Code coverage tests

This page documents the degree to which the PARI/GP source code is tested by our public test suite, distributed with the source distribution in directory src/test/. This is measured by the gcov utility; we then process gcov output using the lcov frond-end.

We test a few variants depending on Configure flags on the pari.math.u-bordeaux.fr machine (x86_64 architecture), and agregate them in the final report:

The target is to exceed 90% coverage for all mathematical modules (given that branches depending on DEBUGLEVEL or DEBUGMEM are not covered). This script is run to produce the results below.

LCOV - code coverage report
Current view: top level - basemath - polmodular.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.16.2 lcov report (development 29375-be3334fb81) Lines: 2281 2352 97.0 %
Date: 2024-05-26 08:08:42 Functions: 142 142 100.0 %
Legend: Lines: hit not hit

          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       39613 : modinv_level(long inv)
      30             : {
      31       39613 :   switch (inv) {
      32       31035 :     case INV_J:     return 1;
      33        1323 :     case INV_G2:
      34        1323 :     case INV_W3W3E2:return 3;
      35        1098 :     case INV_F:
      36             :     case INV_F2:
      37             :     case INV_F4:
      38        1098 :     case INV_F8:    return 6;
      39          70 :     case INV_F3:    return 2;
      40         511 :     case INV_W3W3:  return 6;
      41        1596 :     case INV_W2W7E2:
      42        1596 :     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         644 :     case INV_W2W5E2:
      47         644 :     case INV_W2W5:  return 30;
      48         441 :     case INV_W2W13: return 26;
      49        1725 :     case INV_W3W7:  return 42;
      50         544 :     case INV_W5W7:  return 35;
      51          56 :     case INV_W3W13: return 39;
      52             :   }
      53             :   pari_err_BUG("modinv_level"); return 0;/*LCOV_EXCL_LINE*/
      54             : }
      55             : 
      56             : /* Where applicable, returns N=p1*p2 (possibly p2=1) s.t. two j's
      57             :  * related to the same f are N-isogenous, and 0 otherwise.  This is
      58             :  * often (but not necessarily) equal to the level. */
      59             : long
      60     7243203 : modinv_degree(long *p1, long *p2, long inv)
      61             : {
      62     7243203 :   switch (inv) {
      63      297318 :     case INV_W3W5:  return (*p1 = 3) * (*p2 = 5);
      64      427304 :     case INV_W2W3E2:
      65      427304 :     case INV_W2W3:  return (*p1 = 2) * (*p2 = 3);
      66     1545188 :     case INV_W2W5E2:
      67     1545188 :     case INV_W2W5:  return (*p1 = 2) * (*p2 = 5);
      68      947790 :     case INV_W2W7E2:
      69      947790 :     case INV_W2W7:  return (*p1 = 2) * (*p2 = 7);
      70     1470081 :     case INV_W2W13: return (*p1 = 2) * (*p2 = 13);
      71      510561 :     case INV_W3W7:  return (*p1 = 3) * (*p2 = 7);
      72      782137 :     case INV_W3W3E2:
      73      782137 :     case INV_W3W3:  return (*p1 = 3) * (*p2 = 3);
      74      349380 :     case INV_W5W7:  return (*p1 = 5) * (*p2 = 7);
      75      195062 :     case INV_W3W13: return (*p1 = 3) * (*p2 = 13);
      76             :   }
      77      718382 :   *p1 = *p2 = 1; return 0;
      78             : }
      79             : 
      80             : /* Certain invariants require that D not have 2 in it's conductor, but
      81             :  * this doesn't apply to every invariant with even level so we handle
      82             :  * it separately */
      83             : INLINE int
      84      526621 : modinv_odd_conductor(long inv)
      85             : {
      86      526621 :   switch (inv) {
      87       70942 :     case INV_F:
      88             :     case INV_W3W3:
      89       70942 :     case INV_W3W7: return 1;
      90             :   }
      91      455679 :   return 0;
      92             : }
      93             : 
      94             : long
      95    22758954 : modinv_height_factor(long inv)
      96             : {
      97    22758954 :   switch (inv) {
      98     1880674 :     case INV_J:     return 1;
      99     1700223 :     case INV_G2:    return 3;
     100     3110886 :     case INV_F:     return 72;
     101          28 :     case INV_F2:    return 36;
     102      538020 :     case INV_F3:    return 24;
     103          49 :     case INV_F4:    return 18;
     104          49 :     case INV_F8:    return 9;
     105          63 :     case INV_W2W3:  return 72;
     106     2361072 :     case INV_W3W3:  return 36;
     107     3548202 :     case INV_W2W5:  return 54;
     108     1341537 :     case INV_W2W7:  return 48;
     109        1386 :     case INV_W3W5:  return 36;
     110     3892770 :     case INV_W2W13: return 42;
     111     1143429 :     case INV_W3W7:  return 32;
     112     1171891 :     case INV_W2W3E2:return 36;
     113      149184 :     case INV_W2W5E2:return 27;
     114     1081990 :     case INV_W2W7E2:return 24;
     115          49 :     case INV_W3W3E2:return 18;
     116      837438 :     case INV_W5W7:  return 24;
     117          14 :     case INV_W3W13: return 28;
     118             :     default: pari_err_BUG("modinv_height_factor"); return 0;/*LCOV_EXCL_LINE*/
     119             :   }
     120             : }
     121             : 
     122             : long
     123     1907423 : disc_best_modinv(long D)
     124             : {
     125             :   long ret;
     126     1907423 :   ret = INV_F;     if (modinv_good_disc(ret, D)) return ret;
     127     1534057 :   ret = INV_W2W3;  if (modinv_good_disc(ret, D)) return ret;
     128     1534057 :   ret = INV_W2W5;  if (modinv_good_disc(ret, D)) return ret;
     129     1238755 :   ret = INV_W2W7;  if (modinv_good_disc(ret, D)) return ret;
     130     1139957 :   ret = INV_W2W13; if (modinv_good_disc(ret, D)) return ret;
     131      838012 :   ret = INV_W3W3;  if (modinv_good_disc(ret, D)) return ret;
     132      651805 :   ret = INV_W2W3E2;if (modinv_good_disc(ret, D)) return ret;
     133      579453 :   ret = INV_W3W5;  if (modinv_good_disc(ret, D)) return ret;
     134      579299 :   ret = INV_W3W7;  if (modinv_good_disc(ret, D)) return ret;
     135      511091 :   ret = INV_W3W13; if (modinv_good_disc(ret, D)) return ret;
     136      511091 :   ret = INV_W2W5E2;if (modinv_good_disc(ret, D)) return ret;
     137      494753 :   ret = INV_F3;    if (modinv_good_disc(ret, D)) return ret;
     138      464485 :   ret = INV_W2W7E2;if (modinv_good_disc(ret, D)) return ret;
     139      376656 :   ret = INV_W5W7;  if (modinv_good_disc(ret, D)) return ret;
     140      308581 :   ret = INV_W3W3E2;if (modinv_good_disc(ret, D)) return ret;
     141      308581 :   ret = INV_G2;    if (modinv_good_disc(ret, D)) return ret;
     142      160517 :   return INV_J;
     143             : }
     144             : 
     145             : INLINE long
     146       43420 : modinv_sparse_factor(long inv)
     147             : {
     148       43420 :   switch (inv) {
     149        4855 :   case INV_G2:
     150             :   case INV_F8:
     151             :   case INV_W3W5:
     152             :   case INV_W2W5E2:
     153             :   case INV_W3W3E2:
     154        4855 :     return 3;
     155         625 :   case INV_F:
     156         625 :     return 24;
     157         357 :   case INV_F2:
     158             :   case INV_W2W3:
     159         357 :     return 12;
     160         112 :   case INV_F3:
     161         112 :     return 8;
     162        1645 :   case INV_F4:
     163             :   case INV_W2W3E2:
     164             :   case INV_W2W5:
     165             :   case INV_W3W3:
     166        1645 :     return 6;
     167        1046 :   case INV_W2W7:
     168        1046 :     return 4;
     169        2951 :   case INV_W2W7E2:
     170             :   case INV_W2W13:
     171             :   case INV_W3W7:
     172        2951 :     return 2;
     173             :   }
     174       31829 :   return 1;
     175             : }
     176             : 
     177             : #define IQ_FILTER_1MOD3 1
     178             : #define IQ_FILTER_2MOD3 2
     179             : #define IQ_FILTER_1MOD4 4
     180             : #define IQ_FILTER_3MOD4 8
     181             : 
     182             : INLINE long
     183       14553 : modinv_pfilter(long inv)
     184             : {
     185       14553 :   switch (inv) {
     186        2838 :   case INV_G2:
     187             :   case INV_W3W3:
     188             :   case INV_W3W3E2:
     189             :   case INV_W3W5:
     190             :   case INV_W2W5:
     191             :   case INV_W2W3E2:
     192             :   case INV_W2W5E2:
     193             :   case INV_W5W7:
     194             :   case INV_W3W13:
     195        2838 :     return IQ_FILTER_1MOD3; /* ensure unique cube roots */
     196         529 :   case INV_W2W7:
     197             :   case INV_F3:
     198         529 :     return IQ_FILTER_1MOD4; /* ensure at most two 4th/8th roots */
     199         972 :   case INV_F:
     200             :   case INV_F2:
     201             :   case INV_F4:
     202             :   case INV_F8:
     203             :   case INV_W2W3:
     204             :     /* Ensure unique cube roots and at most two 4th/8th roots */
     205         972 :     return IQ_FILTER_1MOD3 | IQ_FILTER_1MOD4;
     206             :   }
     207       10214 :   return 0;
     208             : }
     209             : 
     210             : int
     211    10592604 : modinv_good_prime(long inv, long p)
     212             : {
     213    10592604 :   switch (inv) {
     214      412678 :   case INV_G2:
     215             :   case INV_W2W3E2:
     216             :   case INV_W3W3:
     217             :   case INV_W3W3E2:
     218             :   case INV_W3W5:
     219             :   case INV_W2W5E2:
     220             :   case INV_W2W5:
     221      412678 :     return (p % 3) == 2;
     222      410256 :   case INV_W2W7:
     223             :   case INV_F3:
     224      410256 :     return (p & 3) != 1;
     225      392888 :   case INV_F2:
     226             :   case INV_F4:
     227             :   case INV_F8:
     228             :   case INV_F:
     229             :   case INV_W2W3:
     230      392888 :     return ((p % 3) == 2) && (p & 3) != 1;
     231             :   }
     232     9376782 :   return 1;
     233             : }
     234             : 
     235             : /* Returns true if the prime p does not divide the conductor of D */
     236             : INLINE int
     237     3257079 : prime_to_conductor(long D, long p)
     238             : {
     239             :   long b;
     240     3257079 :   if (p > 2) return (D % (p * p));
     241     1250577 :   b = D & 0xF;
     242     1250577 :   return (b && b != 4); /* 2 divides the conductor of D <=> D=0,4 mod 16 */
     243             : }
     244             : 
     245             : INLINE GEN
     246     3257079 : red_primeform(long D, long p)
     247             : {
     248     3257079 :   pari_sp av = avma;
     249             :   GEN P;
     250     3257079 :   if (!prime_to_conductor(D, p)) return NULL;
     251     3257079 :   P = primeform_u(stoi(D), p); /* primitive since p \nmid conductor */
     252     3257079 :   return gerepileupto(av, qfbred_i(P));
     253             : }
     254             : 
     255             : /* Computes product of primeforms over primes appearing in the prime
     256             :  * factorization of n (including multiplicity) */
     257             : GEN
     258      135737 : qfb_nform(long D, long n)
     259             : {
     260      135737 :   pari_sp av = avma;
     261      135737 :   GEN N = NULL, fa = factoru(n), P = gel(fa,1), E = gel(fa,2);
     262      135737 :   long i, l = lg(P);
     263             : 
     264      407127 :   for (i = 1; i < l; ++i)
     265             :   {
     266             :     long j, e;
     267      271390 :     GEN Q = red_primeform(D, P[i]);
     268      271390 :     if (!Q) return gc_NULL(av);
     269      271390 :     e = E[i];
     270      271390 :     if (i == 1) { N = Q; j = 1; } else j = 0;
     271      407127 :     for (; j < e; ++j) N = qfbcomp_i(Q, N);
     272             :   }
     273      135737 :   return gerepileupto(av, N);
     274             : }
     275             : 
     276             : INLINE int
     277     1688036 : qfb_is_two_torsion(GEN x)
     278             : {
     279     3376072 :   return equali1(gel(x,1)) || !signe(gel(x,2))
     280     3376072 :     || equalii(gel(x,1), gel(x,2)) || equalii(gel(x,1), gel(x,3));
     281             : }
     282             : 
     283             : /* Returns true iff the products p1*p2, p1*p2^-1, p1^-1*p2, and
     284             :  * p1^-1*p2^-1 are all distinct in cl(D) */
     285             : INLINE int
     286      232590 : qfb_distinct_prods(long D, long p1, long p2)
     287             : {
     288             :   GEN P1, P2;
     289             : 
     290      232590 :   P1 = red_primeform(D, p1);
     291      232590 :   if (!P1) return 0;
     292      232590 :   P1 = qfbsqr_i(P1);
     293             : 
     294      232590 :   P2 = red_primeform(D, p2);
     295      232590 :   if (!P2) return 0;
     296      232590 :   P2 = qfbsqr_i(P2);
     297             : 
     298      232590 :   return !(equalii(gel(P1,1), gel(P2,1)) && absequalii(gel(P1,2), gel(P2,2)));
     299             : }
     300             : 
     301             : /* By Corollary 3.1 of Enge-Schertz Constructing elliptic curves over finite
     302             :  * fields using double eta-quotients, we need p1 != p2 to both be noninert
     303             :  * and prime to the conductor, and if p1=p2=p we want p split and prime to the
     304             :  * conductor. We exclude the case that p1=p2 divides the conductor, even
     305             :  * though this does yield class invariants */
     306             : INLINE int
     307     5315161 : modinv_double_eta_good_disc(long D, long inv)
     308             : {
     309     5315161 :   pari_sp av = avma;
     310             :   GEN P;
     311             :   long i1, i2, p1, p2, N;
     312             : 
     313     5315161 :   N = modinv_degree(&p1, &p2, inv);
     314     5315161 :   if (! N) return 0;
     315     5315161 :   i1 = kross(D, p1);
     316     5315161 :   if (i1 < 0) return 0;
     317             :   /* Exclude ramified case for w_{p,p} */
     318     2407366 :   if (p1 == p2 && !i1) return 0;
     319     2407366 :   i2 = kross(D, p2);
     320     2407366 :   if (i2 < 0) return 0;
     321             :   /* this also verifies that p1 is prime to the conductor */
     322     1371341 :   P = red_primeform(D, p1);
     323     1371341 :   if (!P || gequal1(gel(P,1)) /* don't allow p1 to be principal */
     324             :       /* if p1 is unramified, require it to have order > 2 */
     325     1371341 :       || (i1 && qfb_is_two_torsion(P))) return gc_bool(av,0);
     326     1369717 :   if (p1 == p2) /* if p1=p2 we need p1*p1 to be distinct from its inverse */
     327      220549 :     return gc_bool(av, !qfb_is_two_torsion(qfbsqr_i(P)));
     328             : 
     329             :   /* this also verifies that p2 is prime to the conductor */
     330     1149168 :   P = red_primeform(D, p2);
     331     1149168 :   if (!P || gequal1(gel(P,1)) /* don't allow p2 to be principal */
     332             :       /* if p2 is unramified, require it to have order > 2 */
     333     1149168 :       || (i2 && qfb_is_two_torsion(P))) return gc_bool(av,0);
     334     1147705 :   set_avma(av);
     335             : 
     336             :   /* if p1 and p2 are split, we also require p1*p2, p1*p2^-1, p1^-1*p2,
     337             :    * and p1^-1*p2^-1 to be distinct */
     338     1147705 :   if (i1>0 && i2>0 && !qfb_distinct_prods(D, p1, p2)) return gc_bool(av,0);
     339     1144589 :   if (!i1 && !i2) {
     340             :     /* if both p1 and p2 are ramified, make sure their product is not
     341             :      * principal */
     342      135359 :     P = qfb_nform(D, N);
     343      135359 :     if (equali1(gel(P,1))) return gc_bool(av,0);
     344      135107 :     set_avma(av);
     345             :   }
     346     1144337 :   return 1;
     347             : }
     348             : 
     349             : /* Assumes D is a good discriminant for inv, which implies that the
     350             :  * level is prime to the conductor */
     351             : long
     352         504 : modinv_ramified(long D, long inv, long *pN)
     353             : {
     354         504 :   long p1, p2; *pN = modinv_degree(&p1, &p2, inv);
     355         504 :   if (*pN <= 1) return 0;
     356         504 :   return !(D % p1) && !(D % p2);
     357             : }
     358             : 
     359             : int
     360    14799424 : modinv_good_disc(long inv, long D)
     361             : {
     362    14799424 :   switch (inv) {
     363      836333 :   case INV_J:
     364      836333 :     return 1;
     365      463624 :   case INV_G2:
     366      463624 :     return !!(D % 3);
     367      502845 :   case INV_F3:
     368      502845 :     return (-D & 7) == 7;
     369     2062667 :   case INV_F:
     370             :   case INV_F2:
     371             :   case INV_F4:
     372             :   case INV_F8:
     373     2062667 :     return ((-D & 7) == 7) && (D % 3);
     374      622069 :   case INV_W3W5:
     375      622069 :     return (D % 3) && modinv_double_eta_good_disc(D, inv);
     376      335664 :   case INV_W3W3E2:
     377      335664 :     return (D % 3) && modinv_double_eta_good_disc(D, inv);
     378      897015 :   case INV_W3W3:
     379      897015 :     return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
     380      667688 :   case INV_W2W3E2:
     381      667688 :     return (D % 3) && modinv_double_eta_good_disc(D, inv);
     382     1554721 :   case INV_W2W3:
     383     1554721 :     return ((-D & 7) == 7) && (D % 3) && modinv_double_eta_good_disc(D, inv);
     384     1581685 :   case INV_W2W5:
     385     1581685 :     return ((-D % 80) != 20) && (D % 3) && modinv_double_eta_good_disc(D, inv);
     386      549171 :   case INV_W2W5E2:
     387      549171 :     return (D % 3) && modinv_double_eta_good_disc(D, inv);
     388      566027 :   case INV_W2W7E2:
     389      566027 :     return ((-D % 112) != 84) && modinv_double_eta_good_disc(D, inv);
     390     1324607 :   case INV_W2W7:
     391     1324607 :     return ((-D & 7) == 7) && modinv_double_eta_good_disc(D, inv);
     392     1196839 :   case INV_W2W13:
     393     1196839 :     return ((-D % 208) != 52) && modinv_double_eta_good_disc(D, inv);
     394      666806 :   case INV_W3W7:
     395      666806 :     return (D & 1) && (-D % 21) && modinv_double_eta_good_disc(D, inv);
     396      450975 :   case INV_W5W7: /* NB: This is a guess; avs doesn't have an entry */
     397      450975 :     return (D % 3) && modinv_double_eta_good_disc(D, inv);
     398      520688 :   case INV_W3W13: /* NB: This is a guess; avs doesn't have an entry */
     399      520688 :     return (D & 1) && (D % 3) && modinv_double_eta_good_disc(D, inv);
     400             :   }
     401           0 :   pari_err_BUG("modinv_good_discriminant");
     402             :   return 0;/*LCOV_EXCL_LINE*/
     403             : }
     404             : 
     405             : int
     406         784 : modinv_is_Weber(long inv)
     407             : {
     408           0 :   return inv == INV_F || inv == INV_F2 || inv == INV_F3 || inv == INV_F4
     409         784 :     || inv == INV_F8;
     410             : }
     411             : 
     412             : int
     413      232200 : modinv_is_double_eta(long inv)
     414             : {
     415      232200 :   switch (inv) {
     416       31322 :   case INV_W2W3:
     417             :   case INV_W2W3E2:
     418             :   case INV_W2W5:
     419             :   case INV_W2W5E2:
     420             :   case INV_W2W7:
     421             :   case INV_W2W7E2:
     422             :   case INV_W2W13:
     423             :   case INV_W3W3:
     424             :   case INV_W3W3E2:
     425             :   case INV_W3W5:
     426             :   case INV_W3W7:
     427             :   case INV_W5W7:
     428             :   case INV_W3W13:
     429       31322 :     return 1;
     430             :   }
     431      200878 :   return 0;
     432             : }
     433             : 
     434             : /* END Code from "class_inv.h" */
     435             : 
     436             : INLINE int
     437        9868 : safe_abs_sqrt(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
     438             : {
     439        9868 :   if (krouu(x, p) == -1)
     440             :   {
     441        4619 :     if (p%4 == 1) return 0;
     442        4619 :     x = Fl_neg(x, p);
     443             :   }
     444        9868 :   *r = Fl_sqrt_pre_i(x, s2, p, pi);
     445        9868 :   return 1;
     446             : }
     447             : 
     448             : INLINE int
     449        5094 : eighth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
     450             : {
     451             :   ulong s;
     452        5094 :   if (krouu(x, p) == -1) return 0;
     453        2710 :   s = Fl_sqrt_pre_i(x, s2, p, pi);
     454        2710 :   return safe_abs_sqrt(&s, s, p, pi, s2) && safe_abs_sqrt(r, s, p, pi, s2);
     455             : }
     456             : 
     457             : INLINE ulong
     458        2968 : modinv_f_from_j(ulong j, ulong p, ulong pi, ulong s2, long only_residue)
     459             : {
     460        2968 :   pari_sp av = avma;
     461             :   GEN pol, r;
     462             :   long i;
     463        2968 :   ulong g2, f = ULONG_MAX;
     464             : 
     465             :   /* f^8 must be a root of X^3 - \gamma_2 X - 16 */
     466        2968 :   g2 = Fl_sqrtl_pre(j, 3, p, pi);
     467             : 
     468        2968 :   pol = mkvecsmall5(0UL, Fl_neg(16 % p, p), Fl_neg(g2, p), 0UL, 1UL);
     469        2968 :   r = Flx_roots_pre(pol, p, pi);
     470        5553 :   for (i = 1; i < lg(r); ++i)
     471        5553 :     if (only_residue)
     472        1178 :     { if (krouu(r[i], p) != -1) return gc_ulong(av,r[i]); }
     473        4375 :     else if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
     474           0 :   pari_err_BUG("modinv_f_from_j");
     475             :   return 0;/*LCOV_EXCL_LINE*/
     476             : }
     477             : 
     478             : INLINE ulong
     479         358 : modinv_f3_from_j(ulong j, ulong p, ulong pi, ulong s2)
     480             : {
     481         358 :   pari_sp av = avma;
     482             :   GEN pol, r;
     483             :   long i;
     484         358 :   ulong f = ULONG_MAX;
     485             : 
     486         358 :   pol = mkvecsmall5(0UL,
     487         358 :       Fl_neg(4096 % p, p), Fl_sub(768 % p, j, p), Fl_neg(48 % p, p), 1UL);
     488         358 :   r = Flx_roots_pre(pol, p, pi);
     489         719 :   for (i = 1; i < lg(r); ++i)
     490         719 :     if (eighth_root(&f, r[i], p, pi, s2)) return gc_ulong(av,f);
     491           0 :   pari_err_BUG("modinv_f3_from_j");
     492             :   return 0;/*LCOV_EXCL_LINE*/
     493             : }
     494             : 
     495             : /* Return the exponent e for the double-eta "invariant" w such that
     496             :  * w^e is a class invariant.  For example w2w3^12 is a class
     497             :  * invariant, so double_eta_exponent(INV_W2W3) is 12 and
     498             :  * double_eta_exponent(INV_W2W3E2) is 6. */
     499             : INLINE ulong
     500       54035 : double_eta_exponent(long inv)
     501             : {
     502       54035 :   switch (inv) {
     503        2451 :   case INV_W2W3: return 12;
     504       13257 :   case INV_W2W3E2:
     505             :   case INV_W2W5:
     506       13257 :   case INV_W3W3: return 6;
     507        9768 :   case INV_W2W7: return 4;
     508        5803 :   case INV_W3W5:
     509             :   case INV_W2W5E2:
     510        5803 :   case INV_W3W3E2: return 3;
     511       15554 :   case INV_W2W7E2:
     512             :   case INV_W2W13:
     513       15554 :   case INV_W3W7: return 2;
     514        7202 :   default: return 1;
     515             :   }
     516             : }
     517             : 
     518             : INLINE ulong
     519          49 : weber_exponent(long inv)
     520             : {
     521          49 :   switch (inv)
     522             :   {
     523          42 :   case INV_F:  return 24;
     524           0 :   case INV_F2: return 12;
     525           7 :   case INV_F3: return 8;
     526           0 :   case INV_F4: return 6;
     527           0 :   case INV_F8: return 3;
     528           0 :   default:     return 1;
     529             :   }
     530             : }
     531             : 
     532             : INLINE ulong
     533       29409 : double_eta_power(long inv, ulong w, ulong p, ulong pi)
     534             : {
     535       29409 :   return Fl_powu_pre(w, double_eta_exponent(inv), p, pi);
     536             : }
     537             : 
     538             : static GEN
     539         161 : double_eta_raw_to_Fp(GEN f, GEN p)
     540             : {
     541         161 :   GEN u = FpX_red(RgV_to_RgX(gel(f,1), 0), p);
     542         161 :   GEN v = FpX_red(RgV_to_RgX(gel(f,2), 0), p);
