_printf("Selected %ld discriminants using %ld msecs\n", Dcnt, timer_delay(&T));
4282 0 : for (i = 0 ; i < Dcnt ; i++)
4283 : {
4284 0 : GEN H = classno(stoi(Ds[i].D0));
4285 0 : long h0 = itos(H);
4286 0 : err_printf (" D0=%ld, h(D0)=%ld, D=%ld, L0=%ld, L1=%ld, "
4287 : "cost ratio=%.2f, enum ratio=%.2f,",
4288 0 : Ds[i].D0, h0, Ds[i].D1, Ds[i].L0, Ds[i].L1,
4289 0 : (double)Ds[i].cost/(d*(L-1)),
4290 0 : (double)(Ds[i].n2*(Ds[i].L1 ? 2 : 1))/(d*(L-1)));
4291 0 : err_printf (" %ld primes, %ld bits\n", Ds[i].nprimes, Ds[i].bits);
4292 : }
4293 : }
4294 3228 : return gc_long(ltop, Dcnt);
4295 : }
4296 :
4297 : static int
4298 15420475 : _qsort_cmp(const void *a, const void *b)
4299 : {
4300 15420475 : D_entry *x = (D_entry *)a, *y = (D_entry *)b;
4301 : long u, v;
4302 :
4303 : /* u and v are the class numbers of x and y */
4304 15420475 : u = x->h * (!!(x->m & 2) + 1);
4305 15420475 : v = y->h * (!!(y->m & 2) + 1);
4306 : /* Sort by class number */
4307 15420475 : if (u < v) return -1;
4308 10736035 : if (u > v) return 1;
4309 : /* Sort by discriminant (which is < 0, hence the sign reversal) */
4310 3230579 : if (x->D > y->D) return -1;
4311 0 : if (x->D < y->D) return 1;
4312 0 : return 0;
4313 : }
4314 :
4315 : /* Build a table containing fundamental D, |D| <= maxD whose class groups
4316 : * - are cyclic generated by an element of norm L0
4317 : * - have class number at most maxh
4318 : * The table is ordered using _qsort_cmp above, which ranks the discriminants
4319 : * by class number, then by absolute discriminant.
4320 : *
4321 : * INPUT:
4322 : * - maxd: largest allowed discriminant
4323 : * - maxh: largest allowed class number
4324 : * - L0: norm of class group generator (2, 3, 5, or 7)
4325 : *
4326 : * OUTPUT:
4327 : * - tablelen: length of return value
4328 : *
4329 : * RETURN:
4330 : * - array of {D, h(D), kronecker symbols for small p} */
4331 : static D_entry *
4332 3228 : scanD0(long *tablelen, long *minD, long maxD, long maxh, long L0)
4333 : {
4334 : pari_sp av;
4335 : D_entry *tab;
4336 : long i, lF, cnt;
4337 : GEN F;
4338 :
4339 : /* NB: As seen in the loop below, the real class number of D can be */
4340 : /* 2*maxh if cl(D) is cyclic. */
4341 3228 : tab = (D_entry *) stack_malloc((maxD/4)*sizeof(*tab)); /* Overestimate */
4342 3228 : F = vecfactorsquarefreeu_coprime(*minD, maxD, mkvecsmall(2));
4343 3228 : lF = lg(F);
4344 32263860 : for (av = avma, cnt = 0, i = 1; i < lF; i++, set_avma(av))
4345 : {
4346 32260632 : GEN DD, ordL, f, q = gel(F,i);
4347 : long j, k, n, h, L1, d, D;
4348 : ulong m;
4349 :
4350 32260632 : if (!q) continue; /* not square-free */
4351 : /* restrict to possibly cyclic class groups */
4352 13083068 : k = lg(q) - 1; if (k > 2) continue;
4353 10193544 : d = i + *minD - 1; /* q = prime divisors of d */
4354 10193544 : if ((d & 3) == 1) continue;
4355 5129038 : D = -d; /* d = 3 (mod 4), D = 1 mod 4 fundamental */
4356 5129038 : if (kross(D, L0) < 1) continue;