     543         161 :   return mkvec3(u, v, gel(f,3));
     544             : }
     545             : 
     546             : /* Given a root x of polclass(D, inv) modulo N, returns a root of polclass(D,0)
     547             :  * modulo N by plugging x to a modular polynomial. For double-eta quotients,
     548             :  * this is done by plugging x into the modular polynomial Phi(INV_WpWq, j)
     549             :  * Enge, Morain 2013: Generalised Weber Functions. */
     550             : GEN
     551        1057 : Fp_modinv_to_j(GEN x, long inv, GEN p)
     552             : {
     553        1057 :   switch(inv)
     554             :   {
     555         392 :     case INV_J: return Fp_red(x, p);
     556         455 :     case INV_G2: return Fp_powu(x, 3, p);
     557          49 :     case INV_F: case INV_F2: case INV_F3: case INV_F4: case INV_F8:
     558             :     {
     559          49 :       GEN xe = Fp_powu(x, weber_exponent(inv), p);
     560          49 :       return Fp_div(Fp_powu(subiu(xe, 16), 3, p), xe, p);
     561             :     }
     562         161 :     default:
     563         161 :     if (modinv_is_double_eta(inv))
     564             :     {
     565         161 :       GEN xe = Fp_powu(x, double_eta_exponent(inv), p);
     566         161 :       GEN uvk = double_eta_raw_to_Fp(double_eta_raw(inv), p);
     567         161 :       GEN J0 = FpX_eval(gel(uvk,1), xe, p);
     568         161 :       GEN J1 = FpX_eval(gel(uvk,2), xe, p);
     569         161 :       GEN J2 = Fp_pow(xe, gel(uvk,3), p);
     570         161 :       GEN phi = mkvec3(J0, J1, J2);
     571         161 :       return FpX_oneroot(RgX_to_FpX(RgV_to_RgX(phi,1), p),p);
     572             :     }
     573             :     pari_err_BUG("Fp_modinv_to_j"); return NULL;/* LCOV_EXCL_LINE */
     574             :   }
     575             : }
     576             : 
     577             : /* Assuming p = 2 (mod 3) and p = 3 (mod 4): if the two 12th roots of
     578             :  * x (mod p) exist, set *r to one of them and return 1, otherwise
     579             :  * return 0 (without touching *r). */
     580             : INLINE int
     581         898 : twelth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
     582             : {
     583         898 :   ulong t = Fl_sqrtl_pre(x, 3, p, pi);
     584         898 :   if (krouu(t, p) == -1) return 0;
     585         850 :   t = Fl_sqrt_pre_i(t, s2, p, pi);
     586         850 :   return safe_abs_sqrt(r, t, p, pi, s2);
     587             : }
     588             : 
     589             : INLINE int
     590        5493 : sixth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
     591             : {
     592        5493 :   ulong t = Fl_sqrtl_pre(x, 3, p, pi);
     593        5493 :   if (krouu(t, p) == -1) return 0;
     594        5311 :   *r = Fl_sqrt_pre_i(t, s2, p, pi);
     595        5311 :   return 1;
     596             : }
     597             : 
     598             : INLINE int
     599        3964 : fourth_root(ulong *r, ulong x, ulong p, ulong pi, ulong s2)
     600             : {
     601             :   ulong s;
     602        3964 :   if (krouu(x, p) == -1) return 0;
     603        3598 :   s = Fl_sqrt_pre_i(x, s2, p, pi);
     604        3598 :   return safe_abs_sqrt(r, s, p, pi, s2);
     605             : }
     606             : 
     607             : INLINE int
     608       24465 : double_eta_root(long inv, ulong *r, ulong w, ulong p, ulong pi, ulong s2)
     609             : {
     610       24465 :   switch (double_eta_exponent(inv)) {
     611         898 :   case 12: return twelth_root(r, w, p, pi, s2);
     612        5493 :   case 6: return sixth_root(r, w, p, pi, s2);
     613        3964 :   case 4: return fourth_root(r, w, p, pi, s2);
     614        2594 :   case 3: *r = Fl_sqrtl_pre(w, 3, p, pi); return 1;
     615        8450 :   case 2: return krouu(w, p) != -1 && !!(*r = Fl_sqrt_pre_i(w, s2, p, pi));
     616        3066 :   default: *r = w; return 1; /* case 1 */
     617             :   }
     618             : }
     619             : 
     620             : /* F = double_eta_Fl(inv, p) */
     621             : static GEN
     622       41307 : Flx_double_eta_xpoly(GEN F, ulong j, ulong p, ulong pi)
     623             : {
     624       41307 :   GEN u = gel(F,1), v = gel(F,2), w;
     625       41307 :   long i, k = itos(gel(F,3)), lu = lg(u), lv = lg(v), lw = lu + 1;
     626             : 
     627       41307 :   w = cgetg(lw, t_VECSMALL); /* lu >= max(lv,k) */
     628       41307 :   w[1] = 0; /* variable number */
     629     1156891 :   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);
     630       82614 :   for (     ; i < lu; i++) uel(w, i+1) = uel(u,i);
     631       41307 :   uel(w, k+2) = Fl_add(uel(w, k+2), Fl_sqr_pre(j, p, pi), p);
     632       41307 :   return Flx_renormalize(w, lw);
     633             : }
     634             : 
     635             : /* F = double_eta_Fl(inv, p) */
     636             : static GEN
     637       29409 : Flx_double_eta_jpoly(GEN F, ulong x, ulong p, ulong pi)
     638             : {
     639       29409 :   pari_sp av = avma;
     640       29409 :   GEN u = gel(F,1), v = gel(F,2), xs;
     641       29409 :   long k = itos(gel(F,3));
     642             :   ulong a, b, c;
     643             : 
     644             :   /* u is always longest and the length is bigger than k */
     645       29409 :   xs = Fl_powers_pre(x, lg(u) - 1, p, pi);
     646       29409 :   c = Flv_dotproduct_pre(u, xs, p, pi);
     647       29409 :   b = Flv_dotproduct_pre(v, xs, p, pi);
     648       29409 :   a = uel(xs, k + 1);
     649       29409 :   set_avma(av);
     650       29409 :   return mkvecsmall4(0, c, b, a);
     651             : }
     652             : 
     653             : /* reduce F = double_eta_raw(inv) mod p */
     654             : static GEN
     655       29661 : double_eta_raw_to_Fl(GEN f, ulong p)
     656             : {
     657       29661 :   GEN u = ZV_to_Flv(gel(f,1), p);
     658       29661 :   GEN v = ZV_to_Flv(gel(f,2), p);
     659       29661 :   return mkvec3(u, v, gel(f,3));
     660             : }
     661             : /* double_eta_raw(inv) mod p */
     662             : static GEN
     663       23502 : double_eta_Fl(long inv, ulong p)
     664       23502 : { return double_eta_raw_to_Fl(double_eta_raw(inv), p); }
     665             : 
     666             : /* Go through roots of Psi(X,j) until one has an double_eta_exponent(inv)-th
     667             :  * root, and return that root. F = double_eta_Fl(inv,p) */
     668             : INLINE ulong
     669        5697 : modinv_double_eta_from_j(GEN F, long inv, ulong j, ulong p, ulong pi, ulong s2)
     670             : {
     671        5697 :   pari_sp av = avma;
     672             :   long i;
     673        5697 :   ulong f = ULONG_MAX;
     674        5697 :   GEN a = Flx_double_eta_xpoly(F, j, p, pi);
     675        5697 :   a = Flx_roots_pre(a, p, pi);
     676        6661 :   for (i = 1; i < lg(a); ++i)
     677        6661 :     if (double_eta_root(inv, &f, uel(a, i), p, pi, s2)) break;
     678        5697 :   if (i == lg(a)) pari_err_BUG("modinv_double_eta_from_j");
     679        5697 :   return gc_ulong(av,f);
     680             : }
     681             : 
     682             : /* assume j1 != j2 */
     683             : static long
     684       12108 : modinv_double_eta_from_2j(
     685             :   ulong *r, long inv, ulong j1, ulong j2, ulong p, ulong pi, ulong s2)
     686             : {
     687       12108 :   GEN f, g, d, F = double_eta_Fl(inv, p);
     688       12108 :   f = Flx_double_eta_xpoly(F, j1, p, pi);
     689       12108 :   g = Flx_double_eta_xpoly(F, j2, p, pi);
     690       12108 :   d = Flx_gcd(f, g, p);
     691             :   /* we should have deg(d) = 1, but because j1 or j2 may not have the correct
     692             :    * endomorphism ring, we use the less strict conditional underneath */
     693       24214 :   return (degpol(d) > 2 || (*r = Flx_oneroot_pre(d, p, pi)) == p
     694       24214 :           || ! double_eta_root(inv, r, *r, p, pi, s2));
     695             : }
     696             : 
     697             : long
     698       12293 : modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb)
     699             : {
     700       12293 :   pari_sp av = avma;
     701       12293 :   long p1, p2, v = ne->v, p1_depth;
     702       12293 :   ulong j1, p = ne->p, pi = ne->pi, s2 = ne->s2;
     703             :   GEN phi;
     704             : 
     705       12293 :   (void) modinv_degree(&p1, &p2, inv);
     706       12293 :   p1_depth = u_lval(v, p1);
     707             : 
     708       12293 :   phi = polmodular_db_getp(jdb, p1, p);
     709       12293 :   if (!next_surface_nbr(&j1, phi, p1, p1_depth, j0, NULL, p, pi))
     710           0 :     pari_err_BUG("modfn_unambiguous_root");
     711       12293 :   if (p2 == p1) {
     712        2015 :     if (!next_surface_nbr(&j1, phi, p1, p1_depth, j1, &j0, p, pi))
     713           0 :       pari_err_BUG("modfn_unambiguous_root");
     714             :   } else {
     715       10278 :     long p2_depth = u_lval(v, p2);
     716       10278 :     phi = polmodular_db_getp(jdb, p2, p);
     717       10278 :     if (!next_surface_nbr(&j1, phi, p2, p2_depth, j1, NULL, p, pi))
     718           0 :       pari_err_BUG("modfn_unambiguous_root");
     719             :   }
     720       14041 :   return gc_long(av, j1 != j0
     721       12277 :                      && !modinv_double_eta_from_2j(r, inv, j0, j1, p, pi, s2));
     722             : }
     723             : 
     724             : ulong
     725      190503 : modfn_root(ulong j, norm_eqn_t ne, long inv)
     726             : {
     727      190503 :   ulong f, p = ne->p, pi = ne->pi, s2 = ne->s2;
     728      190503 :   switch (inv) {
     729      179110 :     case INV_J:  return j;
     730        8067 :     case INV_G2: return Fl_sqrtl_pre(j, 3, p, pi);
     731        1603 :     case INV_F:  return modinv_f_from_j(j, p, pi, s2, 0);
     732         196 :     case INV_F2:
     733         196 :       f = modinv_f_from_j(j, p, pi, s2, 0);
     734         196 :       return Fl_sqr_pre(f, p, pi);
     735         358 :     case INV_F3: return modinv_f3_from_j(j, p, pi, s2);
     736         553 :     case INV_F4:
     737         553 :       f = modinv_f_from_j(j, p, pi, s2, 0);
     738         553 :       return Fl_sqr_pre(Fl_sqr_pre(f, p, pi), p, pi);
     739         616 :     case INV_F8: return modinv_f_from_j(j, p, pi, s2, 1);
     740             :   }
     741           0 :   if (modinv_is_double_eta(inv))
     742             :   {
     743           0 :     pari_sp av = avma;
     744           0 :     ulong f = modinv_double_eta_from_j(double_eta_Fl(inv,p), inv, j, p, pi, s2);
     745           0 :     return gc_ulong(av,f);
     746             :   }
     747             :   pari_err_BUG("modfn_root"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
     748             : }
     749             : 
     750             : /* F = double_eta_raw(inv) */
     751             : long
     752        6159 : modinv_j_from_2double_eta(
     753             :   GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi)
     754             : {
     755             :   GEN f, g, d;
     756             : 
     757        6159 :   x0 = double_eta_power(inv, x0, p, pi);
     758        6159 :   x1 = double_eta_power(inv, x1, p, pi);
     759        6159 :   F = double_eta_raw_to_Fl(F, p);
     760        6159 :   f = Flx_double_eta_jpoly(F, x0, p, pi);
     761        6159 :   g = Flx_double_eta_jpoly(F, x1, p, pi);
     762        6159 :   d = Flx_gcd(f, g, p); /* >= 1 */
     763        6159 :   return degpol(d) == 1;
     764             : }
     765             : 
     766             : /* x root of (X^24 - 16)^3 - X^24 * j = 0 => j = (x^24 - 16)^3 / x^24 */
     767             : INLINE ulong
     768        1858 : modinv_j_from_f(ulong x, ulong n, ulong p, ulong pi)
     769             : {
     770        1858 :   ulong x24 = Fl_powu_pre(x, 24 / n, p, pi);
     771        1858 :   return Fl_div(Fl_powu_pre(Fl_sub(x24, 16 % p, p), 3, p, pi), x24, p);
     772             : }
     773             : /* should never be called if modinv_double_eta(inv) is true */
     774             : INLINE ulong
     775       63912 : modfn_preimage(ulong x, ulong p, ulong pi, long inv)
     776             : {
     777       63912 :   switch (inv) {
     778       56197 :     case INV_J:  return x;
     779        5857 :     case INV_G2: return Fl_powu_pre(x, 3, p, pi);
     780             :     /* NB: could replace these with a single call modinv_j_from_f(x,inv,p,pi)
     781             :      * but avoid the dependence on the actual value of inv */
     782         654 :     case INV_F:  return modinv_j_from_f(x, 1, p, pi);
     783         196 :     case INV_F2: return modinv_j_from_f(x, 2, p, pi);
     784         168 :     case INV_F3: return modinv_j_from_f(x, 3, p, pi);
     785         392 :     case INV_F4: return modinv_j_from_f(x, 4, p, pi);
     786         448 :     case INV_F8: return modinv_j_from_f(x, 8, p, pi);
     787             :   }
     788             :   pari_err_BUG("modfn_preimage"); return ULONG_MAX;/*LCOV_EXCL_LINE*/
     789             : }
     790             : 
     791             : /* SECTION: class group bb_group. */
     792             : 
     793             : INLINE GEN
     794      128945 : mkqfis(GEN a, ulong b, ulong c, GEN D) { retmkqfb(a, utoi(b), utoi(c), D); }
     795             : 
     796             : /* SECTION: dot-product-like functions on Fl's with precomputed inverse. */
     797             : 
     798             : /* Computes x0y1 + y0x1 (mod p); assumes p < 2^63. */
     799             : INLINE ulong
     800    55604035 : Fl_addmul2(
     801             :   ulong x0, ulong x1, ulong y0, ulong y1,
     802             :   ulong p, ulong pi)
     803             : {
     804    55604035 :   return Fl_addmulmul_pre(x0,y1,y0,x1,p,pi);
     805             : }
     806             : 
     807             : /* Computes x0y2 + x1y1 + x2y0 (mod p); assumes p < 2^62. */
     808             : INLINE ulong
     809     9667848 : Fl_addmul3(
     810             :   ulong x0, ulong x1, ulong x2, ulong y0, ulong y1, ulong y2,
     811             :   ulong p, ulong pi)
     812             : {
     813             :   ulong l0, l1, h0, h1;
     814             :   LOCAL_OVERFLOW;
     815             :   LOCAL_HIREMAINDER;
     816     9667848 :   l0 = mulll(x0, y2); h0 = hiremainder;
     817     9667848 :   l1 = mulll(x1, y1); h1 = hiremainder;
     818     9667848 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     819     9667848 :   l0 = mulll(x2, y0); h0 = hiremainder;
     820     9667848 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     821     9667848 :   return remll_pre(h1, l1, p, pi);
     822             : }
     823             : 
     824             : /* Computes x0y3 + x1y2 + x2y1 + x3y0 (mod p); assumes p < 2^62. */
     825             : INLINE ulong
     826     5020315 : Fl_addmul4(
     827             :   ulong x0, ulong x1, ulong x2, ulong x3,
     828             :   ulong y0, ulong y1, ulong y2, ulong y3,
     829             :   ulong p, ulong pi)
     830             : {
     831             :   ulong l0, l1, h0, h1;
     832             :   LOCAL_OVERFLOW;
     833             :   LOCAL_HIREMAINDER;
     834     5020315 :   l0 = mulll(x0, y3); h0 = hiremainder;
     835     5020315 :   l1 = mulll(x1, y2); h1 = hiremainder;
     836     5020315 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     837     5020315 :   l0 = mulll(x2, y1); h0 = hiremainder;
     838     5020315 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     839     5020315 :   l0 = mulll(x3, y0); h0 = hiremainder;
     840     5020315 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     841     5020315 :   return remll_pre(h1, l1, p, pi);
     842             : }
     843             : 
     844             : /* Computes x0y4 + x1y3 + x2y2 + x3y1 + x4y0 (mod p); assumes p < 2^62. */
     845             : INLINE ulong
     846    24973838 : Fl_addmul5(
     847             :   ulong x0, ulong x1, ulong x2, ulong x3, ulong x4,
     848             :   ulong y0, ulong y1, ulong y2, ulong y3, ulong y4,
     849             :   ulong p, ulong pi)
     850             : {
     851             :   ulong l0, l1, h0, h1;
     852             :   LOCAL_OVERFLOW;
     853             :   LOCAL_HIREMAINDER;
     854    24973838 :   l0 = mulll(x0, y4); h0 = hiremainder;
     855    24973838 :   l1 = mulll(x1, y3); h1 = hiremainder;
     856    24973838 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     857    24973838 :   l0 = mulll(x2, y2); h0 = hiremainder;
     858    24973838 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     859    24973838 :   l0 = mulll(x3, y1); h0 = hiremainder;
     860    24973838 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     861    24973838 :   l0 = mulll(x4, y0); h0 = hiremainder;
     862    24973838 :   l1 = addll(l0, l1); h1 = addllx(h0, h1);
     863    24973838 :   return remll_pre(h1, l1, p, pi);
     864             : }
     865             : 
     866             : /* A polmodular database for a given class invariant consists of a t_VEC whose
     867             :  * L-th entry is 0 or a GEN pointing to Phi_L.  This function produces a pair
     868             :  * of databases corresponding to the j-invariant and inv */
     869             : GEN
     870       21132 : polmodular_db_init(long inv)
     871             : {
     872       21132 :   const long LEN = 32;
     873       21132 :   GEN res = cgetg_block(3, t_VEC);
     874       21132 :   gel(res, 1) = zerovec_block(LEN);
     875       21132 :   gel(res, 2) = (inv == INV_J)? gen_0: zerovec_block(LEN);
     876       21132 :   return res;
     877             : }
     878             : 
     879             : void
     880       24683 : polmodular_db_add_level(GEN *DB, long L, long inv)
     881             : {
     882       24683 :   GEN db = gel(*DB, (inv == INV_J)? 1: 2);
     883       24683 :   long max_L = lg(db) - 1;
     884       24683 :   if (L > max_L) {
     885             :     GEN newdb;
     886          43 :     long i, newlen = 2 * L;
     887             : 
     888          43 :     newdb = cgetg_block(newlen + 1, t_VEC);
     889        1419 :     for (i = 1; i <= max_L; ++i) gel(newdb, i) = gel(db, i);
     890        2941 :     for (     ; i <= newlen; ++i) gel(newdb, i) = gen_0;
     891          43 :     killblock(db);
     892          43 :     gel(*DB, (inv == INV_J)? 1: 2) = db = newdb;
     893             :   }
     894       24683 :   if (typ(gel(db, L)) == t_INT) {
     895        8058 :     pari_sp av = avma;
     896        8058 :     GEN x = polmodular0_ZM(L, inv, NULL, NULL, 0, DB); /* may set db[L] */
     897        8058 :     GEN y = gel(db, L);
     898        8058 :     gel(db, L) = gclone(x);
     899        8058 :     if (typ(y) != t_INT) gunclone(y);
     900        8058 :     set_avma(av);
     901             :   }
     902       24683 : }
     903             : 
     904             : void
     905        4906 : polmodular_db_add_levels(GEN *db, long *levels, long k, long inv)
     906             : {
     907             :   long i;
     908       10354 :   for (i = 0; i < k; ++i) polmodular_db_add_level(db, levels[i], inv);
     909        4906 : }
     910             : 
     911             : GEN
     912      349712 : polmodular_db_for_inv(GEN db, long inv) { return gel(db, (inv==INV_J)? 1: 2); }
     913             : 
     914             : /* TODO: Also cache modpoly mod p for most recent p (avoid repeated
     915             :  * reductions in, for example, polclass.c:oneroot_of_classpoly(). */
     916             : GEN
     917      509935 : polmodular_db_getp(GEN db, long L, ulong p)
     918             : {
     919      509935 :   GEN f = gel(db, L);
     920      509935 :   if (isintzero(f)) pari_err_BUG("polmodular_db_getp");
     921      509926 :   return ZM_to_Flm(f, p);
     922             : }
     923             : 
     924             : /* SECTION: Table of discriminants to use. */
     925             : typedef struct {
     926             :   long GENcode0;  /* used when serializing the struct to a t_VECSMALL */
     927             :   long inv;      /* invariant */
     928             :   long L;        /* modpoly level */
     929             :   long D0;       /* fundamental discriminant */
     930             :   long D1;       /* chosen discriminant */
     931             :   long L0;       /* first generator norm */
     932             :   long L1;       /* second generator norm */
     933             :   long n1;       /* order of L0 in cl(D1) */
     934             :   long n2;       /* order of L0 in cl(D2) where D2 = L^2 D1 */
     935             :   long dl1;      /* m such that L0^m = L in cl(D1) */
     936             :   long dl2_0;    /* These two are (m, n) such that L0^m L1^n = form of norm L^2 in D2 */
     937             :   long dl2_1;    /* This n is always 1 or 0. */
     938             :   /* this part is not serialized */
     939             :   long nprimes;  /* number of primes needed for D1 */
     940             :   long cost;     /* cost to enumerate  subgroup of cl(L^2D): subgroup size is n2 if L1=0, 2*n2 o.w. */
     941             :   long bits;
     942             :   ulong *primes;
     943             :   ulong *traces;
     944             : } disc_info;
     945             : 
     946             : #define MODPOLY_MAX_DCNT    64
     947             : 
     948             : /* Flag for last parameter of discriminant_with_classno_at_least.
     949             :  * Warning: ignoring the sparse factor makes everything slower by
     950             :  * something like (sparse factor)^3. */
     951             : #define USE_SPARSE_FACTOR 0
     952             : #define IGNORE_SPARSE_FACTOR 1
     953             : 
     954             : static long
     955             : discriminant_with_classno_at_least(disc_info Ds[MODPOLY_MAX_DCNT], long L,
     956             :   long inv, GEN Q, long ignore_sparse);
     957             : 
     958             : /* SECTION: evaluation functions for modular polynomials of small level. */
     959             : 
     960             : /* Based on phi2_eval_ff() in Sutherland's classpoly programme.
     961             :  * Calculates Phi_2(X, j) (mod p) with 6M+7A (4 reductions, not
     962             :  * counting those for Phi_2) */
     963             : INLINE GEN
     964    26265068 : Flm_Fl_phi2_evalx(GEN phi2, ulong j, ulong p, ulong pi)
     965             : {
     966    26265068 :   GEN res = cgetg(6, t_VECSMALL);
     967             :   ulong j2, t1;
     968             : 
     969    26222614 :   res[1] = 0; /* variable name */
     970             : 
     971    26222614 :   j2 = Fl_sqr_pre(j, p, pi);
     972    26262614 :   t1 = Fl_add(j, coeff(phi2, 3, 1), p);
     973    26262684 :   t1 = Fl_addmul2(j, j2, t1, coeff(phi2, 2, 1), p, pi);
     974    26325636 :   res[2] = Fl_add(t1, coeff(phi2, 1, 1), p);
     975             : 
     976    26295011 :   t1 = Fl_addmul2(j, j2, coeff(phi2, 3, 2), coeff(phi2, 2, 2), p, pi);
     977    26345563 :   res[3] = Fl_add(t1, coeff(phi2, 2, 1), p);
     978             : 
     979    26316180 :   t1 = Fl_mul_pre(j, coeff(phi2, 3, 2), p, pi);
     980    26312952 :   t1 = Fl_add(t1, coeff(phi2, 3, 1), p);
     981    26282922 :   res[4] = Fl_sub(t1, j2, p);
     982             : 
     983    26259557 :   res[5] = 1;
     984    26259557 :   return res;
     985             : }
     986             : 
     987             : /* Based on phi3_eval_ff() in Sutherland's classpoly programme.
     988             :  * Calculates Phi_3(X, j) (mod p) with 13M+13A (6 reductions, not
     989             :  * counting those for Phi_3) */
     990             : INLINE GEN
     991     3224577 : Flm_Fl_phi3_evalx(GEN phi3, ulong j, ulong p, ulong pi)
     992             : {
     993     3224577 :   GEN res = cgetg(7, t_VECSMALL);
     994             :   ulong j2, j3, t1;
     995             : 
     996     3222627 :   res[1] = 0; /* variable name */
     997             : 
     998     3222627 :   j2 = Fl_sqr_pre(j, p, pi);
     999     3225587 :   j3 = Fl_mul_pre(j, j2, p, pi);
    1000             : 
    1001     3226678 :   t1 = Fl_add(j, coeff(phi3, 4, 1), p);
    1002     6458204 :   res[2] = Fl_addmul3(j, j2, j3, t1,
    1003     3227035 :                       coeff(phi3, 3, 1), coeff(phi3, 2, 1), p, pi);
    1004             : 
    1005     3231169 :   t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 2),
    1006     3231169 :                   coeff(phi3, 3, 2), coeff(phi3, 2, 2), p, pi);
    1007     3230671 :   res[3] = Fl_add(t1, coeff(phi3, 2, 1), p);
    1008             : 
    1009     3229384 :   t1 = Fl_addmul3(j, j2, j3, coeff(phi3, 4, 3),
    1010     3229384 :                   coeff(phi3, 3, 3), coeff(phi3, 3, 2), p, pi);
    1011     3231730 :   res[4] = Fl_add(t1, coeff(phi3, 3, 1), p);
    1012             : 
    1013     3230518 :   t1 = Fl_addmul2(j, j2, coeff(phi3, 4, 3), coeff(phi3, 4, 2), p, pi);
    1014     3231485 :   t1 = Fl_add(t1, coeff(phi3, 4, 1), p);
    1015     3229967 :   res[5] = Fl_sub(t1, j3, p);
    1016             : 
    1017     3228811 :   res[6] = 1;
    1018     3228811 :   return res;
    1019             : }
    1020             : 
    1021             : /* Based on phi5_eval_ff() in Sutherland's classpoly programme.