4357 :
4358 : /* L1 initially the first factor of d if small enough, otherwise ignored */
4359 2476681 : L1 = (k > 1 && q[1] <= MAX_L1)? q[1]: 0;
4360 :
4361 : /* Check if h(D) is too big */
4362 2476681 : h = hclassno6u(d) / 6;
4363 2476681 : if (h > 2*maxh || (!L1 && h > maxh)) continue;
4364 :
4365 : /* Check if ord(f) is not big enough to generate at least half the
4366 : * class group (where f is the L0-primeform). */
4367 2299563 : DD = stoi(D);
4368 2299563 : f = primeform_u(DD, L0);
4369 2299563 : ordL = qfi_order(qfi_red(f), stoi(h));
4370 2299563 : n = itos(ordL);
4371 2299563 : if (n < h/2 || (!L1 && n < h)) continue;
4372 :
4373 : /* If f is big enough, great! Otherwise, for each potential L1,
4374 : * do a discrete log to see if it is NOT in the subgroup generated
4375 : * by L0; stop as soon as such is found. */
4376 1977079 : for (j = 1;; j++) {
4377 2235158 : if (n == h || (L1 && !qfi_Shanks(primeform_u(DD, L1), f, n))) {
4378 1875817 : dbg_printf(2)("D0=%ld good with L1=%ld\n", D, L1);
4379 1875817 : break;
4380 : }
4381 359341 : if (!L1) break;
4382 258079 : L1 = (j <= k && k > 1 && q[j] <= MAX_L1 ? q[j] : 0);
4383 : }
4384 : /* The first bit of m is set iff f generates a proper subgroup of cl(D)
4385 : * (hence implying that we need L1). */
4386 1977079 : m = (n < h ? 1 : 0);
4387 : /* bits j and j+1 give the 2-bit number 1 + (D|p) where p = prime(j) */
4388 58810576 : for (j = 1 ; j <= SMOOTH_PRIMES; j++)
4389 : {
4390 56833497 : ulong x = (ulong) (1 + kross(D, (long) pari_PRIMES[j]));
4391 56833497 : m |= x << (2*j);
4392 : }
4393 :
4394 : /* Insert d, h and m into the table */
4395 1977079 : tab[cnt].D = D;
4396 1977079 : tab[cnt].h = h;
4397 1977079 : tab[cnt].m = m; cnt++;
4398 : }
4399 :
4400 : /* Sort the table */
4401 3228 : qsort(tab, cnt, sizeof(*tab), _qsort_cmp);
4402 3228 : *tablelen = cnt;
4403 3228 : *minD = maxD + 3 - (maxD & 3); /* smallest d >= maxD, d = 3 (mod 4) */
4404 3228 : return tab;
4405 : }
4406 :
4407 : /* Populate Ds with discriminants (and attached data) that can be
4408 : * used to calculate the modular polynomial of level L and invariant
4409 : * inv. Return the number of discriminants found. */
4410 : static long
4411 3226 : discriminant_with_classno_at_least(disc_info bestD[MODPOLY_MAX_DCNT],
4412 : long L, long inv, GEN Q, long ignore_sparse)
4413 : {
4414 : enum { SMALL_L_BOUND = 101 };
4415 3226 : long max_max_D = 160000 * (inv ? 2 : 1);
4416 : long minD, maxD, maxh, L0, max_L1, minbits, Dcnt, flags, s, d, i, tablen;
4417 : D_entry *tab;
4418 3226 : double eps, cost, best_eps = -1.0, best_cost = -1.0;
4419 : disc_info Ds[MODPOLY_MAX_DCNT];
4420 3226 : long best_cnt = 0;
4421 : pari_timer T;
4422 3226 : timer_start(&T);
4423 :
4424 3226 : s = modinv_sparse_factor(inv);
4425 3226 : d = ceildivuu(L+1, s) + 1;
4426 :
4427 : /* maxD of 10000 allows us to get a satisfactory discriminant in
4428 : * under 250ms in most cases. */