    1022             :  * Calculates Phi_5(X, j) (mod p) with 33M+31A (10 reductions, not
    1023             :  * counting those for Phi_5) */
    1024             : INLINE GEN
    1025     5011393 : Flm_Fl_phi5_evalx(GEN phi5, ulong j, ulong p, ulong pi)
    1026             : {
    1027     5011393 :   GEN res = cgetg(9, t_VECSMALL);
    1028             :   ulong j2, j3, j4, j5, t1;
    1029             : 
    1030     5006637 :   res[1] = 0; /* variable name */
    1031             : 
    1032     5006637 :   j2 = Fl_sqr_pre(j, p, pi);
    1033     5010994 :   j3 = Fl_mul_pre(j, j2, p, pi);
    1034     5012608 :   j4 = Fl_sqr_pre(j2, p, pi);
    1035     5013335 :   j5 = Fl_mul_pre(j, j4, p, pi);
    1036             : 
    1037     5015667 :   t1 = Fl_add(j, coeff(phi5, 6, 1), p);
    1038     5015337 :   t1 = Fl_addmul5(j, j2, j3, j4, j5, t1,
    1039     5015337 :                   coeff(phi5, 5, 1), coeff(phi5, 4, 1),
    1040     5015337 :                   coeff(phi5, 3, 1), coeff(phi5, 2, 1),
    1041             :                   p, pi);
    1042     5021778 :   res[2] = Fl_add(t1, coeff(phi5, 1, 1), p);
    1043             : 
    1044     5019006 :   t1 = Fl_addmul5(j, j2, j3, j4, j5,
    1045     5019006 :                   coeff(phi5, 6, 2), coeff(phi5, 5, 2),
    1046     5019006 :                   coeff(phi5, 4, 2), coeff(phi5, 3, 2), coeff(phi5, 2, 2),
    1047             :                   p, pi);
    1048     5022452 :   res[3] = Fl_add(t1, coeff(phi5, 2, 1), p);
    1049             : 
    1050     5016292 :   t1 = Fl_addmul5(j, j2, j3, j4, j5,
    1051     5016292 :                   coeff(phi5, 6, 3), coeff(phi5, 5, 3),
    1052     5016292 :                   coeff(phi5, 4, 3), coeff(phi5, 3, 3), coeff(phi5, 3, 2),
    1053             :                   p, pi);
    1054     5023198 :   res[4] = Fl_add(t1, coeff(phi5, 3, 1), p);
    1055             : 
    1056     5019877 :   t1 = Fl_addmul5(j, j2, j3, j4, j5,
    1057     5019877 :                   coeff(phi5, 6, 4), coeff(phi5, 5, 4),
    1058     5019877 :                   coeff(phi5, 4, 4), coeff(phi5, 4, 3), coeff(phi5, 4, 2),
    1059             :                   p, pi);
    1060     5023594 :   res[5] = Fl_add(t1, coeff(phi5, 4, 1), p);
    1061             : 
    1062     5020396 :   t1 = Fl_addmul5(j, j2, j3, j4, j5,
    1063     5020396 :                   coeff(phi5, 6, 5), coeff(phi5, 5, 5),
    1064     5020396 :                   coeff(phi5, 5, 4), coeff(phi5, 5, 3), coeff(phi5, 5, 2),
    1065             :                   p, pi);
    1066     5023881 :   res[6] = Fl_add(t1, coeff(phi5, 5, 1), p);
    1067             : 
    1068     5021052 :   t1 = Fl_addmul4(j, j2, j3, j4,
    1069     5021052 :                   coeff(phi5, 6, 5), coeff(phi5, 6, 4),
    1070     5021052 :                   coeff(phi5, 6, 3), coeff(phi5, 6, 2),
    1071             :                   p, pi);
    1072     5024989 :   t1 = Fl_add(t1, coeff(phi5, 6, 1), p);
    1073     5021356 :   res[7] = Fl_sub(t1, j5, p);
    1074             : 
    1075     5018793 :   res[8] = 1;
    1076     5018793 :   return res;
    1077             : }
    1078             : 
    1079             : GEN
    1080    41632075 : Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi)
    1081             : {
    1082    41632075 :   switch (L) {
    1083    26267976 :     case 2: return Flm_Fl_phi2_evalx(phi, j, p, pi);
    1084     3223496 :     case 3: return Flm_Fl_phi3_evalx(phi, j, p, pi);
    1085     5009180 :     case 5: return Flm_Fl_phi5_evalx(phi, j, p, pi);
    1086     7131423 :     default: { /* not GC clean, but gerepileupto-safe */
    1087     7131423 :       GEN j_powers = Fl_powers_pre(j, L + 1, p, pi);
    1088     7210299 :       return Flm_Flc_mul_pre_Flx(phi, j_powers, p, pi, 0);
    1089             :     }
    1090             :   }
    1091             : }
    1092             : 
    1093             : /* SECTION: Velu's formula for the codmain curve (Fl case). */
    1094             : 
    1095             : INLINE ulong
    1096     1670306 : Fl_mul4(ulong x, ulong p)
    1097     1670306 : { return Fl_double(Fl_double(x, p), p); }
    1098             : 
    1099             : INLINE ulong
    1100       89507 : Fl_mul5(ulong x, ulong p)
    1101       89507 : { return Fl_add(x, Fl_mul4(x, p), p); }
    1102             : 
    1103             : INLINE ulong
    1104      835206 : Fl_mul8(ulong x, ulong p)
    1105      835206 : { return Fl_double(Fl_mul4(x, p), p); }
    1106             : 
    1107             : INLINE ulong
    1108      745728 : Fl_mul6(ulong x, ulong p)
    1109      745728 : { return Fl_sub(Fl_mul8(x, p), Fl_double(x, p), p); }
    1110             : 
    1111             : INLINE ulong
    1112       89504 : Fl_mul7(ulong x, ulong p)
    1113       89504 : { return Fl_sub(Fl_mul8(x, p), x, p); }
    1114             : 
    1115             : /* Given an elliptic curve E = [a4, a6] over F_p and a nonzero point
    1116             :  * pt on E, return the quotient E' = E/<P> = [a4_img, a6_img] */
    1117             : static void
    1118       89509 : Fle_quotient_from_kernel_generator(
    1119             :   ulong *a4_img, ulong *a6_img, ulong a4, ulong a6, GEN pt, ulong p, ulong pi)
    1120             : {
    1121       89509 :   pari_sp av = avma;
    1122       89509 :   ulong t = 0, w = 0;
    1123             :   GEN Q;
    1124             :   ulong xQ, yQ, tQ, uQ;
    1125             : 
    1126       89509 :   Q = gcopy(pt);
    1127             :   /* Note that, as L is odd, say L = 2n + 1, we necessarily have
    1128             :    * [(L - 1)/2]P = [n]P = [n - L]P = -[n + 1]P = -[(L + 1)/2]P.  This is
    1129             :    * what the condition Q[1] != xQ tests, so the loop will execute n times. */
    1130             :   do {
    1131      745671 :     xQ = uel(Q, 1);
    1132      745671 :     yQ = uel(Q, 2);
    1133             :     /* tQ = 6 xQ^2 + b2 xQ + b4
    1134             :      *    = 6 xQ^2 + 2 a4 (since b2 = 0 and b4 = 2 a4) */
    1135      745671 :     tQ = Fl_add(Fl_mul6(Fl_sqr_pre(xQ, p, pi), p), Fl_double(a4, p), p);
    1136      745662 :     uQ = Fl_add(Fl_mul4(Fl_sqr_pre(yQ, p, pi), p),
    1137             :                 Fl_mul_pre(tQ, xQ, p, pi), p);
    1138             : 
    1139      745682 :     t = Fl_add(t, tQ, p);
    1140      745658 :     w = Fl_add(w, uQ, p);
    1141      745628 :     Q = gerepileupto(av, Fle_add(pt, Q, a4, p));
    1142      745668 :   } while (uel(Q, 1) != xQ);
    1143             : 
    1144       89506 :   set_avma(av);
    1145             :   /* a4_img = a4 - 5 * t */
    1146       89506 :   *a4_img = Fl_sub(a4, Fl_mul5(t, p), p);
    1147             :   /* a6_img = a6 - b2 * t - 7 * w = a6 - 7 * w (since a1 = a2 = 0 ==> b2 = 0) */
    1148       89504 :   *a6_img = Fl_sub(a6, Fl_mul7(w, p), p);
    1149       89506 : }
    1150             : 
    1151             : /* SECTION: Calculation of modular polynomials. */
    1152             : 
    1153             : /* Given an elliptic curve [a4, a6] over FF_p, try to find a
    1154             :  * nontrivial L-torsion point on the curve by considering n times a
    1155             :  * random point; val controls the maximum L-valuation expected of n
    1156             :  * times a random point */
    1157             : static GEN
    1158      130526 : find_L_tors_point(
    1159             :   ulong *ival,
    1160             :   ulong a4, ulong a6, ulong p, ulong pi,
    1161             :   ulong n, ulong L, ulong val)
    1162             : {
    1163      130526 :   pari_sp av = avma;
    1164             :   ulong i;
    1165             :   GEN P, Q;
    1166             :   do {
    1167      131793 :     Q = random_Flj_pre(a4, a6, p, pi);
    1168      131792 :     P = Flj_mulu_pre(Q, n, a4, p, pi);
    1169      131794 :   } while (P[3] == 0);
    1170             : 
    1171      252800 :   for (i = 0; i < val; ++i) {
    1172      211780 :     Q = Flj_mulu_pre(P, L, a4, p, pi);
    1173      211783 :     if (Q[3] == 0) break;
    1174      122273 :     P = Q;
    1175             :   }
    1176      130530 :   if (ival) *ival = i;
    1177      130530 :   return gerepilecopy(av, P);
    1178             : }
    1179             : 
    1180             : static GEN
    1181       80996 : select_curve_with_L_tors_point(
    1182             :   ulong *a4, ulong *a6,
    1183             :   ulong L, ulong j, ulong n, ulong card, ulong val,
    1184             :   norm_eqn_t ne)
    1185             : {
    1186       80996 :   pari_sp av = avma;
    1187             :   ulong A4, A4t, A6, A6t;
    1188       80996 :   ulong p = ne->p, pi = ne->pi;
    1189             :   GEN P;
    1190       80996 :   if (card % L != 0) {
    1191           0 :     pari_err_BUG("select_curve_with_L_tors_point: "
    1192             :                  "Cardinality not divisible by L");
    1193             :   }
    1194             : 
    1195       80996 :   Fl_ellj_to_a4a6(j, p, &A4, &A6);
    1196       80998 :   Fl_elltwist_disc(A4, A6, ne->T, p, &A4t, &A6t);
    1197             : 
    1198             :   /* Either E = [a4, a6] or its twist has cardinality divisible by L
    1199             :    * because of the choice of p and t earlier on.  We find out which
    1200             :    * by attempting to find a point of order L on each.  See bot p16 of
    1201             :    * Sutherland 2012. */
    1202       41018 :   while (1) {
    1203             :     ulong i;
    1204      122017 :     P = find_L_tors_point(&i, A4, A6, p, pi, n, L, val);
    1205      122019 :     if (i < val)
    1206       81001 :       break;
    1207       41018 :     set_avma(av);
    1208       41018 :     lswap(A4, A4t);
    1209       41018 :     lswap(A6, A6t);
    1210             :   }
    1211       81001 :   *a4 = A4;
    1212       81001 :   *a6 = A6; return gerepilecopy(av, P);
    1213             : }
    1214             : 
    1215             : /* Return 1 if the L-Sylow subgroup of the curve [a4, a6] (mod p) is
    1216             :  * cyclic, return 0 if it is not cyclic with "high" probability (I
    1217             :  * guess around 1/L^3 chance it is still cyclic when we return 0).
    1218             :  *
    1219             :  * Based on Sutherland's velu.c:velu_verify_Sylow_cyclic() in classpoly-1.0.1 */
    1220             : INLINE long
    1221       46161 : verify_L_sylow_is_cyclic(long e, ulong a4, ulong a6, ulong p, ulong pi)
    1222             : {
    1223             :   /* Number of times to try to find a point with maximal order in the
    1224             :    * L-Sylow subgroup. */
    1225             :   enum { N_RETRIES = 3 };
    1226       46161 :   pari_sp av = avma;
    1227       46161 :   long i, res = 0;
    1228             :   GEN P;
    1229       75802 :   for (i = 0; i < N_RETRIES; ++i) {
    1230       67292 :     P = random_Flj_pre(a4, a6, p, pi);
    1231       67288 :     P = Flj_mulu_pre(P, e, a4, p, pi);
    1232       67295 :     if (P[3] != 0) { res = 1; break; }
    1233             :   }
    1234       46164 :   return gc_long(av,res);
    1235             : }
    1236             : 
    1237             : static ulong
    1238       81001 : find_noniso_L_isogenous_curve(
    1239             :   ulong L, ulong n,
    1240             :   norm_eqn_t ne, long e, ulong val, ulong a4, ulong a6, GEN init_pt, long verify)
    1241             : {
    1242             :   pari_sp ltop, av;
    1243       81001 :   ulong p = ne->p, pi = ne->pi, j_res = 0;
    1244       81001 :   GEN pt = init_pt;
    1245       81001 :   ltop = av = avma;
    1246        8509 :   while (1) {
    1247             :     /* c. Use Velu to calculate L-isogenous curve E' = E/<P> */
    1248             :     ulong a4_img, a6_img;
    1249       89510 :     ulong z2 = Fl_sqr_pre(pt[3], p, pi);
    1250       89509 :     pt = mkvecsmall2(Fl_div(pt[1], z2, p),
    1251       89511 :                      Fl_div(pt[2], Fl_mul_pre(z2, pt[3], p, pi), p));
    1252       89509 :     Fle_quotient_from_kernel_generator(&a4_img, &a6_img,
    1253             :                                        a4, a6, pt, p, pi);
    1254             : 
    1255             :     /* d. If j(E') = j_res has a different endo ring to j(E), then
    1256             :      *    return j(E').  Otherwise, go to b. */
    1257       89506 :     if (!verify || verify_L_sylow_is_cyclic(e, a4_img, a6_img, p, pi)) {
    1258       80999 :       j_res = Fl_ellj_pre(a4_img, a6_img, p, pi);
    1259       81005 :       break;
    1260             :     }
    1261             : 
    1262             :     /* b. Generate random point P on E of order L */
    1263        8509 :     set_avma(av);
    1264        8509 :     pt = find_L_tors_point(NULL, a4, a6, p, pi, n, L, val);
    1265             :   }
    1266       81005 :   return gc_ulong(ltop, j_res);
    1267             : }
    1268             : 
    1269             : /* Given a prime L and a j-invariant j (mod p), return the j-invariant
    1270             :  * of a curve which has a different endomorphism ring to j and is
    1271             :  * L-isogenous to j */
    1272             : INLINE ulong
    1273       80997 : compute_L_isogenous_curve(
    1274             :   ulong L, ulong n, norm_eqn_t ne,
    1275             :   ulong j, ulong card, ulong val, long verify)
    1276             : {
    1277             :   ulong a4, a6;
    1278             :   long e;
    1279             :   GEN pt;
    1280             : 
    1281       80997 :   if (ne->p < 5 || j == 0 || j == 1728 % ne->p)
    1282           0 :     pari_err_BUG("compute_L_isogenous_curve");
    1283       80997 :   pt = select_curve_with_L_tors_point(&a4, &a6, L, j, n, card, val, ne);
    1284       81001 :   e = card / L;
    1285       81001 :   if (e * L != card) pari_err_BUG("compute_L_isogenous_curve");
    1286             : 
    1287       81001 :   return find_noniso_L_isogenous_curve(L, n, ne, e, val, a4, a6, pt, verify);
    1288             : }
    1289             : 
    1290             : INLINE GEN
    1291       37654 : get_Lsqr_cycle(const disc_info *dinfo)
    1292             : {
    1293       37654 :   long i, n1 = dinfo->n1, L = dinfo->L;
    1294       37654 :   GEN cyc = cgetg(L, t_VECSMALL);
    1295       37654 :   cyc[1] = 0;
    1296      313921 :   for (i = 2; i <= L / 2; ++i) cyc[i] = cyc[i - 1] + n1;
    1297       37654 :   if ( ! dinfo->L1) {
    1298      124743 :     for ( ; i < L; ++i) cyc[i] = cyc[i - 1] + n1;
    1299             :   } else {
    1300       23044 :     cyc[L - 1] = 2 * dinfo->n2 - n1 / 2;
    1301      203788 :     for (i = L - 2; i > L / 2; --i) cyc[i] = cyc[i + 1] - n1;
    1302             :   }
    1303       37654 :   return cyc;
    1304             : }
    1305             : 
    1306             : INLINE void
    1307      524855 : update_Lsqr_cycle(GEN cyc, const disc_info *dinfo)
    1308             : {
    1309      524855 :   long i, L = dinfo->L;
    1310    15492190 :   for (i = 1; i < L; ++i) ++cyc[i];
    1311      524855 :   if (dinfo->L1 && cyc[L - 1] == 2 * dinfo->n2) {
    1312       21316 :     long n1 = dinfo->n1;
    1313      194799 :     for (i = L / 2 + 1; i < L; ++i) cyc[i] -= n1;
    1314             :   }
    1315      524855 : }
    1316             : 
    1317             : static ulong
    1318       37651 : oneroot_of_classpoly(GEN hilb, GEN factu, norm_eqn_t ne, GEN jdb)
    1319             : {
    1320       37651 :   pari_sp av = avma;
    1321       37651 :   ulong j0, p = ne->p, pi = ne->pi;
    1322       37651 :   long i, nfactors = lg(gel(factu, 1)) - 1;
    1323       37651 :   GEN hilbp = ZX_to_Flx(hilb, p);
    1324             : 
    1325             :   /* TODO: Work out how to use hilb with better invariant */
    1326       37647 :   j0 = Flx_oneroot_split_pre(hilbp, p, pi);
    1327       37646 :   if (j0 == p) {
    1328           0 :     pari_err_BUG("oneroot_of_classpoly: "
    1329             :                  "Didn't find a root of the class polynomial");
    1330             :   }
    1331       39312 :   for (i = 1; i <= nfactors; ++i) {
    1332        1666 :     long L = gel(factu, 1)[i];
    1333        1666 :     long val = gel(factu, 2)[i];
    1334        1666 :     GEN phi = polmodular_db_getp(jdb, L, p);
    1335        1666 :     val += z_lval(ne->v, L);
    1336        1666 :     j0 = descend_volcano(phi, j0, p, pi, 0, L, val, val);
    1337        1666 :     set_avma(av);
    1338             :   }
    1339       37646 :   return gc_ulong(av, j0);
    1340             : }
    1341             : 
    1342             : /* TODO: Precompute the GEN structs and link them to dinfo */
    1343             : INLINE GEN
    1344        2831 : make_pcp_surface(const disc_info *dinfo)
    1345             : {
    1346        2831 :   GEN L = mkvecsmall(dinfo->L0);
    1347        2831 :   GEN n = mkvecsmall(dinfo->n1);
    1348        2831 :   GEN o = mkvecsmall(dinfo->n1);
    1349        2831 :   return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, 1, dinfo->n1));
    1350             : }
    1351             : 
    1352             : INLINE GEN
    1353        2831 : make_pcp_floor(const disc_info *dinfo)
    1354             : {
    1355        2831 :   long k = dinfo->L1 ? 2 : 1;
    1356             :   GEN L, n, o;
    1357        2831 :   if (k==1)
    1358             :   {
    1359        1432 :     L = mkvecsmall(dinfo->L0);
    1360        1432 :     n = mkvecsmall(dinfo->n2);
    1361        1432 :     o = mkvecsmall(dinfo->n2);
    1362             :   } else
    1363             :   {
    1364        1399 :     L = mkvecsmall2(dinfo->L0, dinfo->L1);
    1365        1399 :     n = mkvecsmall2(dinfo->n2, 2);
    1366        1399 :     o = mkvecsmall2(dinfo->n2, 2);
    1367             :   }
    1368        2831 :   return mkvec2(mkvec3(L, n, o), mkvecsmall3(0, k, dinfo->n2*k));
    1369             : }
    1370             : 
    1371             : INLINE GEN
    1372       37652 : enum_volcano_surface(norm_eqn_t ne, ulong j0, GEN fdb, GEN G)
    1373             : {
    1374       37652 :   pari_sp av = avma;
    1375       37652 :   return gerepileupto(av, enum_roots(j0, ne, fdb, G, NULL));
    1376             : }
    1377             : 
    1378             : INLINE GEN
    1379       37651 : enum_volcano_floor(long L, norm_eqn_t ne, ulong j0_pr, GEN fdb, GEN G)
    1380             : {
    1381       37651 :   pari_sp av = avma;
    1382             :   /* L^2 D is the discriminant for the order R = Z + L OO. */
    1383       37651 :   long DR = L * L * ne->D;
    1384       37651 :   long R_cond = L * ne->u; /* conductor(DR); */
    1385       37651 :   long w = R_cond * ne->v;
    1386             :   /* TODO: Calculate these once and for all in polmodular0_ZM(). */
    1387             :   norm_eqn_t eqn;
    1388       37651 :   memcpy(eqn, ne, sizeof *ne);
    1389       37651 :   eqn->D = DR;
    1390       37651 :   eqn->u = R_cond;
    1391       37651 :   eqn->v = w;
    1392       37651 :   return gerepileupto(av, enum_roots(j0_pr, eqn, fdb, G, NULL));
    1393             : }
    1394             : 
    1395             : INLINE void
    1396       18202 : carray_reverse_inplace(long *arr, long n)
    1397             : {
    1398       18202 :   long lim = n>>1, i;
    1399       18202 :   --n;
    1400      184167 :   for (i = 0; i < lim; i++) lswap(arr[i], arr[n - i]);
    1401       18202 : }
    1402             : 
    1403             : INLINE void
    1404      562527 : append_neighbours(GEN rts, GEN surface_js, long njs, long L, long m, long i)
    1405             : {
    1406      562527 :   long r_idx = (((i - 1) + m) % njs) + 1; /* (i + m) % njs */
    1407      562527 :   long l_idx = umodsu((i - 1) - m, njs) + 1; /* (i - m) % njs */
    1408      562514 :   rts[L] = surface_js[l_idx];
    1409      562514 :   rts[L + 1] = surface_js[r_idx];
    1410      562514 : }
    1411             : 
    1412             : INLINE GEN
    1413       39824 : roots_to_coeffs(GEN rts, ulong p, long L)
    1414             : {
    1415       39824 :   long i, k, lrts= lg(rts);
    1416       39824 :   GEN M = cgetg(L+2+1, t_MAT);
    1417      866227 :   for (i = 1; i <= L+2; ++i)
    1418      826397 :     gel(M, i) = cgetg(lrts, t_VECSMALL);
    1419      625799 :   for (i = 1; i < lrts; ++i) {
    1420      586031 :     pari_sp av = avma;
    1421      586031 :     GEN modpol = Flv_roots_to_pol(gel(rts, i), p, 0);
    1422    19297070 :     for (k = 1; k <= L + 2; ++k) mael(M, k, i) = modpol[k + 1];
    1423      585843 :     set_avma(av);
    1424             :   }
    1425       39768 :   return M;
    1426             : }
    1427             : 
    1428             : /* NB: Assumes indices are offset at 0, not at 1 like in GENs;
    1429             :  * i.e. indices[i] will pick out v[indices[i] + 1] from v. */
    1430             : INLINE void
    1431      562529 : vecsmall_pick(GEN res, GEN v, GEN indices)
    1432             : {
    1433             :   long i;
    1434    16158062 :   for (i = 1; i < lg(indices); ++i) res[i] = v[indices[i] + 1];
    1435      562529 : }
    1436             : 
    1437             : /* First element of surface_js must lie above the first element of floor_js.
    1438             :  * Reverse surface_js if it is not oriented in the same direction as floor_js */
    1439             : INLINE GEN
    1440       37654 : root_matrix(long L, const disc_info *dinfo, long njinvs, GEN surface_js,
    1441             :   GEN floor_js, ulong n, ulong card, ulong val, norm_eqn_t ne)
    1442             : {
    1443             :   pari_sp av;
    1444       37654 :   long i, m = dinfo->dl1, njs = lg(surface_js) - 1, inv = dinfo->inv, rev;
    1445       37654 :   GEN rt_mat = zero_Flm_copy(L + 1, njinvs), rts, cyc;
    1446       37654 :   ulong p = ne->p, pi = ne->pi, j;
    1447       37654 :   av = avma;
    1448             : 
    1449       37654 :   i = 1;
    1450       37654 :   cyc = get_Lsqr_cycle(dinfo);
    1451       37654 :   rts = gel(rt_mat, i);
    1452       37654 :   vecsmall_pick(rts, floor_js, cyc);
    1453       37654 :   append_neighbours(rts, surface_js, njs, L, m, i);
    1454             : 
    1455       37653 :   i = 2;
    1456       37653 :   update_Lsqr_cycle(cyc, dinfo);
    1457       37653 :   rts = gel(rt_mat, i);
    1458       37653 :   vecsmall_pick(rts, floor_js, cyc);
    1459             : 
    1460             :   /* Fix orientation if necessary */
    1461       37653 :   if (modinv_is_double_eta(inv)) {
    1462             :     /* TODO: There is potential for refactoring between this,
    1463             :      * double_eta_initial_js and modfn_preimage. */
    1464        5697 :     pari_sp av0 = avma;
    1465        5697 :     GEN F = double_eta_Fl(inv, p);
    1466        5697 :     pari_sp av = avma;
    1467        5697 :     ulong r1 = double_eta_power(inv, uel(rts, 1), p, pi);
    1468        5697 :     GEN r, f = Flx_double_eta_jpoly(F, r1, p, pi);
    1469        5697 :     if ((j = Flx_oneroot_pre(f, p, pi)) == p) pari_err_BUG("root_matrix");
    1470        5697 :     j = compute_L_isogenous_curve(L, n, ne, j, card, val, 0);
    1471        5697 :     set_avma(av);
    1472        5697 :     r1 = double_eta_power(inv, uel(surface_js, i), p, pi);
    1473        5697 :     f = Flx_double_eta_jpoly(F, r1, p, pi);
    1474        5697 :     r = Flx_roots_pre(f, p, pi);
    1475        5697 :     if (lg(r) != 3) pari_err_BUG("root_matrix");
    1476        5697 :     rev = (j != uel(r, 1)) && (j != uel(r, 2));
    1477        5697 :     set_avma(av0);
    1478             :   } else {
    1479             :     ulong j1pr, j1;
    1480       31957 :     j1pr = modfn_preimage(uel(rts, 1), p, pi, dinfo->inv);
    1481       31957 :     j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
    1482       31956 :     rev = j1 != modfn_preimage(uel(surface_js, i), p, pi, dinfo->inv);
    1483             :   }
    1484       37653 :   if (rev)
    1485       18202 :     carray_reverse_inplace(surface_js + 2, njs - 1);
    1486       37653 :   append_neighbours(rts, surface_js, njs, L, m, i);
    1487             : 
    1488      524872 :   for (i = 3; i <= njinvs; ++i) {
    1489      487219 :     update_Lsqr_cycle(cyc, dinfo);
    1490      487233 :     rts = gel(rt_mat, i);
    1491      487233 :     vecsmall_pick(rts, floor_js, cyc);
    1492      487231 :     append_neighbours(rts, surface_js, njs, L, m, i);
    1493             :   }
    1494       37653 :   set_avma(av); return rt_mat;
    1495             : }
    1496             : 
    1497             : INLINE void
    1498       40173 : interpolate_coeffs(GEN phi_modp, ulong p, GEN j_invs, GEN coeff_mat)
    1499             : {
    1500       40173 :   pari_sp av = avma;
    1501             :   long i;
    1502       40173 :   GEN pols = Flv_Flm_polint(j_invs, coeff_mat, p, 0);
    1503      868894 :   for (i = 1; i < lg(pols); ++i) {
    1504      828722 :     GEN pol = gel(pols, i);
    1505      828722 :     long k, maxk = lg(pol);
    1506    18308831 :     for (k = 2; k < maxk; ++k) coeff(phi_modp, k - 1, i) = pol[k];
    1507             :   }
    1508       40172 :   set_avma(av);
    1509       40174 : }
    1510             : 
    1511             : INLINE long
    1512      350552 : Flv_lastnonzero(GEN v)
    1513             : {
    1514             :   long i;
    1515    27394212 :   for (i = lg(v) - 1; i > 0; --i)
    1516    27393494 :     if (v[i]) break;
    1517      350552 :   return i;
    1518             : }
    1519             : 
    1520             : /* Assuming the matrix of coefficients in phi corresponds to polynomials
    1521             :  * phi_k^* satisfying Y^c phi_k^*(Y^s) for c in {0, 1, ..., s} satisfying
    1522             :  * c + Lk = L + 1 (mod s), change phi so that the coefficients are for the
    1523             :  * polynomials Y^c phi_k^*(Y^s) (s is the sparsity factor) */
    1524             : INLINE void
    1525       10849 : inflate_polys(GEN phi, long L, long s)
    1526             : {
    1527       10849 :   long k, deg = L + 1;
    1528             :   long maxr;
    1529       10849 :   maxr = nbrows(phi);
    1530      361401 :   for (k = 0; k <= deg; ) {
    1531      350552 :     long i, c = umodsu(L * (1 - k) + 1, s);
    1532             :     /* TODO: We actually know that the last nonzero element of gel(phi, k)
    1533             :      * can't be later than index n+1, where n is about (L + 1)/s. */
    1534      350552 :     ++k;
    1535     5552596 :     for (i = Flv_lastnonzero(gel(phi, k)); i > 0; --i) {
    1536     5202044 :       long r = c + (i - 1) * s + 1;
    1537     5202044 :       if (r > maxr) { coeff(phi, i, k) = 0; continue; }
    1538     5130650 :       if (r != i) {
    1539     5024278 :         coeff(phi, r, k) = coeff(phi, i, k);
    1540     5024278 :         coeff(phi, i, k) = 0;
    1541             :       }
    1542             :     }
    1543             :   }
    1544       10849 : }
    1545             : 
    1546             : INLINE void
    1547       42146 : Flv_powu_inplace_pre(GEN v, ulong n, ulong p, ulong pi)
    1548             : {
    1549             :   long i;
    1550      349865 :   for (i = 1; i < lg(v); ++i) v[i] = Fl_powu_pre(v[i], n, p, pi);
    1551       42145 : }
    1552             : 
    1553             : INLINE void
    1554       10849 : normalise_coeffs(GEN coeffs, GEN js, long L, long s, ulong p, ulong pi)
    1555             : {
    1556       10849 :   pari_sp av = avma;
    1557             :   long k;
    1558             :   GEN pows, modinv_js;
    1559             : 
    1560             :   /* NB: In fact it would be correct to return the coefficients "as is" when
    1561             :    * s = 1, but we make that an error anyway since this function should never
    1562             :    * be called with s = 1. */
    1563       10849 :   if (s <= 1) pari_err_BUG("normalise_coeffs");
    1564             : 
    1565             :   /* pows[i + 1] contains 1 / js[i + 1]^i for i = 0, ..., s - 1. */
    1566       10849 :   pows = cgetg(s + 1, t_VEC);
    1567       10849 :   gel(pows, 1) = const_vecsmall(lg(js) - 1, 1);
    1568       10849 :   modinv_js = Flv_inv_pre(js, p, pi);
    1569       10849 :   gel(pows, 2) = modinv_js;
    1570       39780 :   for (k = 3; k <= s; ++k) {
    1571       28931 :     gel(pows, k) = gcopy(modinv_js);
    1572       28931 :     Flv_powu_inplace_pre(gel(pows, k), k - 1, p, pi);
    1573             :   }
    1574             : 
    1575             :   /* For each column of coefficients coeffs[k] = [a0 .. an],
    1576             :    *   replace ai by ai / js[i]^c.
    1577             :    * Said in another way, normalise each row i of coeffs by
    1578             :    * dividing through by js[i - 1]^c (where c depends on i). */
    1579      361407 :   for (k = 1; k < lg(coeffs); ++k) {
    1580      350549 :     long i, c = umodsu(L * (1 - (k - 1)) + 1, s);
    1581      350549 :     GEN col = gel(coeffs, k), C = gel(pows, c + 1);
    1582     5938224 :     for (i = 1; i < lg(col); ++i)
    1583     5587666 :       col[i] = Fl_mul_pre(col[i], C[i], p, pi);
    1584             :   }
    1585       10858 :   set_avma(av);
    1586       10849 : }
    1587             : 
    1588             : INLINE void
    1589        5697 : double_eta_initial_js(
    1590             :   ulong *x0, ulong *x0pr, ulong j0, ulong j0pr, norm_eqn_t ne,
    1591             :   long inv, ulong L, ulong n, ulong card, ulong val)
    1592             : {
    1593        5697 :   pari_sp av0 = avma;
    1594        5697 :   ulong p = ne->p, pi = ne->pi, s2 = ne->s2;
    1595        5697 :   GEN F = double_eta_Fl(inv, p);
    1596        5697 :   pari_sp av = avma;
    1597             :   ulong j1pr, j1, r, t;
    1598             :   GEN f, g;
    1599             : 
    1600        5697 :   *x0pr = modinv_double_eta_from_j(F, inv, j0pr, p, pi, s2);
    1601        5697 :   t = double_eta_power(inv, *x0pr, p, pi);
    1602        5697 :   f = Flx_div_by_X_x(Flx_double_eta_jpoly(F, t, p, pi), j0pr, p, &r);
    1603        5697 :   if (r) pari_err_BUG("double_eta_initial_js");
    1604        5697 :   j1pr = Flx_deg1_root(f, p);
    1605        5697 :   set_avma(av);
    1606             : 
    1607        5697 :   j1 = compute_L_isogenous_curve(L, n, ne, j1pr, card, val, 0);
    1608        5697 :   f = Flx_double_eta_xpoly(F, j0, p, pi);
    1609        5697 :   g = Flx_double_eta_xpoly(F, j1, p, pi);
    1610             :   /* x0 is the unique common root of f and g */
    1611        5697 :   *x0 = Flx_deg1_root(Flx_gcd(f, g, p), p);
    1612        5697 :   set_avma(av0);
    1613             : 
    1614        5697 :   if ( ! double_eta_root(inv, x0, *x0, p, pi, s2))
    1615           0 :     pari_err_BUG("double_eta_initial_js");
    1616        5697 : }
    1617             : 
    1618             : /* This is Sutherland 2012, Algorithm 2.1, p16. */
    1619             : static GEN
    1620       37646 : polmodular_split_p_Flm(ulong L, GEN hilb, GEN factu, norm_eqn_t ne, GEN db,
    1621             :   GEN G_surface, GEN G_floor, const disc_info *dinfo)
    1622             : {
    1623             :   ulong j0, j0_rt, j0pr, j0pr_rt;
    1624       37646 :   ulong n, card, val, p = ne->p, pi = ne->pi;
    1625       37646 :   long inv = dinfo->inv, s = modinv_sparse_factor(inv);
    1626       37647 :   long nj_selected = ceil((L + 1)/(double)s) + 1;
    1627             :   GEN surface_js, floor_js, rts, phi_modp, jdb, fdb;
    1628       37647 :   long switched_signs = 0;
    1629             : 
    1630       37647 :   jdb = polmodular_db_for_inv(db, INV_J);
    1631       37648 :   fdb = polmodular_db_for_inv(db, inv);
    1632             : 
    1633             :   /* Precomputation */
    1634       37651 :   card = p + 1 - ne->t;
    1635       37651 :   val = u_lvalrem(card, L, &n); /* n = card / L^{v_L(card)} */
    1636             : 
    1637       37651 :   j0 = oneroot_of_classpoly(hilb, factu, ne, jdb);
    1638       37646 :   j0pr = compute_L_isogenous_curve(L, n, ne, j0, card, val, 1);
    1639       37654 :   if (modinv_is_double_eta(inv)) {
    1640        5697 :     double_eta_initial_js(&j0_rt, &j0pr_rt, j0, j0pr, ne, inv, L, n, card, val);
    1641             :   } else {
    1642       31957 :     j0_rt = modfn_root(j0, ne, inv);
    1643       31957 :     j0pr_rt = modfn_root(j0pr, ne, inv);
    1644             :   }
    1645       37652 :   surface_js = enum_volcano_surface(ne, j0_rt, fdb, G_surface);
    1646       37651 :   floor_js = enum_volcano_floor(L, ne, j0pr_rt, fdb, G_floor);
    1647       37654 :   rts = root_matrix(L, dinfo, nj_selected, surface_js, floor_js,
    1648             :                     n, card, val, ne);
    1649        2171 :   do {
    1650       39824 :     pari_sp btop = avma;
    1651             :     long i;
    1652             :     GEN coeffs, surf;
    1653             : 
    1654       39824 :     coeffs = roots_to_coeffs(rts, p, L);
    1655       39817 :     surf = vecsmall_shorten(surface_js, nj_selected);
    1656       39818 :     if (s > 1) {
    1657       10849 :       normalise_coeffs(coeffs, surf, L, s, p, pi);
    1658       10849 :       Flv_powu_inplace_pre(surf, s, p, pi);
    1659             :     }
    1660       39817 :     phi_modp = zero_Flm_copy(L + 2, L + 2);
    1661       39823 :     interpolate_coeffs(phi_modp, p, surf, coeffs);
    1662       39824 :     if (s > 1) inflate_polys(phi_modp, L, s);
    1663             : 
    1664             :     /* TODO: Calculate just this coefficient of X^L Y^L, so we can do this
    1665             :      * test, then calculate the other coefficients; at the moment we are
    1666             :      * sometimes doing all the roots-to-coeffs, normalisation and interpolation
    1667             :      * work twice. */
    1668       39824 :     if (ucoeff(phi_modp, L + 1, L + 1) == p - 1) break;
    1669             : 
    1670        2171 :     if (switched_signs) pari_err_BUG("polmodular_split_p_Flm");
    1671             : 
    1672        2171 :     set_avma(btop);
    1673       25998 :     for (i = 1; i < lg(rts); ++i) {
    1674       23827 :       surface_js[i] = Fl_neg(surface_js[i], p);
    1675       23827 :       coeff(rts, L, i) = Fl_neg(coeff(rts, L, i), p);
    1676       23827 :       coeff(rts, L + 1, i) = Fl_neg(coeff(rts, L + 1, i), p);
    1677             :     }
    1678        2171 :     switched_signs = 1;
    1679             :   } while (1);
    1680       37653 :   dbg_printf(4)("  Phi_%lu(X, Y) (mod %lu) = %Ps\n", L, p, phi_modp);
    1681             : 
    1682       37653 :   return phi_modp;
    1683             : }
    1684             : 
    1685             : INLINE void
    1686        2464 : Flv_deriv_pre_inplace(GEN v, long deg, ulong p, ulong pi)
    1687             : {
    1688        2464 :   long i, ln = lg(v), d = deg % p;
    1689       57213 :   for (i = ln - 1; i > 1; --i, --d) v[i] = Fl_mul_pre(v[i - 1], d, p, pi);
    1690        2465 :   v[1] = 0;
    1691        2465 : }
    1692             : 
    1693             : INLINE GEN
    1694        2674 : eval_modpoly_modp(GEN Tp, GEN j_powers, ulong p, ulong pi, int compute_derivs)
    1695             : {
    1696        2674 :   long L = lg(j_powers) - 3;
    1697        2674 :   GEN j_pows_p = ZV_to_Flv(j_powers, p);
    1698        2674 :   GEN tmp = cgetg(2 + 2 * compute_derivs, t_VEC);
    1699             :   /* We wrap the result in this t_VEC Tp to trick the
    1700             :    * ZM_*_CRT() functions into thinking it's a matrix. */
    1701        2674 :   gel(tmp, 1) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
    1702        2674 :   if (compute_derivs) {
    1703        1232 :     Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
    1704        1232 :     gel(tmp, 2) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
    1705        1232 :     Flv_deriv_pre_inplace(j_pows_p, L + 1, p, pi);
    1706        1232 :     gel(tmp, 3) = Flm_Flc_mul_pre(Tp, j_pows_p, p, pi);
    1707             :   }
    1708        2674 :   return tmp;
    1709             : }
    1710             : 
    1711             : /* Parallel interface */
    1712             : GEN
    1713       37653 : polmodular_worker(GEN tp, ulong L, GEN hilb, GEN factu, GEN vne, GEN vinfo,
    1714             :                   long derivs, GEN j_powers, GEN G_surface, GEN G_floor,
    1715             :                   GEN fdb)
    1716             : {
    1717       37653 :   pari_sp av = avma;
    1718             :   norm_eqn_t ne;
    1719       37653 :   long D = vne[1], u = vne[2];
    1720       37653 :   ulong vL, t = tp[1], p = tp[2];
    1721             :   GEN Tp;
    1722             : 
    1723       37653 :   if (! uissquareall((4 * p - t * t) / -D, &vL))
    1724           0 :     pari_err_BUG("polmodular_worker");
    1725       37651 :   norm_eqn_set(ne, D, t, u, vL, NULL, p); /* L | vL */
    1726       37645 :   Tp = polmodular_split_p_Flm(L, hilb, factu, ne, fdb,
    1727             :                               G_surface, G_floor, (const disc_info*)vinfo);
    1728       37653 :   if (!isintzero(j_powers))
    1729        2674 :     Tp = eval_modpoly_modp(Tp, j_powers, ne->p, ne->pi, derivs);
    1730       37651 :   return gerepileupto(av, Tp);
    1731             : }
    1732             : 
    1733             : static GEN
    1734       24201 : sympol_to_ZM(GEN phi, long L)
    1735             : {
    1736       24201 :   pari_sp av = avma;
    1737       24201 :   GEN res = zeromatcopy(L + 2, L + 2);
    1738       24201 :   long i, j, c = 1;
    1739      104963 :   for (i = 1; i <= L + 1; ++i)
    1740      265259 :     for (j = 1; j <= i; ++j, ++c)
    1741      184497 :       gcoeff(res, i, j) = gcoeff(res, j, i) = gel(phi, c);
    1742       24201 :   gcoeff(res, L + 2, 1) = gcoeff(res, 1, L + 2) = gen_1;
    1743       24201 :   return gerepilecopy(av, res);
    1744             : }
    1745             : 
    1746             : static GEN polmodular_small_ZM(long L, long inv, GEN *db);
    1747             : 
    1748             : INLINE long
    1749       27286 : modinv_max_internal_level(long inv)
    1750             : {
    1751       27286 :   switch (inv) {
    1752       24665 :     case INV_J: return 5;
    1753         364 :     case INV_G2: return 2;
    1754         443 :     case INV_F:
    1755             :     case INV_F2:
    1756             :     case INV_F4:
    1757         443 :     case INV_F8: return 5;
    1758         252 :     case INV_W2W5:
    1759         252 :     case INV_W2W5E2: return 7;
    1760         462 :     case INV_W2W3:
    1761             :     case INV_W2W3E2:
    1762             :     case INV_W3W3:
    1763         462 :     case INV_W3W7:  return 5;
    1764          63 :     case INV_W3W3E2:return 2;
    1765         729 :     case INV_F3:
    1766             :     case INV_W2W7:
    1767             :     case INV_W2W7E2:
    1768         729 :     case INV_W2W13: return 3;
    1769         308 :     case INV_W3W5:
    1770             :     case INV_W5W7:
    1771         308 :     case INV_W3W13: return 2;
    1772             :   }
    1773             :   pari_err_BUG("modinv_max_internal_level"); return LONG_MAX;/*LCOV_EXCL_LINE*/
    1774             : }
    1775             : static void
    1776          45 : db_add_levels(GEN *db, GEN P, long inv)
    1777          45 : { polmodular_db_add_levels(db, zv_to_longptr(P), lg(P)-1, inv); }
    1778             : 
    1779             : GEN
    1780       27167 : polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db)
    1781             : {
    1782       27167 :   pari_sp ltop = avma;
    1783       27167 :   long k, d, Dcnt, nprimes = 0;
    1784             :   GEN modpoly, plist, tp, j_powers;
    1785             :   disc_info Ds[MODPOLY_MAX_DCNT];
    1786       27167 :   long lvl = modinv_level(inv);
    1787       27167 :   if (ugcd(L, lvl) != 1)
    1788           7 :     pari_err_DOMAIN("polmodular0_ZM", "invariant",
    1789             :                     "incompatible with", stoi(L), stoi(lvl));
    1790             : 
    1791       27160 :   dbg_printf(1)("Calculating modular polynomial of level %lu for invariant %d\n", L, inv);
    1792       27160 :   if (L <= modinv_max_internal_level(inv)) return polmodular_small_ZM(L,inv,db);
    1793             : 
    1794        2812 :   Dcnt = discriminant_with_classno_at_least(Ds, L, inv, Q, USE_SPARSE_FACTOR);
    1795        5643 :   for (d = 0; d < Dcnt; d++) nprimes += Ds[d].nprimes;
    1796        2812 :   modpoly = cgetg(nprimes+1, t_VEC);
    1797        2812 :   plist = cgetg(nprimes+1, t_VECSMALL);
    1798        2812 :   tp = mkvec(mkvecsmall2(0,0));
    1799        2812 :   j_powers = gen_0;
    1800        2812 :   if (J) {
    1801          63 :     compute_derivs = !!compute_derivs;
    1802          63 :     j_powers = Fp_powers(J, L+1, Q);
    1803             :   }
    1804        5643 :   for (d = 0, k = 1; d < Dcnt; d++)
    1805             :   {
    1806        2831 :     disc_info *dinfo = &Ds[d];
    1807             :     struct pari_mt pt;
    1808        2831 :     const long D = dinfo->D1, DK = dinfo->D0;
    1809        2831 :     const ulong cond = usqrt(D / DK);
    1810        2831 :     long i, pending = 0;
    1811        2831 :     GEN worker, hilb, factu = factoru(cond);
    1812             : 
    1813        2831 :     polmodular_db_add_level(db, dinfo->L0, inv);
    1814        2831 :     if (dinfo->L1) polmodular_db_add_level(db, dinfo->L1, inv);
    1815        2831 :     dbg_printf(1)("Selected discriminant D = %ld = %ld^2 * %ld.\n", D,cond,DK);
    1816        2831 :     hilb = polclass0(DK, INV_J, 0, db);
    1817        2831 :     if (cond > 1) db_add_levels(db, gel(factu,1), INV_J);
    1818        2831 :     dbg_printf(1)("D = %ld, L0 = %lu, L1 = %lu, ", dinfo->D1, dinfo->L0, dinfo->L1);
    1819        2831 :     dbg_printf(1)("n1 = %lu, n2 = %lu, dl1 = %lu, dl2_0 = %lu, dl2_1 = %lu\n",
    1820             :           dinfo->n1, dinfo->n2, dinfo->dl1, dinfo->dl2_0, dinfo->dl2_1);
    1821        2831 :     dbg_printf(0)("Calculating modular polynomial of level %lu:", L);
    1822             : 
    1823        2831 :     worker = snm_closure(is_entry("_polmodular_worker"),
    1824             :                          mkvecn(10, utoi(L), hilb, factu, mkvecsmall2(D, cond),
    1825             :                                    (GEN)dinfo, stoi(compute_derivs), j_powers,
    1826             :                                    make_pcp_surface(dinfo),
    1827             :                                    make_pcp_floor(dinfo), *db));
    1828        2831 :     mt_queue_start_lim(&pt, worker, dinfo->nprimes);
    1829       44362 :     for (i = 0; i < dinfo->nprimes || pending; i++)
    1830             :     {
    1831             :       long workid;
    1832             :       GEN done;
    1833       41531 :       if (i < dinfo->nprimes)
    1834             :       {