4429 3226 : maxD = 10000;
4430 : /* Allow the class number to overshoot L by 50%. Must be at least
4431 : * 1.1*L, and higher values don't seem to provide much benefit,
4432 : * except when L is small, in which case it's necessary to get any
4433 : * discriminant at all in some cases. */
4434 3226 : maxh = (L / s < SMALL_L_BOUND) ? 10 * L : 1.5 * L;
4435 :
4436 3226 : flags = ignore_sparse ? MODPOLY_IGNORE_SPARSE_FACTOR : 0;
4437 3226 : L0 = select_L0(L, inv, 0);
4438 3226 : max_L1 = L / 2 + 2; /* for L=11 we need L1=7 for j */
4439 3226 : minbits = modpoly_height_bound(L, inv);
4440 3226 : if (Q) minbits += expi(Q);
4441 3226 : minD = 7;
4442 :
4443 6452 : while ( ! best_cnt) {
4444 3228 : while (maxD <= max_max_D) {
4445 : /* TODO: Find a way to re-use tab when we need multiple modpolys */
4446 3228 : tab = scanD0(&tablen, &minD, maxD, maxh, L0);
4447 3228 : dbg_printf(1)("Found %ld potential fundamental discriminants\n", tablen);
4448 :
4449 3228 : Dcnt = modpoly_pickD(Ds, L, inv, L0, max_L1, minbits, flags, tab, tablen);
4450 3228 : eps = 0.0;
4451 3228 : cost = 0.0;
4452 :
4453 3228 : if (Dcnt) {
4454 3226 : long n1 = 0;
4455 6470 : for (i = 0; i < Dcnt; i++) {
4456 3244 : n1 = maxss(n1, Ds[i].n1);
4457 3244 : cost += Ds[i].cost;
4458 : }
4459 3226 : eps = (n1 * s - L) / (double)L;
4460 :
4461 3226 : if (best_cost < 0.0 || cost < best_cost) {
4462 3226 : if (best_cnt)
4463 0 : for (i = 0; i < best_cnt; i++) killblock((GEN)bestD[i].primes);
4464 3226 : (void) memcpy(bestD, Ds, Dcnt * sizeof(disc_info));
4465 3226 : best_cost = cost;
4466 3226 : best_cnt = Dcnt;
4467 3226 : best_eps = eps;
4468 : /* We're satisfied if n1 is within 5% of L. */
4469 3226 : if (L / s <= SMALL_L_BOUND || eps < 0.05) break;
4470 : } else {
4471 0 : for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
4472 : }
4473 : } else {
4474 2 : if (log2(maxD) > BITS_IN_LONG - 2 * (log2(L) + 2))
4475 : {
4476 0 : char *err = stack_sprintf("modular polynomial of level %ld and invariant %ld",L,inv);
4477 0 : pari_err(e_ARCH, err);
4478 : }
4479 : }
4480 2 : maxD *= 2;
4481 2 : minD += 4;
4482 2 : dbg_printf(0)(" Doubling discriminant search space (closest: %.1f%%, cost ratio: %.1f)...\n", eps*100, cost/(double)(d*(L-1)));
4483 : }
4484 3226 : max_max_D *= 2;
4485 : }
4486 :
4487 3226 : if (DEBUGLEVEL > 3) {
4488 0 : pari_sp av = avma;
4489 0 : err_printf("Found discriminant(s):\n");
4490 0 : for (i = 0; i < best_cnt; ++i) {
4491 0 : long h = itos(classno(stoi(bestD[i].D1)));
4492 0 : set_avma(av);
4493 0 : err_printf(" D = %ld, h = %ld, u = %ld, L0 = %ld, L1 = %ld, n1 = %ld, n2 = %ld, cost = %ld\n",
4494 0 : bestD[i].D1, h, usqrt(bestD[i].D1 / bestD[i].D0), bestD[i].L0,
4495 0 : bestD[i].L1, bestD[i].n1, bestD[i].n2, bestD[i].cost);
4496 : }
4497 0 : err_printf("(off target by %.1f%%, cost ratio: %.1f)\n",
4498 0 : best_eps*100, best_cost/(double)(d*(L-1)));
4499 : }
4500 3226 : return best_cnt;
4501 : }
|