    1835       37654 :         mael(tp, 1, 1) = dinfo->traces[i];
    1836       37654 :         mael(tp, 1, 2) = dinfo->primes[i];
    1837             :       }
    1838       41531 :       mt_queue_submit(&pt, i, i < dinfo->nprimes? tp: NULL);
    1839       41531 :       done = mt_queue_get(&pt, &workid, &pending);
    1840       41531 :       if (done)
    1841             :       {
    1842       37654 :         plist[k] = dinfo->primes[workid];
    1843       37654 :         gel(modpoly, k) = done; k++;
    1844       37654 :         dbg_printf(0)(" %ld%%", k*100/nprimes);
    1845             :       }
    1846             :     }
    1847        2831 :     dbg_printf(0)(" done\n");
    1848        2831 :     mt_queue_end(&pt);
    1849        2831 :     killblock((GEN)dinfo->primes);
    1850             :   }
    1851        2812 :   modpoly = nmV_chinese_center(modpoly, plist, NULL);
    1852        2812 :   if (J) modpoly = FpM_red(modpoly, Q);
    1853        2812 :   return gerepileupto(ltop, modpoly);
    1854             : }
    1855             : 
    1856             : GEN
    1857       18913 : polmodular_ZM(long L, long inv)
    1858             : {
    1859             :   GEN db, Phi;
    1860             : 
    1861       18913 :   if (L < 2)
    1862           7 :     pari_err_DOMAIN("polmodular_ZM", "L", "<", gen_2, stoi(L));
    1863             : 
    1864             :   /* TODO: Handle nonprime L. Algorithm 1.1 and Corollary 3.4 in Sutherland,
    1865             :    * "Class polynomials for nonholomorphic modular functions" */
    1866       18906 :   if (! uisprime(L)) pari_err_IMPL("composite level");
    1867             : 
    1868       18899 :   db = polmodular_db_init(inv);
    1869       18899 :   Phi = polmodular0_ZM(L, inv, NULL, NULL, 0, &db);
    1870       18892 :   gunclone_deep(db); return Phi;
    1871             : }
    1872             : 
    1873             : GEN
    1874       18829 : polmodular_ZXX(long L, long inv, long vx, long vy)
    1875             : {
    1876       18829 :   pari_sp av = avma;
    1877       18829 :   GEN phi = polmodular_ZM(L, inv);
    1878             : 
    1879       18808 :   if (vx < 0) vx = 0;
    1880       18808 :   if (vy < 0) vy = 1;
    1881       18808 :   if (varncmp(vx, vy) >= 0)
    1882          14 :     pari_err_PRIORITY("polmodular_ZXX", pol_x(vx), "<=", vy);
    1883       18794 :   return gerepilecopy(av, RgM_to_RgXX(phi, vx, vy));
    1884             : }
    1885             : 
    1886             : INLINE GEN
    1887          56 : FpV_deriv(GEN v, long deg, GEN P)
    1888             : {
    1889          56 :   long i, ln = lg(v);
    1890          56 :   GEN dv = cgetg(ln, t_VEC);
    1891         392 :   for (i = ln-1; i > 1; i--, deg--) gel(dv, i) = Fp_mulu(gel(v, i-1), deg, P);
    1892          56 :   gel(dv, 1) = gen_0; return dv;
    1893             : }
    1894             : 
    1895             : GEN
    1896         126 : Fp_polmodular_evalx(long L, long inv, GEN J, GEN P, long v, int compute_derivs)
    1897             : {
    1898         126 :   pari_sp av = avma;
    1899             :   GEN db, phi;
    1900             : 
    1901         126 :   if (L <= modinv_max_internal_level(inv)) {
    1902             :     GEN tmp;
    1903          63 :     GEN phi = RgM_to_FpM(polmodular_ZM(L, inv), P);
    1904          63 :     GEN j_powers = Fp_powers(J, L + 1, P);
    1905          63 :     GEN modpol = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
    1906          63 :     if (compute_derivs) {
    1907          28 :       tmp = cgetg(4, t_VEC);
    1908          28 :       gel(tmp, 1) = modpol;
    1909          28 :       j_powers = FpV_deriv(j_powers, L + 1, P);
    1910          28 :       gel(tmp, 2) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
    1911          28 :       j_powers = FpV_deriv(j_powers, L + 1, P);
    1912          28 :       gel(tmp, 3) = RgV_to_RgX(FpM_FpC_mul(phi, j_powers, P), v);
    1913             :     } else
    1914          35 :       tmp = modpol;
    1915          63 :     return gerepilecopy(av, tmp);
    1916             :   }
    1917             : 
    1918          63 :   db = polmodular_db_init(inv);
    1919          63 :   phi = polmodular0_ZM(L, inv, J, P, compute_derivs, &db);
    1920          63 :   phi = RgM_to_RgXV(phi, v);
    1921          63 :   gunclone_deep(db);
    1922          63 :   return gerepilecopy(av, compute_derivs? phi: gel(phi, 1));
    1923             : }
    1924             : 
    1925             : GEN
    1926         630 : polmodular(long L, long inv, GEN x, long v, long compute_derivs)
    1927             : {
    1928         630 :   pari_sp av = avma;
    1929             :   long tx;
    1930         630 :   GEN J = NULL, P = NULL, res = NULL, one = NULL;
    1931             : 
    1932         630 :   check_modinv(inv);
    1933         623 :   if (!x || gequalX(x)) {
    1934         483 :     long xv = 0;
    1935         483 :     if (x) xv = varn(x);
    1936         483 :     if (compute_derivs) pari_err_FLAG("polmodular");
    1937         476 :     return polmodular_ZXX(L, inv, xv, v);
    1938             :   }
    1939             : 
    1940         140 :   tx = typ(x);
    1941         140 :   if (tx == t_INTMOD) {
    1942          63 :     J = gel(x, 2);
    1943          63 :     P = gel(x, 1);
    1944          63 :     one = mkintmod(gen_1, P);
    1945          77 :   } else if (tx == t_FFELT) {
    1946          70 :     J = FF_to_FpXQ_i(x);
    1947          70 :     if (degpol(J) > 0)
    1948           7 :       pari_err_DOMAIN("polmodular", "x", "not in prime subfield ", gen_0, x);
    1949          63 :     J = constant_coeff(J);
    1950          63 :     P = FF_p_i(x);
    1951          63 :     one = FF_1(x);
    1952             :   } else
    1953           7 :     pari_err_TYPE("polmodular", x);
    1954             : 
    1955         126 :   if (v < 0) v = 1;
    1956         126 :   res = Fp_polmodular_evalx(L, inv, J, P, v, compute_derivs);
    1957         126 :   return gerepileupto(av, gmul(res, one));
    1958             : }
    1959             : 
    1960             : /* SECTION: Modular polynomials of level <= MAX_INTERNAL_MODPOLY_LEVEL. */
    1961             : 
    1962             : /* These functions return a vector of coefficients of classical modular
    1963             :  * polynomials Phi_L(X,Y) of small level L.  The number of such coefficients is
    1964             :  * (L+1)(L+2)/2 since Phi is symmetric. We omit the common coefficient of
    1965             :  * X^{L+1} and Y^{L+1} since it is always 1. Use sympol_to_ZM() to get the
    1966             :  * corresponding desymmetrised matrix of coefficients */
    1967             : 
    1968             : /*  Phi2, the modular polynomial of level 2:
    1969             :  *
    1970             :  *  X^3 + X^2 * (-Y^2 + 1488*Y - 162000)
    1971             :  *      + X * (1488*Y^2 + 40773375*Y + 8748000000)
    1972             :  *      + Y^3 - 162000*Y^2 + 8748000000*Y - 157464000000000
    1973             :  *
    1974             :  *  [[3, 0, 1],
    1975             :  *   [2, 2, -1],
    1976             :  *   [2, 1, 1488],
    1977             :  *   [2, 0, -162000],
    1978             :  *   [1, 1, 40773375],
    1979             :  *   [1, 0, 8748000000],
    1980             :  *   [0, 0, -157464000000000]], */
    1981             : static GEN
    1982       19935 : phi2_ZV(void)
    1983             : {
    1984       19935 :   GEN phi2 = cgetg(7, t_VEC);
    1985       19935 :   gel(phi2, 1) = uu32toi(36662, 1908994048);
    1986       19935 :   setsigne(gel(phi2, 1), -1);
    1987       19935 :   gel(phi2, 2) = uu32toi(2, 158065408);
    1988       19935 :   gel(phi2, 3) = stoi(40773375);
    1989       19935 :   gel(phi2, 4) = stoi(-162000);
    1990       19935 :   gel(phi2, 5) = stoi(1488);
    1991       19935 :   gel(phi2, 6) = gen_m1;
    1992       19935 :   return phi2;
    1993             : }
    1994             : 
    1995             : /* L = 3
    1996             :  *
    1997             :  * [4, 0, 1],
    1998             :  * [3, 3, -1],
    1999             :  * [3, 2, 2232],
    2000             :  * [3, 1, -1069956],
    2001             :  * [3, 0, 36864000],
    2002             :  * [2, 2, 2587918086],
    2003             :  * [2, 1, 8900222976000],
    2004             :  * [2, 0, 452984832000000],
    2005             :  * [1, 1, -770845966336000000],
    2006             :  * [1, 0, 1855425871872000000000]
    2007             :  * [0, 0, 0]
    2008             :  *
    2009             :  * 1855425871872000000000 = 2^32 * (100 * 2^32 + 2503270400) */
    2010             : static GEN
    2011        1812 : phi3_ZV(void)
    2012             : {
    2013        1812 :   GEN phi3 = cgetg(11, t_VEC);
    2014        1812 :   pari_sp av = avma;
    2015        1812 :   gel(phi3, 1) = gen_0;
    2016        1812 :   gel(phi3, 2) = gerepileupto(av, shifti(uu32toi(100, 2503270400UL), 32));
    2017        1812 :   gel(phi3, 3) = uu32toi(179476562, 2147483648UL);
    2018        1812 :   setsigne(gel(phi3, 3), -1);
    2019        1812 :   gel(phi3, 4) = uu32toi(105468, 3221225472UL);
    2020        1812 :   gel(phi3, 5) = uu32toi(2072, 1050738688);
    2021        1812 :   gel(phi3, 6) = utoi(2587918086UL);
    2022        1812 :   gel(phi3, 7) = stoi(36864000);
    2023        1812 :   gel(phi3, 8) = stoi(-1069956);
    2024        1812 :   gel(phi3, 9) = stoi(2232);
    2025        1812 :   gel(phi3, 10) = gen_m1;
    2026        1812 :   return phi3;
    2027             : }
    2028             : 
    2029             : static GEN
    2030        1502 : phi5_ZV(void)
    2031             : {
    2032        1502 :   GEN phi5 = cgetg(22, t_VEC);
    2033        1502 :   gel(phi5, 1) = mkintn(5, 0x18c2cc9cUL, 0x484382b2UL, 0xdc000000UL, 0x0UL, 0x0UL);
    2034        1502 :   gel(phi5, 2) = mkintn(5, 0x2638fUL, 0x2ff02690UL, 0x68026000UL, 0x0UL, 0x0UL);
    2035        1502 :   gel(phi5, 3) = mkintn(5, 0x308UL, 0xac9d9a4UL, 0xe0fdab12UL, 0xc0000000UL, 0x0UL);
    2036        1502 :   setsigne(gel(phi5, 3), -1);
    2037        1502 :   gel(phi5, 4) = mkintn(5, 0x13UL, 0xaae09f9dUL, 0x1b5ef872UL, 0x30000000UL, 0x0UL);
    2038        1502 :   gel(phi5, 5) = mkintn(4, 0x1b802fa9UL, 0x77ba0653UL, 0xd2f78000UL, 0x0UL);
    2039        1502 :   gel(phi5, 6) = mkintn(4, 0xfbfdUL, 0x278e4756UL, 0xdf08a7c4UL, 0x40000000UL);
    2040        1502 :   gel(phi5, 7) = mkintn(4, 0x35f922UL, 0x62ccea6fUL, 0x153d0000UL, 0x0UL);
    2041        1502 :   gel(phi5, 8) = mkintn(4, 0x97dUL, 0x29203fafUL, 0xc3036909UL, 0x80000000UL);
    2042        1502 :   setsigne(gel(phi5, 8), -1);
    2043        1502 :   gel(phi5, 9) = mkintn(3, 0x56e9e892UL, 0xd7781867UL, 0xf2ea0000UL);
    2044        1502 :   gel(phi5, 10) = mkintn(3, 0x5d6dUL, 0xe0a58f4eUL, 0x9ee68c14UL);
    2045        1502 :   setsigne(gel(phi5, 10), -1);
    2046        1502 :   gel(phi5, 11) = mkintn(3, 0x1100dUL, 0x85cea769UL, 0x40000000UL);
    2047        1502 :   gel(phi5, 12) = mkintn(3, 0x1b38UL, 0x43cf461fUL, 0x3a900000UL);
    2048        1502 :   gel(phi5, 13) = mkintn(3, 0x14UL, 0xc45a616eUL, 0x4801680fUL);
    2049        1502 :   gel(phi5, 14) = uu32toi(0x17f4350UL, 0x493ca3e0UL);
    2050        1502 :   gel(phi5, 15) = uu32toi(0x183UL, 0xe54ce1f8UL);
    2051        1502 :   gel(phi5, 16) = uu32toi(0x1c9UL, 0x18860000UL);
    2052        1502 :   gel(phi5, 17) = uu32toi(0x39UL, 0x6f7a2206UL);
    2053        1502 :   setsigne(gel(phi5, 17), -1);
    2054        1502 :   gel(phi5, 18) = stoi(2028551200);
    2055        1502 :   gel(phi5, 19) = stoi(-4550940);
    2056        1502 :   gel(phi5, 20) = stoi(3720);
    2057        1502 :   gel(phi5, 21) = gen_m1;
    2058        1502 :   return phi5;
    2059             : }
    2060             : 
    2061             : static GEN
    2062         182 : phi5_f_ZV(void)
    2063             : {
    2064         182 :   GEN phi = zerovec(21);
    2065         182 :   gel(phi, 3) = stoi(4);
    2066         182 :   gel(phi, 21) = gen_m1;
    2067         182 :   return phi;
    2068             : }
    2069             : 
    2070             : static GEN
    2071          21 : phi3_f3_ZV(void)
    2072             : {
    2073          21 :   GEN phi = zerovec(10);
    2074          21 :   gel(phi, 3) = stoi(8);
    2075          21 :   gel(phi, 10) = gen_m1;
    2076          21 :   return phi;
    2077             : }
    2078             : 
    2079             : static GEN
    2080         119 : phi2_g2_ZV(void)
    2081             : {
    2082         119 :   GEN phi = zerovec(6);
    2083         119 :   gel(phi, 1) = stoi(-54000);
    2084         119 :   gel(phi, 3) = stoi(495);
    2085         119 :   gel(phi, 6) = gen_m1;
    2086         119 :   return phi;
    2087             : }
    2088             : 
    2089             : static GEN
    2090          56 : phi5_w2w3_ZV(void)
    2091             : {
    2092          56 :   GEN phi = zerovec(21);
    2093          56 :   gel(phi, 3) = gen_m1;
    2094          56 :   gel(phi, 10) = stoi(5);
    2095          56 :   gel(phi, 21) = gen_m1;
    2096          56 :   return phi;
    2097             : }
    2098             : 
    2099             : static GEN
    2100         112 : phi7_w2w5_ZV(void)
    2101             : {
    2102         112 :   GEN phi = zerovec(36);
    2103         112 :   gel(phi, 3) = gen_m1;
    2104         112 :   gel(phi, 15) = stoi(56);
    2105         112 :   gel(phi, 19) = stoi(42);
    2106         112 :   gel(phi, 24) = stoi(21);
    2107         112 :   gel(phi, 30) = stoi(7);
    2108         112 :   gel(phi, 36) = gen_m1;
    2109         112 :   return phi;
    2110             : }
    2111             : 
    2112             : static GEN
    2113          63 : phi5_w3w3_ZV(void)
    2114             : {
    2115          63 :   GEN phi = zerovec(21);
    2116          63 :   gel(phi, 3) = stoi(9);
    2117          63 :   gel(phi, 6) = stoi(-15);
    2118          63 :   gel(phi, 15) = stoi(5);
    2119          63 :   gel(phi, 21) = gen_m1;
    2120          63 :   return phi;
    2121             : }
    2122             : 
    2123             : static GEN
    2124         182 : phi3_w2w7_ZV(void)
    2125             : {
    2126         182 :   GEN phi = zerovec(10);
    2127         182 :   gel(phi, 3) = gen_m1;
    2128         182 :   gel(phi, 6) = stoi(3);
    2129         182 :   gel(phi, 10) = gen_m1;
    2130         182 :   return phi;
    2131             : }
    2132             : 
    2133             : static GEN
    2134          35 : phi2_w3w5_ZV(void)
    2135             : {
    2136          35 :   GEN phi = zerovec(6);
    2137          35 :   gel(phi, 3) = gen_1;
    2138          35 :   gel(phi, 6) = gen_m1;
    2139          35 :   return phi;
    2140             : }
    2141             : 
    2142             : static GEN
    2143          42 : phi5_w3w7_ZV(void)
    2144             : {
    2145          42 :   GEN phi = zerovec(21);
    2146          42 :   gel(phi, 3) = gen_m1;
    2147          42 :   gel(phi, 6) = stoi(10);
    2148          42 :   gel(phi, 8) = stoi(5);
    2149          42 :   gel(phi, 10) = stoi(35);
    2150          42 :   gel(phi, 13) = stoi(20);
    2151          42 :   gel(phi, 15) = stoi(10);
    2152          42 :   gel(phi, 17) = stoi(5);
    2153          42 :   gel(phi, 19) = stoi(5);
    2154          42 :   gel(phi, 21) = gen_m1;
    2155          42 :   return phi;
    2156             : }
    2157             : 
    2158             : static GEN
    2159          49 : phi3_w2w13_ZV(void)
    2160             : {
    2161          49 :   GEN phi = zerovec(10);
    2162          49 :   gel(phi, 3) = gen_m1;
    2163          49 :   gel(phi, 6) = stoi(3);
    2164          49 :   gel(phi, 8) = stoi(3);
    2165          49 :   gel(phi, 10) = gen_m1;
    2166          49 :   return phi;
    2167             : }
    2168             : 
    2169             : static GEN
    2170          21 : phi2_w3w3e2_ZV(void)
    2171             : {
    2172          21 :   GEN phi = zerovec(6);
    2173          21 :   gel(phi, 3) = stoi(3);
    2174          21 :   gel(phi, 6) = gen_m1;
    2175          21 :   return phi;
    2176             : }
    2177             : 
    2178             : static GEN
    2179          56 : phi2_w5w7_ZV(void)
    2180             : {
    2181          56 :   GEN phi = zerovec(6);
    2182          56 :   gel(phi, 3) = gen_1;
    2183          56 :   gel(phi, 5) = gen_2;
    2184          56 :   gel(phi, 6) = gen_m1;
    2185          56 :   return phi;
    2186             : }
    2187             : 
    2188             : static GEN
    2189          14 : phi2_w3w13_ZV(void)
    2190             : {
    2191          14 :   GEN phi = zerovec(6);
    2192          14 :   gel(phi, 3) = gen_m1;
    2193          14 :   gel(phi, 5) = gen_2;
    2194          14 :   gel(phi, 6) = gen_m1;
    2195          14 :   return phi;
    2196             : }
    2197             : 
    2198             : INLINE long
    2199         147 : modinv_parent(long inv)
    2200             : {
    2201         147 :   switch (inv) {
    2202          42 :     case INV_F2:
    2203             :     case INV_F4:
    2204          42 :     case INV_F8:     return INV_F;
    2205          14 :     case INV_W2W3E2: return INV_W2W3;
    2206          28 :     case INV_W2W5E2: return INV_W2W5;
    2207          63 :     case INV_W2W7E2: return INV_W2W7;
    2208           0 :     case INV_W3W3E2: return INV_W3W3;
    2209             :     default: pari_err_BUG("modinv_parent"); return -1;/*LCOV_EXCL_LINE*/
    2210             :   }
    2211             : }
    2212             : 
    2213             : /* TODO: Think of a better name than "parent power"; sheesh. */
    2214             : INLINE long
    2215         147 : modinv_parent_power(long inv)
    2216             : {
    2217         147 :   switch (inv) {
    2218          14 :     case INV_F4: return 4;
    2219          14 :     case INV_F8: return 8;
    2220         119 :     case INV_F2:
    2221             :     case INV_W2W3E2:
    2222             :     case INV_W2W5E2:
    2223             :     case INV_W2W7E2:
    2224         119 :     case INV_W3W3E2: return 2;
    2225             :     default: pari_err_BUG("modinv_parent_power"); return -1;/*LCOV_EXCL_LINE*/
    2226             :   }
    2227             : }
    2228             : 
    2229             : static GEN
    2230         147 : polmodular0_powerup_ZM(long L, long inv, GEN *db)
    2231             : {
    2232         147 :   pari_sp ltop = avma, av;
    2233             :   long s, D, nprimes, N;
    2234             :   GEN mp, pol, P, H;
    2235         147 :   long parent = modinv_parent(inv);
    2236         147 :   long e = modinv_parent_power(inv);
    2237             :   disc_info Ds[MODPOLY_MAX_DCNT];
    2238             :   /* FIXME: We throw away the table of fundamental discriminants here. */
    2239         147 :   long nDs = discriminant_with_classno_at_least(Ds, L, inv, NULL, IGNORE_SPARSE_FACTOR);
    2240         147 :   if (nDs != 1) pari_err_BUG("polmodular0_powerup_ZM");
    2241         147 :   D = Ds[0].D1;
    2242         147 :   nprimes = Ds[0].nprimes + 1;
    2243         147 :   mp = polmodular0_ZM(L, parent, NULL, NULL, 0, db);
    2244         147 :   H = polclass0(D, parent, 0, db);
    2245             : 
    2246         147 :   N = L + 2;
    2247         147 :   if (degpol(H) < N) pari_err_BUG("polmodular0_powerup_ZM");
    2248             : 
    2249         147 :   av = avma;
    2250         147 :   pol = ZM_init_CRT(zero_Flm_copy(N, L + 2), 1);
    2251         147 :   P = gen_1;
    2252         497 :   for (s = 1; s < nprimes; ++s) {
    2253             :     pari_sp av1, av2;
    2254         350 :     ulong p = Ds[0].primes[s-1], pi = get_Fl_red(p);
    2255             :     long i;
    2256             :     GEN Hrts, js, Hp, Phip, coeff_mat, phi_modp;
    2257             : 
    2258         350 :     phi_modp = zero_Flm_copy(N, L + 2);
    2259         350 :     av1 = avma;
    2260         350 :     Hp = ZX_to_Flx(H, p);
    2261         350 :     Hrts = Flx_roots_pre(Hp, p, pi);
    2262         350 :     if (lg(Hrts)-1 < N) pari_err_BUG("polmodular0_powerup_ZM");
    2263         350 :     js = cgetg(N + 1, t_VECSMALL);
    2264        2716 :     for (i = 1; i <= N; ++i)
    2265        2366 :       uel(js, i) = Fl_powu_pre(uel(Hrts, i), e, p, pi);
    2266             : 
    2267         350 :     Phip = ZM_to_Flm(mp, p);
    2268         350 :     coeff_mat = zero_Flm_copy(N, L + 2);
    2269         350 :     av2 = avma;
    2270        2716 :     for (i = 1; i <= N; ++i) {
    2271             :       long k;
    2272             :       GEN phi_at_ji, mprts;
    2273             : 
    2274        2366 :       phi_at_ji = Flm_Fl_polmodular_evalx(Phip, L, uel(Hrts, i), p, pi);
    2275        2366 :       mprts = Flx_roots_pre(phi_at_ji, p, pi);
    2276        2366 :       if (lg(mprts) != L + 2) pari_err_BUG("polmodular0_powerup_ZM");
    2277             : 
    2278        2366 :       Flv_powu_inplace_pre(mprts, e, p, pi);
    2279        2366 :       phi_at_ji = Flv_roots_to_pol(mprts, p, 0);
    2280             : 
    2281       19180 :       for (k = 1; k <= L + 2; ++k)
    2282       16814 :         ucoeff(coeff_mat, i, k) = uel(phi_at_ji, k + 1);
    2283        2366 :       set_avma(av2);
    2284             :     }
    2285             : 
    2286         350 :     interpolate_coeffs(phi_modp, p, js, coeff_mat);
    2287         350 :     set_avma(av1);
    2288             : 
    2289         350 :     (void) ZM_incremental_CRT(&pol, phi_modp, &P, p);
    2290         350 :     if (gc_needed(av, 2)) gerepileall(av, 2, &pol, &P);
    2291             :   }
    2292         147 :   killblock((GEN)Ds[0].primes); return gerepileupto(ltop, pol);
    2293             : }
    2294             : 
    2295             : /* Returns the modular polynomial with the smallest level for the given
    2296             :  * invariant, except if inv is INV_J, in which case return the modular
    2297             :  * polynomial of level L in {2,3,5}.  NULL is returned if the modular
    2298             :  * polynomial can be calculated using polmodular0_powerup_ZM. */
    2299             : INLINE GEN
    2300       24348 : internal_db(long L, long inv)
    2301             : {
    2302       24348 :   switch (inv) {
    2303       23249 :   case INV_J: switch (L) {
    2304       19935 :     case 2: return phi2_ZV();
    2305        1812 :     case 3: return phi3_ZV();
    2306        1502 :     case 5: return phi5_ZV();
    2307           0 :     default: break;
    2308             :   }
    2309         182 :   case INV_F: return phi5_f_ZV();
    2310          14 :   case INV_F2: return NULL;
    2311          21 :   case INV_F3: return phi3_f3_ZV();
    2312          14 :   case INV_F4: return NULL;
    2313         119 :   case INV_G2: return phi2_g2_ZV();
    2314          56 :   case INV_W2W3: return phi5_w2w3_ZV();
    2315          14 :   case INV_F8: return NULL;
    2316          63 :   case INV_W3W3: return phi5_w3w3_ZV();
    2317         112 :   case INV_W2W5: return phi7_w2w5_ZV();
    2318         182 :   case INV_W2W7: return phi3_w2w7_ZV();
    2319          35 :   case INV_W3W5: return phi2_w3w5_ZV();
    2320          42 :   case INV_W3W7: return phi5_w3w7_ZV();
    2321          14 :   case INV_W2W3E2: return NULL;
    2322          28 :   case INV_W2W5E2: return NULL;
    2323          49 :   case INV_W2W13: return phi3_w2w13_ZV();
    2324          63 :   case INV_W2W7E2: return NULL;
    2325          21 :   case INV_W3W3E2: return phi2_w3w3e2_ZV();
    2326          56 :   case INV_W5W7: return phi2_w5w7_ZV();
    2327          14 :   case INV_W3W13: return phi2_w3w13_ZV();
    2328             :   }
    2329           0 :   pari_err_BUG("internal_db");
    2330             :   return NULL;/*LCOV_EXCL_LINE*/
    2331             : }
    2332             : 
    2333             : /* NB: Should only be called if L <= modinv_max_internal_level(inv) */
    2334             : static GEN
    2335       24348 : polmodular_small_ZM(long L, long inv, GEN *db)
    2336             : {
    2337       24348 :   GEN f = internal_db(L, inv);
    2338       24348 :   if (!f) return polmodular0_powerup_ZM(L, inv, db);
    2339       24201 :   return sympol_to_ZM(f, L);
    2340             : }
    2341             : 
    2342             : /* Each function phi_w?w?_j() returns a vector V containing two
    2343             :  * vectors u and v, and a scalar k, which together represent the
    2344             :  * bivariate polnomial
    2345             :  *
    2346             :  *   phi(X, Y) = \sum_i u[i] X^i + Y \sum_i v[i] X^i + Y^2 X^k
    2347             :  */
    2348             : static GEN
    2349        1060 : phi_w2w3_j(void)
    2350             : {
    2351             :   GEN phi, phi0, phi1;
    2352        1060 :   phi = cgetg(4, t_VEC);
    2353             : 
    2354        1060 :   phi0 = cgetg(14, t_VEC);
    2355        1060 :   gel(phi0, 1) = gen_1;
    2356        1060 :   gel(phi0, 2) = utoineg(0x3cUL);
    2357        1060 :   gel(phi0, 3) = utoi(0x702UL);
    2358        1060 :   gel(phi0, 4) = utoineg(0x797cUL);
    2359        1060 :   gel(phi0, 5) = utoi(0x5046fUL);
    2360        1060 :   gel(phi0, 6) = utoineg(0x1be0b8UL);
    2361        1060 :   gel(phi0, 7) = utoi(0x28ef9cUL);
    2362        1060 :   gel(phi0, 8) = utoi(0x15e2968UL);
    2363        1060 :   gel(phi0, 9) = utoi(0x1b8136fUL);
    2364        1060 :   gel(phi0, 10) = utoi(0xa67674UL);
    2365        1060 :   gel(phi0, 11) = utoi(0x23982UL);
    2366        1060 :   gel(phi0, 12) = utoi(0x294UL);
    2367        1060 :   gel(phi0, 13) = gen_1;
    2368             : 
    2369        1060 :   phi1 = cgetg(13, t_VEC);
    2370        1060 :   gel(phi1, 1) = gen_0;
    2371        1060 :   gel(phi1, 2) = gen_0;
    2372        1060 :   gel(phi1, 3) = gen_m1;
    2373        1060 :   gel(phi1, 4) = utoi(0x23UL);
    2374        1060 :   gel(phi1, 5) = utoineg(0xaeUL);
    2375        1060 :   gel(phi1, 6) = utoineg(0x5b8UL);
    2376        1060 :   gel(phi1, 7) = utoi(0x12d7UL);
    2377        1060 :   gel(phi1, 8) = utoineg(0x7c86UL);
    2378        1060 :   gel(phi1, 9) = utoi(0x37c8UL);
    2379        1060 :   gel(phi1, 10) = utoineg(0x69cUL);
    2380        1060 :   gel(phi1, 11) = utoi(0x48UL);
    2381        1060 :   gel(phi1, 12) = gen_m1;
    2382             : 
    2383        1060 :   gel(phi, 1) = phi0;
    2384        1060 :   gel(phi, 2) = phi1;
    2385        1060 :   gel(phi, 3) = utoi(5); return phi;
    2386             : }
    2387             : 
    2388             : static GEN
    2389        3535 : phi_w3w3_j(void)
    2390             : {
    2391             :   GEN phi, phi0, phi1;
    2392        3535 :   phi = cgetg(4, t_VEC);
    2393             : 
    2394        3535 :   phi0 = cgetg(14, t_VEC);
    2395        3535 :   gel(phi0, 1) = utoi(0x2d9UL);
    2396        3535 :   gel(phi0, 2) = utoi(0x4fbcUL);
    2397        3535 :   gel(phi0, 3) = utoi(0x5828aUL);
    2398        3535 :   gel(phi0, 4) = utoi(0x3a7a3cUL);
    2399        3535 :   gel(phi0, 5) = utoi(0x1bd8edfUL);
    2400        3535 :   gel(phi0, 6) = utoi(0x8348838UL);
    2401        3535 :   gel(phi0, 7) = utoi(0x1983f8acUL);
    2402        3535 :   gel(phi0, 8) = utoi(0x14e4e098UL);
    2403        3535 :   gel(phi0, 9) = utoi(0x69ed1a7UL);
    2404        3535 :   gel(phi0, 10) = utoi(0xc3828cUL);
    2405        3535 :   gel(phi0, 11) = utoi(0x2696aUL);
    2406        3535 :   gel(phi0, 12) = utoi(0x2acUL);
    2407        3535 :   gel(phi0, 13) = gen_1;
    2408             : 
    2409        3535 :   phi1 = cgetg(13, t_VEC);
    2410        3535 :   gel(phi1, 1) = gen_0;
    2411        3535 :   gel(phi1, 2) = utoineg(0x1bUL);
    2412        3535 :   gel(phi1, 3) = utoineg(0x5d6UL);
    2413        3535 :   gel(phi1, 4) = utoineg(0x1c7bUL);
    2414        3535 :   gel(phi1, 5) = utoi(0x7980UL);
    2415        3535 :   gel(phi1, 6) = utoi(0x12168UL);
    2416        3535 :   gel(phi1, 7) = utoineg(0x3528UL);
    2417        3535 :   gel(phi1, 8) = utoineg(0x6174UL);
    2418        3535 :   gel(phi1, 9) = utoi(0x2208UL);
    2419        3535 :   gel(phi1, 10) = utoineg(0x41dUL);
    2420        3535 :   gel(phi1, 11) = utoi(0x36UL);
    2421        3535 :   gel(phi1, 12) = gen_m1;
    2422             : 
    2423        3535 :   gel(phi, 1) = phi0;
    2424        3535 :   gel(phi, 2) = phi1;
    2425        3535 :   gel(phi, 3) = gen_2; return phi;
    2426             : }
    2427             : 
    2428             : static GEN
    2429        3242 : phi_w2w5_j(void)
    2430             : {
    2431             :   GEN phi, phi0, phi1;
    2432        3242 :   phi = cgetg(4, t_VEC);
    2433             : 
    2434        3242 :   phi0 = cgetg(20, t_VEC);
    2435        3242 :   gel(phi0, 1) = gen_1;
    2436        3242 :   gel(phi0, 2) = utoineg(0x2aUL);
    2437        3242 :   gel(phi0, 3) = utoi(0x549UL);
    2438        3242 :   gel(phi0, 4) = utoineg(0x6530UL);
    2439        3242 :   gel(phi0, 5) = utoi(0x60504UL);
    2440        3242 :   gel(phi0, 6) = utoineg(0x3cbbc8UL);
    2441        3242 :   gel(phi0, 7) = utoi(0x1d1ee74UL);
    2442        3242 :   gel(phi0, 8) = utoineg(0x7ef9ab0UL);
    2443        3242 :   gel(phi0, 9) = utoi(0x12b888beUL);
    2444        3242 :   gel(phi0, 10) = utoineg(0x15fa174cUL);
    2445        3242 :   gel(phi0, 11) = utoi(0x615d9feUL);
    2446        3242 :   gel(phi0, 12) = utoi(0xbeca070UL);
    2447        3242 :   gel(phi0, 13) = utoineg(0x88de74cUL);
    2448        3242 :   gel(phi0, 14) = utoineg(0x2b3a268UL);
    2449        3242 :   gel(phi0, 15) = utoi(0x24b3244UL);
    2450        3242 :   gel(phi0, 16) = utoi(0xb56270UL);
    2451        3242 :   gel(phi0, 17) = utoi(0x25989UL);
    2452        3242 :   gel(phi0, 18) = utoi(0x2a6UL);
    2453        3242 :   gel(phi0, 19) = gen_1;
    2454             : 
    2455        3242 :   phi1 = cgetg(19, t_VEC);
    2456        3242 :   gel(phi1, 1) = gen_0;
    2457        3242 :   gel(phi1, 2) = gen_0;
    2458        3242 :   gel(phi1, 3) = gen_m1;
    2459        3242 :   gel(phi1, 4) = utoi(0x1eUL);
    2460        3242 :   gel(phi1, 5) = utoineg(0xffUL);
    2461        3242 :   gel(phi1, 6) = utoi(0x243UL);
    2462        3242 :   gel(phi1, 7) = utoineg(0xf3UL);
    2463        3242 :   gel(phi1, 8) = utoineg(0x5c4UL);
    2464        3242 :   gel(phi1, 9) = utoi(0x107bUL);
    2465        3242 :   gel(phi1, 10) = utoineg(0x11b2fUL);
    2466        3242 :   gel(phi1, 11) = utoi(0x48fa8UL);
    2467        3242 :   gel(phi1, 12) = utoineg(0x6ff7cUL);
    2468        3242 :   gel(phi1, 13) = utoi(0x4bf48UL);
    2469        3242 :   gel(phi1, 14) = utoineg(0x187efUL);
    2470        3242 :   gel(phi1, 15) = utoi(0x404cUL);
    2471        3242 :   gel(phi1, 16) = utoineg(0x582UL);
    2472        3242 :   gel(phi1, 17) = utoi(0x3cUL);
    2473        3242 :   gel(phi1, 18) = gen_m1;
    2474             : 
    2475        3242 :   gel(phi, 1) = phi0;
    2476        3242 :   gel(phi, 2) = phi1;
    2477        3242 :   gel(phi, 3) = utoi(7); return phi;
    2478             : }
    2479             : 
    2480             : static GEN
    2481        6520 : phi_w2w7_j(void)
    2482             : {
    2483             :   GEN phi, phi0, phi1;
    2484        6520 :   phi = cgetg(4, t_VEC);
    2485             : 
    2486        6520 :   phi0 = cgetg(26, t_VEC);
    2487        6520 :   gel(phi0, 1) = gen_1;
    2488        6520 :   gel(phi0, 2) = utoineg(0x24UL);
    2489        6520 :   gel(phi0, 3) = utoi(0x4ceUL);
    2490        6520 :   gel(phi0, 4) = utoineg(0x5d60UL);
    2491        6520 :   gel(phi0, 5) = utoi(0x62b05UL);
    2492        6520 :   gel(phi0, 6) = utoineg(0x47be78UL);
    2493        6520 :   gel(phi0, 7) = utoi(0x2a3880aUL);
    2494        6520 :   gel(phi0, 8) = utoineg(0x114bccf4UL);
    2495        6520 :   gel(phi0, 9) = utoi(0x4b95e79aUL);
    2496        6520 :   gel(phi0, 10) = utoineg(0xe2cfee1cUL);
    2497        6520 :   gel(phi0, 11) = uu32toi(0x1UL, 0xe43d1126UL);
    2498        6520 :   gel(phi0, 12) = uu32toineg(0x2UL, 0xf04dc6f8UL);
    2499        6520 :   gel(phi0, 13) = uu32toi(0x3UL, 0x5384987dUL);
    2500        6520 :   gel(phi0, 14) = uu32toineg(0x2UL, 0xa5ccbe18UL);
    2501        6520 :   gel(phi0, 15) = uu32toi(0x1UL, 0x4c52c8a6UL);
    2502        6520 :   gel(phi0, 16) = utoineg(0x2643fdecUL);
    2503        6520 :   gel(phi0, 17) = utoineg(0x49f5ab66UL);
    2504        6520 :   gel(phi0, 18) = utoi(0x33074d3cUL);
    2505        6520 :   gel(phi0, 19) = utoineg(0x6a3e376UL);
    2506        6520 :   gel(phi0, 20) = utoineg(0x675aa58UL);
    2507        6520 :   gel(phi0, 21) = utoi(0x2674005UL);
    2508        6520 :   gel(phi0, 22) = utoi(0xba5be0UL);
    2509        6520 :   gel(phi0, 23) = utoi(0x2644eUL);
    2510        6520 :   gel(phi0, 24) = utoi(0x2acUL);
    2511        6520 :   gel(phi0, 25) = gen_1;
    2512             : 
    2513        6520 :   phi1 = cgetg(25, t_VEC);
    2514        6520 :   gel(phi1, 1) = gen_0;
    2515        6520 :   gel(phi1, 2) = gen_0;
    2516        6520 :   gel(phi1, 3) = gen_m1;
    2517        6520 :   gel(phi1, 4) = utoi(0x1cUL);
    2518        6520 :   gel(phi1, 5) = utoineg(0x10aUL);
    2519        6520 :   gel(phi1, 6) = utoi(0x3f0UL);
    2520        6520 :   gel(phi1, 7) = utoineg(0x5d3UL);
    2521        6520 :   gel(phi1, 8) = utoi(0x3efUL);
    2522        6520 :   gel(phi1, 9) = utoineg(0x102UL);
    2523        6520 :   gel(phi1, 10) = utoineg(0x5c8UL);
    2524        6520 :   gel(phi1, 11) = utoi(0x102fUL);
    2525        6520 :   gel(phi1, 12) = utoineg(0x13f8aUL);
    2526        6520 :   gel(phi1, 13) = utoi(0x86538UL);
    2527        6520 :   gel(phi1, 14) = utoineg(0x1bbd10UL);
    2528        6520 :   gel(phi1, 15) = utoi(0x3614e8UL);
    2529        6520 :   gel(phi1, 16) = utoineg(0x42f793UL);
    2530        6520 :   gel(phi1, 17) = utoi(0x364698UL);
    2531        6520 :   gel(phi1, 18) = utoineg(0x1c7a10UL);
    2532        6520 :   gel(phi1, 19) = utoi(0x97cc8UL);
    2533        6520 :   gel(phi1, 20) = utoineg(0x1fc8aUL);
    2534        6520 :   gel(phi1, 21) = utoi(0x4210UL);
    2535        6520 :   gel(phi1, 22) = utoineg(0x524UL);
    2536        6520 :   gel(phi1, 23) = utoi(0x38UL);
    2537        6520 :   gel(phi1, 24) = gen_m1;
    2538             : 
    2539        6520 :   gel(phi, 1) = phi0;
    2540        6520 :   gel(phi, 2) = phi1;
    2541        6520 :   gel(phi, 3) = utoi(9); return phi;
    2542             : }
    2543             : 
    2544             : static GEN
    2545        2937 : phi_w2w13_j(void)
    2546             : {
    2547             :   GEN phi, phi0, phi1;
    2548        2937 :   phi = cgetg(4, t_VEC);
    2549             : 
    2550        2937 :   phi0 = cgetg(44, t_VEC);
    2551        2937 :   gel(phi0, 1) = gen_1;
    2552        2937 :   gel(phi0, 2) = utoineg(0x1eUL);
    2553        2937 :   gel(phi0, 3) = utoi(0x45fUL);
    2554        2937 :   gel(phi0, 4) = utoineg(0x5590UL);
    2555        2937 :   gel(phi0, 5) = utoi(0x64407UL);
    2556        2937 :   gel(phi0, 6) = utoineg(0x53a792UL);
    2557        2937 :   gel(phi0, 7) = utoi(0x3b21af3UL);
    2558        2937 :   gel(phi0, 8) = utoineg(0x20d056d0UL);
    2559        2937 :   gel(phi0, 9) = utoi(0xe02db4a6UL);
    2560        2937 :   gel(phi0, 10) = uu32toineg(0x4UL, 0xb23400b0UL);
    2561        2937 :   gel(phi0, 11) = uu32toi(0x14UL, 0x57fbb906UL);
    2562        2937 :   gel(phi0, 12) = uu32toineg(0x49UL, 0xcf80c00UL);
    2563        2937 :   gel(phi0, 13) = uu32toi(0xdeUL, 0x84ff421UL);
    2564        2937 :   gel(phi0, 14) = uu32toineg(0x244UL, 0xc500c156UL);
    2565        2937 :   gel(phi0, 15) = uu32toi(0x52cUL, 0x79162979UL);
    2566        2937 :   gel(phi0, 16) = uu32toineg(0xa64UL, 0x8edc5650UL);
    2567        2937 :   gel(phi0, 17) = uu32toi(0x1289UL, 0x4225bb41UL);
    2568        2937 :   gel(phi0, 18) = uu32toineg(0x1d89UL, 0x2a15229aUL);
    2569        2937 :   gel(phi0, 19) = uu32toi(0x2a3eUL, 0x4539f1ebUL);
    2570        2937 :   gel(phi0, 20) = uu32toineg(0x366aUL, 0xa5ea1130UL);
    2571        2937 :   gel(phi0, 21) = uu32toi(0x3f47UL, 0xa19fecb4UL);
    2572        2937 :   gel(phi0, 22) = uu32toineg(0x4282UL, 0x91a3c4a0UL);
    2573        2937 :   gel(phi0, 23) = uu32toi(0x3f30UL, 0xbaa305b4UL);
    2574        2937 :   gel(phi0, 24) = uu32toineg(0x3635UL, 0xd11c2530UL);
    2575        2937 :   gel(phi0, 25) = uu32toi(0x29e2UL, 0x89df27ebUL);
    2576        2937 :   gel(phi0, 26) = uu32toineg(0x1d03UL, 0x6509d48aUL);
    2577        2937 :   gel(phi0, 27) = uu32toi(0x11e2UL, 0x272cc601UL);
    2578        2937 :   gel(phi0, 28) = uu32toineg(0x9b0UL, 0xacd58ff0UL);
    2579        2936 :   gel(phi0, 29) = uu32toi(0x485UL, 0x608d7db9UL);
    2580        2937 :   gel(phi0, 30) = uu32toineg(0x1bfUL, 0xa941546UL);
    2581        2937 :   gel(phi0, 31) = uu32toi(0x82UL, 0x56e48b21UL);
    2582        2937 :   gel(phi0, 32) = uu32toineg(0x13UL, 0xc36b2340UL);
    2583        2937 :   gel(phi0, 33) = uu32toineg(0x5UL, 0x6637257aUL);
    2584        2937 :   gel(phi0, 34) = uu32toi(0x5UL, 0x40f70bd0UL);
    2585        2937 :   gel(phi0, 35) = uu32toineg(0x1UL, 0xf70842daUL);
    2586        2937 :   gel(phi0, 36) = utoi(0x53eea5f0UL);
    2587        2937 :   gel(phi0, 37) = utoi(0xda17bf3UL);
    2588        2937 :   gel(phi0, 38) = utoineg(0xaf246c2UL);
    2589        2937 :   gel(phi0, 39) = utoi(0x278f847UL);
    2590        2937 :   gel(phi0, 40) = utoi(0xbf5550UL);
    2591        2937 :   gel(phi0, 41) = utoi(0x26f1fUL);
    2592        2937 :   gel(phi0, 42) = utoi(0x2b2UL);
    2593        2937 :   gel(phi0, 43) = gen_1;
    2594             : 
    2595        2937 :   phi1 = cgetg(43, t_VEC);
    2596        2937 :   gel(phi1, 1) = gen_0;
    2597        2937 :   gel(phi1, 2) = gen_0;
    2598        2937 :   gel(phi1, 3) = gen_m1;
    2599        2937 :   gel(phi1, 4) = utoi(0x1aUL);
    2600        2937 :   gel(phi1, 5) = utoineg(0x111UL);
    2601        2937 :   gel(phi1, 6) = utoi(0x5e4UL);
    2602        2937 :   gel(phi1, 7) = utoineg(0x1318UL);
    2603        2937 :   gel(phi1, 8) = utoi(0x2804UL);
    2604        2937 :   gel(phi1, 9) = utoineg(0x3cd6UL);
    2605        2937 :   gel(phi1, 10) = utoi(0x467cUL);
    2606        2937 :   gel(phi1, 11) = utoineg(0x3cd6UL);
    2607        2937 :   gel(phi1, 12) = utoi(0x2804UL);
    2608        2937 :   gel(phi1, 13) = utoineg(0x1318UL);
    2609        2937 :   gel(phi1, 14) = utoi(0x5e3UL);
    2610        2937 :   gel(phi1, 15) = utoineg(0x10dUL);
    2611        2937 :   gel(phi1, 16) = utoineg(0x5ccUL);
    2612        2937 :   gel(phi1, 17) = utoi(0x100bUL);
    2613        2937 :   gel(phi1, 18) = utoineg(0x160e1UL);
    2614        2937 :   gel(phi1, 19) = utoi(0xd2cb0UL);
    2615        2937 :   gel(phi1, 20) = utoineg(0x4c85fcUL);
    2616        2937 :   gel(phi1, 21) = utoi(0x137cb98UL);
    2617        2937 :   gel(phi1, 22) = utoineg(0x3c75568UL);
    2618        2937 :   gel(phi1, 23) = utoi(0x95c69c8UL);
    2619        2937 :   gel(phi1, 24) = utoineg(0x131557bcUL);
    2620        2937 :   gel(phi1, 25) = utoi(0x20aacfd0UL);
    2621        2937 :   gel(phi1, 26) = utoineg(0x2f9164e6UL);
    2622        2937 :   gel(phi1, 27) = utoi(0x3b6a5e40UL);
    2623        2937 :   gel(phi1, 28) = utoineg(0x3ff54344UL);
    2624        2937 :   gel(phi1, 29) = utoi(0x3b6a9140UL);
    2625        2937 :   gel(phi1, 30) = utoineg(0x2f927fa6UL);
    2626        2937 :   gel(phi1, 31) = utoi(0x20ae6450UL);
    2627        2937 :   gel(phi1, 32) = utoineg(0x131cd87cUL);
    2628        2937 :   gel(phi1, 33) = utoi(0x967d1e8UL);
    2629        2937 :   gel(phi1, 34) = utoineg(0x3d48ca8UL);
    2630        2937 :   gel(phi1, 35) = utoi(0x14333b8UL);
    2631        2937 :   gel(phi1, 36) = utoineg(0x5406bcUL);
    2632        2937 :   gel(phi1, 37) = utoi(0x10c130UL);
    2633        2937 :   gel(phi1, 38) = utoineg(0x27ba1UL);
    2634        2937 :   gel(phi1, 39) = utoi(0x433cUL);
    2635        2937 :   gel(phi1, 40) = utoineg(0x4c6UL);
    2636        2937 :   gel(phi1, 41) = utoi(0x34UL);
    2637        2937 :   gel(phi1, 42) = gen_m1;
    2638             : 
    2639        2937 :   gel(phi, 1) = phi0;
    2640        2937 :   gel(phi, 2) = phi1;
    2641        2937 :   gel(phi, 3) = utoi(15); return phi;
    2642             : }
    2643             : 
    2644             : static GEN
    2645        1136 : phi_w3w5_j(void)
    2646             : {
    2647             :   GEN phi, phi0, phi1;
    2648        1136 :   phi = cgetg(4, t_VEC);
    2649             : 
    2650        1136 :   phi0 = cgetg(26, t_VEC);
    2651        1136 :   gel(phi0, 1) = gen_1;
    2652        1136 :   gel(phi0, 2) = utoi(0x18UL);
    2653        1136 :   gel(phi0, 3) = utoi(0xb4UL);
    2654        1136 :   gel(phi0, 4) = utoineg(0x178UL);
    2655        1136 :   gel(phi0, 5) = utoineg(0x2d7eUL);
    2656        1136 :   gel(phi0, 6) = utoineg(0x89b8UL);
    2657        1136 :   gel(phi0, 7) = utoi(0x35c24UL);
    2658        1136 :   gel(phi0, 8) = utoi(0x128a18UL);
    2659        1136 :   gel(phi0, 9) = utoineg(0x12a911UL);
    2660        1136 :   gel(phi0, 10) = utoineg(0xcc0190UL);
    2661        1136 :   gel(phi0, 11) = utoi(0x94368UL);
    2662        1136 :   gel(phi0, 12) = utoi(0x1439d0UL);
    2663        1136 :   gel(phi0, 13) = utoi(0x96f931cUL);
    2664        1136 :   gel(phi0, 14) = utoineg(0x1f59ff0UL);
    2665        1136 :   gel(phi0, 15) = utoi(0x20e7e8UL);
    2666        1136 :   gel(phi0, 16) = utoineg(0x25fdf150UL);
    2667        1136 :   gel(phi0, 17) = utoineg(0x7091511UL);
    2668        1136 :   gel(phi0, 18) = utoi(0x1ef52f8UL);
    2669        1136 :   gel(phi0, 19) = utoi(0x341f2de4UL);
    2670        1136 :   gel(phi0, 20) = utoi(0x25d72c28UL);
    2671        1136 :   gel(phi0, 21) = utoi(0x95d2082UL);
    2672        1136 :   gel(phi0, 22) = utoi(0xd2d828UL);
    2673        1136 :   gel(phi0, 23) = utoi(0x281f4UL);
    2674        1136 :   gel(phi0, 24) = utoi(0x2b8UL);
    2675        1136 :   gel(phi0, 25) = gen_1;
    2676             : 
    2677        1136 :   phi1 = cgetg(25, t_VEC);
    2678        1136 :   gel(phi1, 1) = gen_0;
    2679        1136 :   gel(phi1, 2) = gen_0;
    2680        1136 :   gel(phi1, 3) = gen_0;
    2681        1136 :   gel(phi1, 4) = gen_1;
    2682        1136 :   gel(phi1, 5) = utoi(0xfUL);
    2683        1136 :   gel(phi1, 6) = utoi(0x2eUL);
    2684        1136 :   gel(phi1, 7) = utoineg(0x1fUL);
    2685        1136 :   gel(phi1, 8) = utoineg(0x2dUL);
    2686        1136 :   gel(phi1, 9) = utoineg(0x5caUL);
    2687        1136 :   gel(phi1, 10) = utoineg(0x358UL);
    2688        1136 :   gel(phi1, 11) = utoi(0x2f1cUL);
    2689        1136 :   gel(phi1, 12) = utoi(0xd8eaUL);
    2690        1136 :   gel(phi1, 13) = utoineg(0x38c70UL);
    2691        1136 :   gel(phi1, 14) = utoineg(0x1a964UL);
    2692        1136 :   gel(phi1, 15) = utoi(0x93512UL);
    2693        1136 :   gel(phi1, 16) = utoineg(0x58f2UL);
    2694        1136 :   gel(phi1, 17) = utoineg(0x5af1eUL);
    2695        1136 :   gel(phi1, 18) = utoi(0x1afb8UL);
    2696        1136 :   gel(phi1, 19) = utoi(0xc084UL);
    2697        1136 :   gel(phi1, 20) = utoineg(0x7fcbUL);
    2698        1136 :   gel(phi1, 21) = utoi(0x1c89UL);
    2699        1136 :   gel(phi1, 22) = utoineg(0x32aUL);
    2700        1136 :   gel(phi1, 23) = utoi(0x2dUL);
    2701        1136 :   gel(phi1, 24) = gen_m1;
    2702             : 
    2703        1136 :   gel(phi, 1) = phi0;
    2704        1136 :   gel(phi, 2) = phi1;
    2705        1136 :   gel(phi, 3) = utoi(8); return phi;
    2706             : }
    2707             : 
    2708             : static GEN
    2709        2412 : phi_w3w7_j(void)
    2710             : {
    2711             :   GEN phi, phi0, phi1;
    2712        2412 :   phi = cgetg(4, t_VEC);
    2713             : 
    2714        2412 :   phi0 = cgetg(34, t_VEC);
    2715        2412 :   gel(phi0, 1) = gen_1;
    2716        2412 :   gel(phi0, 2) = utoineg(0x14UL);
    2717        2412 :   gel(phi0, 3) = utoi(0x82UL);
    2718        2412 :   gel(phi0, 4) = utoi(0x1f8UL);
    2719        2412 :   gel(phi0, 5) = utoineg(0x2a45UL);
    2720        2412 :   gel(phi0, 6) = utoi(0x9300UL);
    2721        2412 :   gel(phi0, 7) = utoi(0x32abeUL);
    2722        2412 :   gel(phi0, 8) = utoineg(0x19c91cUL);
    2723        2412 :   gel(phi0, 9) = utoi(0xc1ba9UL);
    2724        2412 :   gel(phi0, 10) = utoi(0x1788f68UL);
    2725        2412 :   gel(phi0, 11) = utoineg(0x2b1989cUL);
    2726        2412 :   gel(phi0, 12) = utoineg(0x7a92408UL);
    2727        2412 :   gel(phi0, 13) = utoi(0x1238d56eUL);
    2728        2412 :   gel(phi0, 14) = utoi(0x13dd66a0UL);
    2729        2412 :   gel(phi0, 15) = utoineg(0x2dbedca8UL);
    2730        2412 :   gel(phi0, 16) = utoineg(0x34282eb8UL);
    2731        2412 :   gel(phi0, 17) = utoi(0x2c2a54d2UL);
    2732        2412 :   gel(phi0, 18) = utoi(0x98db81a8UL);
    2733        2412 :   gel(phi0, 19) = utoineg(0x4088be8UL);
    2734        2412 :   gel(phi0, 20) = utoineg(0xe424a220UL);
    2735        2412 :   gel(phi0, 21) = utoineg(0x67bbb232UL);
    2736        2412 :   gel(phi0, 22) = utoi(0x7dd8bb98UL);
    2737        2412 :   gel(phi0, 23) = uu32toi(0x1UL, 0xcaff744UL);
    2738        2412 :   gel(phi0, 24) = utoineg(0x1d46a378UL);
    2739        2412 :   gel(phi0, 25) = utoineg(0x82fa50f7UL);
    2740        2412 :   gel(phi0, 26) = utoineg(0x700ef38cUL);
    2741        2412 :   gel(phi0, 27) = utoi(0x20aa202eUL);
    2742        2412 :   gel(phi0, 28) = utoi(0x299b3440UL);
    2743        2412 :   gel(phi0, 29) = utoi(0xa476c4bUL);
    2744        2412 :   gel(phi0, 30) = utoi(0xd80558UL);
    2745        2412 :   gel(phi0, 31) = utoi(0x28a32UL);
    2746        2412 :   gel(phi0, 32) = utoi(0x2bcUL);
    2747        2412 :   gel(phi0, 33) = gen_1;
    2748             : 
    2749        2412 :   phi1 = cgetg(33, t_VEC);
    2750        2412 :   gel(phi1, 1) = gen_0;
    2751        2412 :   gel(phi1, 2) = gen_0;
    2752        2412 :   gel(phi1, 3) = gen_0;
    2753        2412 :   gel(phi1, 4) = gen_m1;
    2754        2412 :   gel(phi1, 5) = utoi(0xeUL);
    2755        2412 :   gel(phi1, 6) = utoineg(0x31UL);
    2756        2412 :   gel(phi1, 7) = utoineg(0xeUL);
    2757        2412 :   gel(phi1, 8) = utoi(0x99UL);
    2758        2412 :   gel(phi1, 9) = utoineg(0x8UL);
    2759        2412 :   gel(phi1, 10) = utoineg(0x2eUL);
    2760        2412 :   gel(phi1, 11) = utoineg(0x5ccUL);
    2761        2412 :   gel(phi1, 12) = utoi(0x308UL);
    2762        2412 :   gel(phi1, 13) = utoi(0x2904UL);
    2763        2412 :   gel(phi1, 14) = utoineg(0x15700UL);
    2764        2412 :   gel(phi1, 15) = utoineg(0x2b9ecUL);
    2765        2412 :   gel(phi1, 16) = utoi(0xf0966UL);
    2766        2412 :   gel(phi1, 17) = utoi(0xb3cc8UL);
    2767        2412 :   gel(phi1, 18) = utoineg(0x38241cUL);
    2768        2412 :   gel(phi1, 19) = utoineg(0x8604cUL);
    2769        2412 :   gel(phi1, 20) = utoi(0x578a64UL);
    2770        2412 :   gel(phi1, 21) = utoineg(0x11a798UL);
    2771        2412 :   gel(phi1, 22) = utoineg(0x39c85eUL);
    2772        2412 :   gel(phi1, 23) = utoi(0x1a5084UL);
    2773        2412 :   gel(phi1, 24) = utoi(0xcdeb4UL);
    2774        2412 :   gel(phi1, 25) = utoineg(0xb0364UL);
    2775        2412 :   gel(phi1, 26) = utoi(0x129d4UL);
    2776        2412 :   gel(phi1, 27) = utoi(0x126fcUL);
    2777        2412 :   gel(phi1, 28) = utoineg(0x8649UL);
    2778        2412 :   gel(phi1, 29) = utoi(0x1aa2UL);
    2779        2412 :   gel(phi1, 30) = utoineg(0x2dfUL);
    2780        2412 :   gel(phi1, 31) = utoi(0x2aUL);
    2781        2412 :   gel(phi1, 32) = gen_m1;
    2782             : 
    2783        2412 :   gel(phi, 1) = phi0;
    2784        2412 :   gel(phi, 2) = phi1;
    2785        2412 :   gel(phi, 3) = utoi(10); return phi;
    2786             : }
    2787             : 
    2788             : static GEN
    2789         210 : phi_w3w13_j(void)
    2790             : {
    2791             :   GEN phi, phi0, phi1;
    2792         210 :   phi = cgetg(4, t_VEC);
    2793             : 
    2794         210 :   phi0 = cgetg(58, t_VEC);
    2795         210 :   gel(phi0, 1) = gen_1;
    2796         210 :   gel(phi0, 2) = utoineg(0x10UL);
    2797         210 :   gel(phi0, 3) = utoi(0x58UL);
    2798         210 :   gel(phi0, 4) = utoi(0x258UL);
    2799         210 :   gel(phi0, 5) = utoineg(0x270cUL);
    2800         210 :   gel(phi0, 6) = utoi(0x9c00UL);
    2801         210 :   gel(phi0, 7) = utoi(0x2b40cUL);
    2802         210 :   gel(phi0, 8) = utoineg(0x20e250UL);
    2803         210 :   gel(phi0, 9) = utoi(0x4f46baUL);
    2804         210 :   gel(phi0, 10) = utoi(0x1869448UL);
    2805         210 :   gel(phi0, 11) = utoineg(0xa49ab68UL);
    2806         210 :   gel(phi0, 12) = utoi(0x96c7630UL);
    2807         210 :   gel(phi0, 13) = utoi(0x4f7e0af6UL);
    2808         210 :   gel(phi0, 14) = utoineg(0xea093590UL);
    2809         210 :   gel(phi0, 15) = utoineg(0x6735bc50UL);
    2810         210 :   gel(phi0, 16) = uu32toi(0x5UL, 0x971a2e08UL);
    2811         210 :   gel(phi0, 17) = uu32toineg(0x6UL, 0x29c9d965UL);
    2812         210 :   gel(phi0, 18) = uu32toineg(0xdUL, 0xeb9aa360UL);
    2813         210 :   gel(phi0, 19) = uu32toi(0x26UL, 0xe9c0584UL);
    2814         210 :   gel(phi0, 20) = uu32toineg(0x1UL, 0xb0cadce8UL);
    2815         210 :   gel(phi0, 21) = uu32toineg(0x62UL, 0x73586014UL);
    2816         210 :   gel(phi0, 22) = uu32toi(0x66UL, 0xaf672e38UL);
    2817         210 :   gel(phi0, 23) = uu32toi(0x6bUL, 0x93c28cdcUL);
    2818         210 :   gel(phi0, 24) = uu32toineg(0x11eUL, 0x4f633080UL);
    2819         210 :   gel(phi0, 25) = uu32toi(0x3cUL, 0xcc42461bUL);
    2820         210 :   gel(phi0, 26) = uu32toi(0x17bUL, 0xdec0a78UL);
    2821         210 :   gel(phi0, 27) = uu32toineg(0x166UL, 0x910d8bd0UL);
    2822         210 :   gel(phi0, 28) = uu32toineg(0xd4UL, 0x47873030UL);
    2823         210 :   gel(phi0, 29) = uu32toi(0x204UL, 0x811828baUL);
    2824         210 :   gel(phi0, 30) = uu32toineg(0x50UL, 0x5d713960UL);
    2825         210 :   gel(phi0, 31) = uu32toineg(0x198UL, 0xa27e42b0UL);
    2826         210 :   gel(phi0, 32) = uu32toi(0xe1UL, 0x25685138UL);
    2827         210 :   gel(phi0, 33) = uu32toi(0xe3UL, 0xaa5774bbUL);
    2828         210 :   gel(phi0, 34) = uu32toineg(0xcfUL, 0x392a9a00UL);
    2829         210 :   gel(phi0, 35) = uu32toineg(0x81UL, 0xfb334d04UL);
    2830         210 :   gel(phi0, 36) = uu32toi(0xabUL, 0x59594a68UL);
    2831         210 :   gel(phi0, 37) = uu32toi(0x42UL, 0x356993acUL);
    2832         210 :   gel(phi0, 38) = uu32toineg(0x86UL, 0x307ba678UL);
    2833         210 :   gel(phi0, 39) = uu32toineg(0xbUL, 0x7a9e59dcUL);
    2834         210 :   gel(phi0, 40) = uu32toi(0x4cUL, 0x27935f20UL);
    2835         210 :   gel(phi0, 41) = uu32toineg(0x2UL, 0xe0ac9045UL);
    2836         210 :   gel(phi0, 42) = uu32toineg(0x24UL, 0x14495758UL);
    2837         210 :   gel(phi0, 43) = utoi(0x20973410UL);
    2838         210 :   gel(phi0, 44) = uu32toi(0x13UL, 0x99ff4e00UL);
    2839         210 :   gel(phi0, 45) = uu32toineg(0x1UL, 0xa710d34aUL);
    2840         210 :   gel(phi0, 46) = uu32toineg(0x7UL, 0xfe5405c0UL);
    2841         210 :   gel(phi0, 47) = uu32toi(0x1UL, 0xcdee0f8UL);
    2842         210 :   gel(phi0, 48) = uu32toi(0x2UL, 0x660c92a8UL);
    2843         210 :   gel(phi0, 49) = utoi(0x3f13a35aUL);
    2844         210 :   gel(phi0, 50) = utoineg(0xe4eb4ba0UL);
    2845         210 :   gel(phi0, 51) = utoineg(0x6420f4UL);
    2846         210 :   gel(phi0, 52) = utoi(0x2c624370UL);
    2847         210 :   gel(phi0, 53) = utoi(0xb31b814UL);
    2848         210 :   gel(phi0, 54) = utoi(0xdd3ad8UL);
    2849         210 :   gel(phi0, 55) = utoi(0x29278UL);
    2850         210 :   gel(phi0, 56) = utoi(0x2c0UL);
    2851         210 :   gel(phi0, 57) = gen_1;
    2852             : 
    2853         210 :   phi1 = cgetg(57, t_VEC);
    2854         210 :   gel(phi1, 1) = gen_0;
    2855         210 :   gel(phi1, 2) = gen_0;
    2856         210 :   gel(phi1, 3) = gen_0;
    2857         210 :   gel(phi1, 4) = gen_m1;
    2858         210 :   gel(phi1, 5) = utoi(0xdUL);
    2859         210 :   gel(phi1, 6) = utoineg(0x34UL);
    2860         210 :   gel(phi1, 7) = utoi(0x1aUL);
    2861         210 :   gel(phi1, 8) = utoi(0xf7UL);
    2862         210 :   gel(phi1, 9) = utoineg(0x16cUL);
    2863         210 :   gel(phi1, 10) = utoineg(0xddUL);
    2864         210 :   gel(phi1, 11) = utoi(0x28aUL);
    2865         210 :   gel(phi1, 12) = utoineg(0xddUL);
    2866         210 :   gel(phi1, 13) = utoineg(0x16cUL);
    2867         210 :   gel(phi1, 14) = utoi(0xf6UL);
    2868         210 :   gel(phi1, 15) = utoi(0x1dUL);
    2869         210 :   gel(phi1, 16) = utoineg(0x31UL);
    2870         210 :   gel(phi1, 17) = utoineg(0x5ceUL);
    2871         210 :   gel(phi1, 18) = utoi(0x2e4UL);
    2872         210 :   gel(phi1, 19) = utoi(0x252cUL);
    2873         210 :   gel(phi1, 20) = utoineg(0x1b34cUL);
    2874         210 :   gel(phi1, 21) = utoi(0xaf80UL);
    2875         210 :   gel(phi1, 22) = utoi(0x1cc5f9UL);
    2876         210 :   gel(phi1, 23) = utoineg(0x3e1aa5UL);
    2877         210 :   gel(phi1, 24) = utoineg(0x86d17aUL);
    2878         210 :   gel(phi1, 25) = utoi(0x2427264UL);
    2879         210 :   gel(phi1, 26) = utoineg(0x691c1fUL);
    2880         210 :   gel(phi1, 27) = utoineg(0x862ad4eUL);
    2881         210 :   gel(phi1, 28) = utoi(0xab21e1fUL);
    2882         210 :   gel(phi1, 29) = utoi(0xbc19ddcUL);
    2883         210 :   gel(phi1, 30) = utoineg(0x24331db8UL);
    2884         210 :   gel(phi1, 31) = utoi(0x972c105UL);
    2885         210 :   gel(phi1, 32) = utoi(0x363d7107UL);
    2886         210 :   gel(phi1, 33) = utoineg(0x39696450UL);
    2887         210 :   gel(phi1, 34) = utoineg(0x1bce7c48UL);
    2888         210 :   gel(phi1, 35) = utoi(0x552ecba0UL);
    2889         210 :   gel(phi1, 36) = utoineg(0x1c7771b8UL);
    2890         210 :   gel(phi1, 37) = utoineg(0x393029b8UL);
    2891         210 :   gel(phi1, 38) = utoi(0x3755be97UL);
    2892         210 :   gel(phi1, 39) = utoi(0x83402a9UL);
    2893         210 :   gel(phi1, 40) = utoineg(0x24d5be62UL);
    2894         210 :   gel(phi1, 41) = utoi(0xdb6d90aUL);
    2895         210 :   gel(phi1, 42) = utoi(0xa0ef177UL);
    2896         210 :   gel(phi1, 43) = utoineg(0x99ff162UL);
    2897         210 :   gel(phi1, 44) = utoi(0xb09e27UL);
    2898         210 :   gel(phi1, 45) = utoi(0x26a7adcUL);
    2899         210 :   gel(phi1, 46) = utoineg(0x116e2fcUL);
    2900         210 :   gel(phi1, 47) = utoineg(0x1383b5UL);
    2901         210 :   gel(phi1, 48) = utoi(0x35a9e7UL);
    2902         210 :   gel(phi1, 49) = utoineg(0x1082a0UL);
    2903         210 :   gel(phi1, 50) = utoineg(0x4696UL);
    2904         210 :   gel(phi1, 51) = utoi(0x19f98UL);
    2905         210 :   gel(phi1, 52) = utoineg(0x8bb3UL);
    2906         210 :   gel(phi1, 53) = utoi(0x18bbUL);
    2907         210 :   gel(phi1, 54) = utoineg(0x297UL);
    2908         210 :   gel(phi1, 55) = utoi(0x27UL);
    2909         210 :   gel(phi1, 56) = gen_m1;
    2910             : 
    2911         210 :   gel(phi, 1) = phi0;
    2912         210 :   gel(phi, 2) = phi1;
    2913         210 :   gel(phi, 3) = utoi(16); return phi;
    2914             : }
    2915             : 
    2916             : static GEN
    2917        2884 : phi_w5w7_j(void)
    2918             : {
    2919             :   GEN phi, phi0, phi1;
    2920        2884 :   phi = cgetg(4, t_VEC);
    2921             : 
    2922        2884 :   phi0 = cgetg(50, t_VEC);
    2923        2884 :   gel(phi0, 1) = gen_1;
    2924        2884 :   gel(phi0, 2) = utoi(0xcUL);
    2925        2884 :   gel(phi0, 3) = utoi(0x2aUL);
    2926        2884 :   gel(phi0, 4) = utoi(0x10UL);
    2927        2884 :   gel(phi0, 5) = utoineg(0x69UL);
    2928        2884 :   gel(phi0, 6) = utoineg(0x318UL);
    2929        2884 :   gel(phi0, 7) = utoineg(0x148aUL);
    2930        2884 :   gel(phi0, 8) = utoineg(0x17c4UL);
    2931        2884 :   gel(phi0, 9) = utoi(0x1a73UL);
    2932        2884 :   gel(phi0, 10) = gen_0;
    2933        2884 :   gel(phi0, 11) = utoi(0x338a0UL);
    2934        2884 :   gel(phi0, 12) = utoi(0x61698UL);
    2935        2884 :   gel(phi0, 13) = utoineg(0x96e8UL);
    2936        2884 :   gel(phi0, 14) = utoi(0x140910UL);
    2937        2884 :   gel(phi0, 15) = utoineg(0x45f6b4UL);
    2938        2884 :   gel(phi0, 16) = utoineg(0x309f50UL);
    2939        2884 :   gel(phi0, 17) = utoineg(0xef9f8bUL);
    2940        2884 :   gel(phi0, 18) = utoineg(0x283167cUL);
    2941        2884 :   gel(phi0, 19) = utoi(0x625e20aUL);
    2942        2884 :   gel(phi0, 20) = utoineg(0x16186350UL);
    2943        2884 :   gel(phi0, 21) = utoi(0x46861281UL);
    2944        2884 :   gel(phi0, 22) = utoineg(0x754b96a0UL);
    2945        2884 :   gel(phi0, 23) = uu32toi(0x1UL, 0x421ca02aUL);
    2946        2884 :   gel(phi0, 24) = uu32toineg(0x2UL, 0xdb76a5cUL);
    2947        2884 :   gel(phi0, 25) = uu32toi(0x4UL, 0xf6afd8eUL);
    2948        2884 :   gel(phi0, 26) = uu32toineg(0x6UL, 0xaafd3cb4UL);
    2949        2884 :   gel(phi0, 27) = uu32toi(0x8UL, 0xda2539caUL);
    2950        2884 :   gel(phi0, 28) = uu32toineg(0xfUL, 0x84343790UL);
    2951        2884 :   gel(phi0, 29) = uu32toi(0xfUL, 0x914ff421UL);
    2952        2884 :   gel(phi0, 30) = uu32toineg(0x19UL, 0x3c123950UL);
    2953        2884 :   gel(phi0, 31) = uu32toi(0x15UL, 0x381f722aUL);
    2954        2884 :   gel(phi0, 32) = uu32toineg(0x15UL, 0xe01c0c24UL);
    2955        2884 :   gel(phi0, 33) = uu32toi(0x19UL, 0x3360b375UL);
    2956        2884 :   gel(phi0, 34) = utoineg(0x59fda9c0UL);
    2957        2884 :   gel(phi0, 35) = uu32toi(0x20UL, 0xff55024cUL);
    2958        2884 :   gel(phi0, 36) = uu32toi(0x16UL, 0xcc600800UL);
    2959        2884 :   gel(phi0, 37) = uu32toi(0x24UL, 0x1879c898UL);
    2960        2884 :   gel(phi0, 38) = uu32toi(0x1cUL, 0x37f97498UL);
    2961        2884 :   gel(phi0, 39) = uu32toi(0x19UL, 0x39ec4b60UL);
    2962        2884 :   gel(phi0, 40) = uu32toi(0x10UL, 0x52c660d0UL);
    2963        2884 :   gel(phi0, 41) = uu32toi(0x9UL, 0xcab00333UL);
    2964        2884 :   gel(phi0, 42) = uu32toi(0x4UL, 0x7fe69be4UL);
    2965        2884 :   gel(phi0, 43) = uu32toi(0x1UL, 0xa0c6f116UL);
    2966        2884 :   gel(phi0, 44) = utoi(0x69244638UL);
    2967        2884 :   gel(phi0, 45) = utoi(0xed560f7UL);
    2968        2884 :   gel(phi0, 46) = utoi(0xe7b660UL);
    2969        2884 :   gel(phi0, 47) = utoi(0x29d8aUL);
    2970        2884 :   gel(phi0, 48) = utoi(0x2c4UL);
    2971        2884 :   gel(phi0, 49) = gen_1;
    2972             : 
    2973        2884 :   phi1 = cgetg(49, t_VEC);
    2974        2884 :   gel(phi1, 1) = gen_0;
    2975        2884 :   gel(phi1, 2) = gen_0;
    2976        2884 :   gel(phi1, 3) = gen_0;
    2977        2884 :   gel(phi1, 4) = gen_0;
    2978        2884 :   gel(phi1, 5) = gen_0;
    2979        2884 :   gel(phi1, 6) = gen_1;
    2980        2884 :   gel(phi1, 7) = utoi(0x7UL);
    2981        2884 :   gel(phi1, 8) = utoi(0x8UL);
    2982        2884 :   gel(phi1, 9) = utoineg(0x9UL);
    2983        2884 :   gel(phi1, 10) = gen_0;
    2984        2884 :   gel(phi1, 11) = utoineg(0x13UL);
    2985        2884 :   gel(phi1, 12) = utoineg(0x7UL);
    2986        2884 :   gel(phi1, 13) = utoineg(0x5ceUL);
    2987        2884 :   gel(phi1, 14) = utoineg(0xb0UL);
    2988        2884 :   gel(phi1, 15) = utoi(0x460UL);
    2989        2884 :   gel(phi1, 16) = utoineg(0x194bUL);
    2990        2884 :   gel(phi1, 17) = utoi(0x87c3UL);
    2991        2884 :   gel(phi1, 18) = utoi(0x3cdeUL);
    2992        2884 :   gel(phi1, 19) = utoineg(0xd683UL);
    2993        2884 :   gel(phi1, 20) = utoi(0x6099bUL);
    2994        2884 :   gel(phi1, 21) = utoineg(0x111ea8UL);
    2995        2884 :   gel(phi1, 22) = utoi(0xfa113UL);
    2996        2884 :   gel(phi1, 23) = utoineg(0x1a6561UL);
    2997        2884 :   gel(phi1, 24) = utoineg(0x1e997UL);
    2998        2884 :   gel(phi1, 25) = utoi(0x214e54UL);
    2999        2884 :   gel(phi1, 26) = utoineg(0x29c3f4UL);
    3000        2884 :   gel(phi1, 27) = utoi(0x67e102UL);
    3001        2884 :   gel(phi1, 28) = utoineg(0x227eaaUL);
    3002        2884 :   gel(phi1, 29) = utoi(0x191d10UL);
    3003        2884 :   gel(phi1, 30) = utoi(0x1a9cd5UL);
    3004        2884 :   gel(phi1, 31) = utoineg(0x58386fUL);
    3005        2884 :   gel(phi1, 32) = utoi(0x2e49f6UL);
    3006        2884 :   gel(phi1, 33) = utoineg(0x31194bUL);
    3007        2884 :   gel(phi1, 34) = utoi(0x9e07aUL);
    3008        2884 :   gel(phi1, 35) = utoi(0x260d59UL);
    3009        2884 :   gel(phi1, 36) = utoineg(0x189921UL);
    3010        2884 :   gel(phi1, 37) = utoi(0xeca4aUL);
    3011        2884 :   gel(phi1, 38) = utoineg(0xa3d9cUL);
    3012        2884 :   gel(phi1, 39) = utoineg(0x426daUL);
    3013        2884 :   gel(phi1, 40) = utoi(0x91875UL);
    3014        2884 :   gel(phi1, 41) = utoineg(0x3b55bUL);
    3015        2884 :   gel(phi1, 42) = utoineg(0x56f4UL);
    3016        2884 :   gel(phi1, 43) = utoi(0xcd1bUL);
    3017        2884 :   gel(phi1, 44) = utoineg(0x5159UL);
    3018        2884 :   gel(phi1, 45) = utoi(0x10f4UL);
    3019        2884 :   gel(phi1, 46) = utoineg(0x20dUL);
    3020        2884 :   gel(phi1, 47) = utoi(0x23UL);
    3021        2884 :   gel(phi1, 48) = gen_m1;
    3022             : 
    3023        2884 :   gel(phi, 1) = phi0;
    3024        2884 :   gel(phi, 2) = phi1;
    3025        2884 :   gel(phi, 3) = utoi(12); return phi;
    3026             : }
    3027             : 
    3028             : GEN
    3029       23936 : double_eta_raw(long inv)
    3030             : {
    3031       23936 :   switch (inv) {
    3032        1060 :     case INV_W2W3:
    3033        1060 :     case INV_W2W3E2: return phi_w2w3_j();
    3034        3535 :     case INV_W3W3:
    3035        3535 :     case INV_W3W3E2: return phi_w3w3_j();
    3036        3242 :     case INV_W2W5:
    3037        3242 :     case INV_W2W5E2: return phi_w2w5_j();
    3038        6520 :     case INV_W2W7:
    3039        6520 :     case INV_W2W7E2: return phi_w2w7_j();
    3040        1136 :     case INV_W3W5:   return phi_w3w5_j();
    3041        2412 :     case INV_W3W7:   return phi_w3w7_j();
    3042        2937 :     case INV_W2W13:  return phi_w2w13_j();
    3043         210 :     case INV_W3W13:  return phi_w3w13_j();
    3044        2884 :     case INV_W5W7:   return phi_w5w7_j();
    3045             :     default: pari_err_BUG("double_eta_raw"); return NULL;/*LCOV_EXCL_LINE*/
    3046             :   }
    3047             : }
    3048             : 
    3049             : /* SECTION: Select discriminant for given modpoly level. */
    3050             : 
    3051             : /* require an L1, useful for multi-threading */
    3052             : #define MODPOLY_USE_L1    1
    3053             : /* no bound on L1 other than the fixed bound MAX_L1 - needed to
    3054             :  * handle small L for certain invariants (but not for j) */
    3055             : #define MODPOLY_NO_MAX_L1 2
    3056             : /* don't use any auxilliary primes - needed to handle small L for
    3057             :  * certain invariants (but not for j) */
    3058             : #define MODPOLY_NO_AUX_L  4
    3059             : #define MODPOLY_IGNORE_SPARSE_FACTOR 8
    3060             : 
    3061             : INLINE double
    3062        2959 : modpoly_height_bound(long L, long inv)
    3063             : {
    3064             :   double nbits, nbits2;
    3065             :   double c;
    3066             :   long hf;
    3067             : 
    3068             :   /* proven bound (in bits), derived from: 6l*log(l)+16*l+13*sqrt(l)*log(l) */
    3069        2959 :   nbits = 6.0*L*log2(L)+16/M_LN2*L+8.0*sqrt((double)L)*log2(L);
    3070             :   /* alternative proven bound (in bits), derived from: 6l*log(l)+17*l */
    3071        2959 :   nbits2 = 6.0*L*log2(L)+17/M_LN2*L;
    3072        2959 :   if ( nbits2 < nbits ) nbits = nbits2;
    3073        2959 :   hf = modinv_height_factor(inv);
    3074        2959 :   if (hf > 1) {
    3075             :    /* IMPORTANT: when dividing by the height factor, we only want to reduce
    3076             :    terms related to the bound on j (the roots of Phi_l(X,y)), not terms arising
    3077             :    from binomial coefficients. These arise in lemmas 2 and 3 of the height
    3078             :    bound paper, terms of (log 2)*L and 2.085*(L+1) which we convert here to
    3079             :    binary logs */
    3080             :     /* Massive overestimate: if you care about speed, determine a good height
    3081             :      * bound empirically as done for INV_F below */
    3082        1669 :     nbits2 = nbits - 4.01*L -3.0;
    3083        1669 :     nbits = nbits2/hf + 4.01*L + 3.0;
    3084             :   }
    3085        2959 :   if (inv == INV_F) {
    3086         149 :     if (L < 30) c = 45;
    3087          35 :     else if (L < 100) c = 36;
    3088          21 :     else if (L < 300) c = 32;
    3089           7 :     else if (L < 600) c = 26;
    3090           0 :     else if (L < 1200) c = 24;
    3091           0 :     else if (L < 2400) c = 22;
    3092           0 :     else c = 20;
    3093         149 :     nbits = (6.0*L*log2(L) + c*L)/hf;
    3094             :   }
    3095        2959 :   return nbits;
    3096             : }
    3097             : 
    3098             : /* small enough to write the factorization of a smooth in a BIL bit integer */
    3099             : #define SMOOTH_PRIMES  ((BITS_IN_LONG >> 1) - 1)
    3100             : 
    3101             : #define MAX_ATKIN 255
    3102             : 
    3103             : /* Must have primes at least up to MAX_ATKIN */
    3104             : static const long PRIMES[] = {
    3105             :     0,   2,   3,   5,   7,  11,  13,  17,  19,  23,
    3106             :    29,  31,  37,  41,  43,  47,  53,  59,  61,  67,
    3107             :    71,  73,  79,  83,  89,  97, 101, 103, 107, 109,
    3108             :   113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
    3109             :   173, 179, 181, 191, 193, 197, 199, 211, 223, 227,
    3110             :   229, 233, 239, 241, 251, 257, 263, 269, 271, 277
    3111             : };
    3112             : 
    3113             : #define MAX_L1      255
    3114             : 
    3115             : typedef struct D_entry_struct {
    3116             :   ulong m;
    3117             :   long D, h;
    3118             : } D_entry;
    3119             : 
    3120             : /* Returns a form that generates the classes of norm p^2 in cl(p^2D)
    3121             :  * (i.e. one with order p-1), where p is an odd prime that splits in D
    3122             :  * and does not divide its conductor (but this is not verified) */
    3123             : INLINE GEN
    3124       73534 : qform_primeform2(long p, long D)
    3125             : {
    3126       73534 :   GEN a = sqru(p), Dp2 = mulis(a, D), M = Z_factor(utoipos(p - 1));
    3127       73534 :   pari_sp av = avma;
    3128             :   long k;
    3129             : 
    3130      149211 :   for (k = D & 1; k <= p; k += 2)
    3131             :   {
    3132      149211 :     long ord, c = (k * k - D) / 4;
    3133             :     GEN Q, q;
    3134             : 
    3135      149211 :     if (!(c % p)) continue;
    3136      128945 :     q = mkqfis(a, k * p, c, Dp2); Q = qfbred_i(q);
    3137             :     /* TODO: How do we know that Q has order dividing p - 1? If we don't, then
    3138             :      * the call to gen_order should be replaced with a call to something with
    3139             :      * fastorder semantics (i.e. return 0 if ord(Q) \ndiv M). */
    3140      128945 :     ord = itos(qfi_order(Q, M));
    3141      128945 :     if (ord == p - 1) {
    3142             :       /* TODO: This check that gen_order returned the correct result should be
    3143             :        * removed when gen_order is replaced with fastorder semantics. */
    3144       73534 :       if (qfb_equal1(gpowgs(Q, p - 1))) return q;
    3145           0 :       break;
    3146             :     }
    3147       55411 :     set_avma(av);
    3148             :   }
    3149           0 :   return NULL;
    3150             : }
    3151             : 
    3152             : /* Let n = #cl(D); return x such that [L0]^x = [L] in cl(D), or -1 if x was
    3153             :  * not found */
    3154             : INLINE long
    3155      197606 : primeform_discrete_log(long L0, long L, long n, long D)
    3156             : {
    3157      197606 :   pari_sp av = avma;
    3158      197606 :   GEN X, Q, R, DD = stoi(D);
    3159      197606 :   Q = primeform_u(DD, L0);
    3160      197606 :   R = primeform_u(DD, L);
    3161      197606 :   X = qfi_Shanks(R, Q, n);
    3162      197606 :   return gc_long(av, X? itos(X): -1);
    3163             : }
    3164             : 
    3165             : /* Return the norm of a class group generator appropriate for a discriminant
    3166             :  * that will be used to calculate the modular polynomial of level L and
    3167             :  * invariant inv.  Don't consider norms less than initial_L0 */
    3168             : static long
    3169        2959 : select_L0(long L, long inv, long initial_L0)
    3170             : {
    3171        2959 :   long L0, modinv_N = modinv_level(inv);
    3172             : 
    3173        2959 :   if (modinv_N % L == 0) pari_err_BUG("select_L0");
    3174             : 
    3175             :   /* TODO: Clean up these anomolous L0 choices */
    3176             : 
    3177             :   /* I've no idea why the discriminant-finding code fails with L0=5
    3178             :    * when L=19 and L=29, nor why L0=7 and L0=11 don't work for L=19
    3179             :    * either, nor why this happens for the otherwise unrelated
    3180             :    * invariants Weber-f and (2,3) double-eta. */
    3181        2959 :   if (inv == INV_W3W3E2 && L == 5) return 2;
    3182             : 
    3183        2945 :   if (inv == INV_F || inv == INV_F2 || inv == INV_F4 || inv == INV_F8
    3184        2684 :       || inv == INV_W2W3 || inv == INV_W2W3E2
    3185        2621 :       || inv == INV_W3W3 /* || inv == INV_W3W3E2 */) {
    3186         422 :     if (L == 19) return 13;
    3187         372 :     else if (L == 29 || L == 5) return 7;
    3188         309 :     return 5;
    3189             :   }
    3190        2523 :   if ((inv == INV_W2W5 || inv == INV_W2W5E2)
    3191         140 :       && (L == 7 || L == 19)) return 13;
    3192        2481 :   if ((inv == INV_W2W7 || inv == INV_W2W7E2)
    3193         358 :       && L == 11) return 13;
    3194        2453 :   if (inv == INV_W3W5) {
    3195          63 :     if (L == 7) return 13;
    3196          56 :     else if (L == 17) return 7;
    3197             :   }
    3198        2446 :   if (inv == INV_W3W7) {
    3199         140 :     if (L == 29 || L == 101) return 11;
    3200         112 :     if (L == 11 || L == 19) return 13;
    3201             :   }
    3202        2390 :   if (inv == INV_W5W7 && L == 17) return 3;
    3203             : 
    3204             :   /* L0 = smallest small prime different from L that doesn't divide modinv_N */
    3205        3343 :   for (L0 = unextprime(initial_L0 + 1);
    3206        3280 :        L0 == L || modinv_N % L0 == 0;
    3207         974 :        L0 = unextprime(L0 + 1))
    3208             :     ;
    3209        2369 :   return L0;
    3210             : }
    3211             : 
    3212             : /* Return the order of [L]^n in cl(D), where #cl(D) = ord. */
    3213             : INLINE long
    3214     1048955 : primeform_exp_order(long L, long n, long D, long ord)
    3215             : {
    3216     1048955 :   pari_sp av = avma;
    3217     1048955 :   GEN Q = gpowgs(primeform_u(stoi(D), L), n);
    3218     1048955 :   long m = itos(qfi_order(Q, Z_factor(stoi(ord))));
    3219     1048955 :   return gc_long(av,m);
    3220             : }
    3221             : 
    3222             : /* If an ideal of norm modinv_deg is equivalent to an ideal of norm L0, we
    3223             :  * have an orientation ambiguity that we need to avoid. Note that we need to
    3224             :  * check all the possibilities (up to 8), but we can cheaply check inverses
    3225             :  * (so at most 2) */
    3226             : static long
    3227       33902 : orientation_ambiguity(long D1, long L0, long modinv_p1, long modinv_p2, long modinv_N)
    3228             : {
    3229       33902 :   pari_sp av = avma;
    3230       33902 :   long ambiguity = 0;
    3231       33902 :   GEN D = stoi(D1), Q1 = primeform_u(D, modinv_p1), Q2 = NULL;
    3232             : 
    3233       33902 :   if (modinv_p2 > 1)
    3234             :   {
    3235       33902 :     if (modinv_p1 == modinv_p2) Q1 = gsqr(Q1);
    3236             :     else
    3237             :     {
    3238       27792 :       GEN P2 = primeform_u(D, modinv_p2);
    3239       27792 :       GEN Q = gsqr(P2), R = gsqr(Q1);
    3240             :       /* check that p1^2 != p2^{+/-2}, since this leads to
    3241             :        * ambiguities when converting j's to f's */
    3242       27792 :       if (equalii(gel(Q,1), gel(R,1)) && absequalii(gel(Q,2), gel(R,2)))
    3243             :       {
    3244           0 :         dbg_printf(3)("Bad D=%ld, a^2=b^2 problem between modinv_p1=%ld and modinv_p2=%ld\n",
    3245             :                       D1, modinv_p1, modinv_p2);
    3246           0 :         ambiguity = 1;
    3247             :       }
    3248             :       else
    3249             :       { /* generate both p1*p2 and p1*p2^{-1} */
    3250       27792 :         Q2 = gmul(Q1, P2);
    3251       27792 :         P2 = ginv(P2);
    3252       27792 :         Q1 = gmul(Q1, P2);
    3253             :       }
    3254             :     }
    3255             :   }
    3256       33902 :   if (!ambiguity)
    3257             :   {
    3258       33902 :     GEN P = gsqr(primeform_u(D, L0));
    3259       33902 :     if (equalii(gel(P,1), gel(Q1,1))
    3260       32872 :         || (modinv_p2 && modinv_p1 != modinv_p2
    3261       26776 :                       && equalii(gel(P,1), gel(Q2,1)))) {
    3262        1487 :       dbg_printf(3)("Bad D=%ld, a=b^{+/-2} problem between modinv_N=%ld and L0=%ld\n",
    3263             :                     D1, modinv_N, L0);
    3264        1487 :       ambiguity = 1;
    3265             :     }
    3266             :   }
    3267       33902 :   return gc_long(av, ambiguity);
    3268             : }
    3269             : 
    3270             : static long
    3271      761483 : check_generators(
    3272             :   long *n1_, long *m_,
    3273             :   long D, long h, long n, long subgrp_sz, long L0, long L1)
    3274             : {
    3275      761483 :   long n1, m = primeform_exp_order(L0, n, D, h);
    3276      761483 :   if (m_) *m_ = m;
    3277      761483 :   n1 = n * m;
    3278      761483 :   if (!n1) pari_err_BUG("check_generators");
    3279      761483 :   *n1_ = n1;
    3280      761483 :   if (n1 < subgrp_sz/2 || ( ! L1 && n1 < subgrp_sz))  {
    3281       27936 :     dbg_printf(3)("Bad D1=%ld with n1=%ld, h1=%ld, L1=%ld: "
    3282             :                   "L0 and L1 don't span subgroup of size d in cl(D1)\n",
    3283             :                   D, n, h, L1);
    3284       27936 :     return 0;
    3285             :   }
    3286      733547 :   if (n1 < subgrp_sz && ! (n1 & 1)) {
    3287             :     int res;
    3288             :     /* check whether L1 is generated by L0, use the fact that it has order 2 */
    3289       17515 :     pari_sp av = avma;
    3290       17515 :     GEN D1 = stoi(D);
    3291       17515 :     GEN Q = gpowgs(primeform_u(D1, L0), n1 / 2);
    3292       17515 :     res = gequal(Q, qfbred_i(primeform_u(D1, L1)));
    3293       17515 :     set_avma(av);
    3294       17515 :     if (res) {
    3295        5118 :       dbg_printf(3)("Bad D1=%ld, with n1=%ld, h1=%ld, L1=%ld: "
    3296             :                     "L1 generated by L0 in cl(D1)\n", D, n, h, L1);
    3297        5118 :       return 0;
    3298             :     }
    3299             :   }
    3300      728429 :   return 1;
    3301             : }
    3302             : 
    3303             : /* Calculate solutions (p, t) to the norm equation
    3304             :  *   4 p = t^2 - v^2 L^2 D   (*)
    3305             :  * corresponding to the descriminant described by Dinfo.
    3306             :  *
    3307             :  * INPUT:
    3308             :  * - max: length of primes and traces
    3309             :  * - xprimes: p to exclude from primes (if they arise)
    3310             :  * - xcnt: length of xprimes
    3311             :  * - minbits: sum of log2(p) must be larger than this
    3312             :  * - Dinfo: discriminant, invariant and L for which we seek solutions to (*)
    3313             :  *
    3314             :  * OUTPUT:
    3315             :  * - primes: array of p in (*)
    3316             :  * - traces: array of t in (*)
    3317             :  * - totbits: sum of log2(p) for p in primes.
    3318             :  *
    3319             :  * RETURN:
    3320             :  * - the number of primes and traces found (these are always the same).
    3321             :  *
    3322             :  * NOTE: primes and traces are both NULL or both non-NULL.
    3323             :  * xprimes can be zero, in which case it is treated as empty. */
    3324             : static long
    3325       11592 : modpoly_pickD_primes(
    3326             :   ulong *primes, ulong *traces, long max, ulong *xprimes, long xcnt,
    3327             :   long *totbits, long minbits, disc_info *Dinfo)
    3328             : {
    3329             :   double bits;
    3330             :   long D, m, n, vcnt, pfilter, one_prime, inv;
    3331             :   ulong maxp;
    3332             :   ulong a1, a2, v, t, p, a1_start, a1_delta, L0, L1, L, absD;
    3333       11592 :   ulong FF_BITS = BITS_IN_LONG - 2; /* BITS_IN_LONG - NAIL_BITS */
    3334             : 
    3335       11592 :   D = Dinfo->D1; absD = -D;
    3336       11592 :   L0 = Dinfo->L0;
    3337       11592 :   L1 = Dinfo->L1;
    3338       11592 :   L = Dinfo->L;
    3339       11592 :   inv = Dinfo->inv;
    3340             : 
    3341             :   /* make sure pfilter and D don't preclude the possibility of p=(t^2-v^2D)/4 being prime */
    3342       11592 :   pfilter = modinv_pfilter(inv);
    3343       11592 :   if ((pfilter & IQ_FILTER_1MOD3) && ! (D % 3)) return 0;
    3344       11543 :   if ((pfilter & IQ_FILTER_1MOD4) && ! (D & 0xF)) return 0;
    3345             : 
    3346             :   /* Naively estimate the number of primes satisfying 4p=t^2-L^2D with
    3347             :    * t=2 mod L and pfilter. This is roughly
    3348             :    * #{t: t^2 < max p and t=2 mod L} / pi(max p) * filter_density,
    3349             :    * where filter_density is 1, 2, or 4 depending on pfilter.  If this quantity
    3350             :    * is already more than twice the number of bits we need, assume that,
    3351             :    * barring some obstruction, we should have no problem getting enough primes.
    3352             :    * In this case we just verify we can get one prime (which should always be
    3353             :    * true, assuming we chose D properly). */
    3354       11543 :   one_prime = 0;
    3355       11543 :   *totbits = 0;
    3356       11543 :   if (max <= 1 && ! one_prime) {
    3357        8563 :     p = ((pfilter & IQ_FILTER_1MOD3) ? 2 : 1) * ((pfilter & IQ_FILTER_1MOD4) ? 2 : 1);
    3358        8563 :     one_prime = (1UL << ((FF_BITS+1)/2)) * (log2(L*L*(-D))-1)
    3359        8563 :         > p*L*minbits*FF_BITS*M_LN2;
    3360        8563 :     if (one_prime) *totbits = minbits+1;   /* lie */
    3361             :   }
    3362             : 
    3363       11543 :   m = n = 0;
    3364       11543 :   bits = 0.0;
    3365       11543 :   maxp = 0;
    3366       28781 :   for (v = 1; v < 100 && bits < minbits; v++) {
    3367             :     /* Don't allow v dividing the conductor. */
    3368       25748 :     if (ugcd(absD, v) != 1) continue;
    3369             :     /* Avoid v dividing the level. */
    3370       25550 :     if (v > 2 && modinv_is_double_eta(inv) && ugcd(modinv_level(inv), v) != 1)
    3371         966 :       continue;
    3372             :     /* can't get odd p with D=1 mod 8 unless v is even */
    3373       24584 :     if ((v & 1) && (D & 7) == 1) continue;
    3374             :     /* disallow 4 | v for L0=2 (removing this restriction is costly) */
    3375       12173 :     if (L0 == 2 && !(v & 3)) continue;
    3376             :     /* can't get p=3mod4 if v^2D is 0 mod 16 */
    3377       11923 :     if ((pfilter & IQ_FILTER_1MOD4) && !((v*v*D) & 0xF)) continue;
    3378       11840 :     if ((pfilter & IQ_FILTER_1MOD3) && !(v%3) ) continue;
    3379             :     /* avoid L0-volcanos with nonzero height */
    3380       11782 :     if (L0 != 2 && ! (v % L0)) continue;
    3381             :     /* ditto for L1 */
    3382       11761 :     if (L1 && !(v % L1)) continue;
    3383       11761 :     vcnt = 0;
    3384       11761 :     if ((v*v*absD)/4 > (1L<<FF_BITS)/(L*L)) break;
    3385       11679 :     if (both_odd(v,D)) {
    3386           0 :       a1_start = 1;
    3387           0 :       a1_delta = 2;
    3388             :     } else {
    3389       11679 :       a1_start = ((v*v*D) & 7)? 2: 0;
    3390       11679 :       a1_delta = 4;
    3391             :     }
    3392      558105 :     for (a1 = a1_start; bits < minbits; a1 += a1_delta) {
    3393      555086 :       a2 = (a1*a1 + v*v*absD) >> 2;
    3394      555086 :       if (!(a2 % L)) continue;
    3395      470870 :       t = a1*L + 2;
    3396      470870 :       p = a2*L*L + t - 1;
    3397             :       /* double check calculation just in case of overflow or other weirdness */
    3398      470870 :       if (!odd(p) || t*t + v*v*L*L*absD != 4*p)
    3399           0 :         pari_err_BUG("modpoly_pickD_primes");
    3400      470870 :       if (p > (1UL<<FF_BITS)) break;
    3401      470638 :       if (xprimes) {
    3402      351136 :         while (m < xcnt && xprimes[m] < p) m++;
    3403      350708 :         if (m < xcnt && p == xprimes[m]) {
    3404           0 :           dbg_printf(1)("skipping duplicate prime %ld\n", p);
    3405           0 :           continue;
    3406             :         }
    3407             :       }
    3408      470638 :       if (!modinv_good_prime(inv, p) || !uisprime(p)) continue;
    3409       51653 :       if (primes) {
    3410       38028 :         if (n >= max) goto done;
    3411             :         /* TODO: Implement test to filter primes that lead to
    3412             :          * L-valuation != 2 */
    3413       38028 :         primes[n] = p;
    3414       38028 :         traces[n] = t;
    3415             :       }
    3416       51653 :       n++;
    3417       51653 :       vcnt++;
    3418       51653 :       bits += log2(p);
    3419       51653 :       if (p > maxp) maxp = p;
    3420       51653 :       if (one_prime) goto done;
    3421             :     }
    3422        3251 :     if (vcnt)
    3423        3248 :       dbg_printf(3)("%ld primes with v=%ld, maxp=%ld (%.2f bits)\n",
    3424             :                  vcnt, v, maxp, log2(maxp));
    3425             :   }
    3426        3033 : done:
    3427       11543 :   if (!n) {
    3428           9 :     dbg_printf(3)("check_primes failed completely for D=%ld\n", D);
    3429           9 :     return 0;
    3430             :   }
    3431       11534 :   dbg_printf(3)("D=%ld: Found %ld primes totalling %0.2f of %ld bits\n",
    3432             :              D, n, bits, minbits);
    3433       11534 :   if (!*totbits) *totbits = (long)bits;
    3434       11534 :   return n;
    3435             : }
    3436             : 
    3437             : #define MAX_VOLCANO_FLOOR_SIZE 100000000
    3438             : 
    3439             : static long
    3440        2961 : calc_primes_for_discriminants(disc_info Ds[], long Dcnt, long L, long minbits)
    3441             : {
    3442        2961 :   pari_sp av = avma;
    3443             :   long i, j, k, m, n, D1, pcnt, totbits;
    3444             :   ulong *primes, *Dprimes, *Dtraces;
    3445             : 
    3446             :   /* D1 is the discriminant with smallest absolute value among those we found */
    3447        2961 :   D1 = Ds[0].D1;
    3448        8554 :   for (i = 1; i < Dcnt; i++)
    3449        5593 :     if (Ds[i].D1 > D1) D1 = Ds[i].D1;
    3450             : 
    3451             :   /* n is an upper bound on the number of primes we might get. */
    3452        2961 :   n = ceil(minbits / (log2(L * L * (-D1)) - 2)) + 1;
    3453        2961 :   primes = (ulong *) stack_malloc(n * sizeof(*primes));
    3454        2961 :   Dprimes = (ulong *) stack_malloc(n * sizeof(*Dprimes));
    3455        2961 :   Dtraces = (ulong *) stack_malloc(n * sizeof(*Dtraces));
    3456        2980 :   for (i = 0, totbits = 0, pcnt = 0; i < Dcnt && totbits < minbits; i++)
    3457             :   {
    3458        2980 :     long np = modpoly_pickD_primes(Dprimes, Dtraces, n, primes, pcnt,
    3459        2980 :                                    &Ds[i].bits, minbits - totbits, Ds + i);
    3460        2980 :     ulong *T = (ulong *)newblock(2*np);
    3461        2980 :     Ds[i].nprimes = np;
    3462        2980 :     Ds[i].primes = T;    memcpy(T   , Dprimes, np * sizeof(*Dprimes));
    3463        2980 :     Ds[i].traces = T+np; memcpy(T+np, Dtraces, np * sizeof(*Dtraces));
    3464             : 
    3465        2980 :     totbits += Ds[i].bits;
    3466        2980 :     pcnt += np;
    3467             : 
    3468        2980 :     if (totbits >= minbits || i == Dcnt - 1) { Dcnt = i + 1; break; }
    3469             :     /* merge lists */
    3470         599 :     for (j = pcnt - np - 1, k = np - 1, m = pcnt - 1; m >= 0; m--) {
    3471         580 :       if (k >= 0) {
    3472         555 :         if (j >= 0 && primes[j] > Dprimes[k])
    3473         301 :           primes[m] = primes[j--];
    3474             :         else
    3475         254 :           primes[m] = Dprimes[k--];
    3476             :       } else {
    3477          25 :         primes[m] = primes[j--];
    3478             :       }
    3479             :     }
    3480             :   }
    3481        2961 :   if (totbits < minbits) {
    3482           2 :     dbg_printf(1)("Only obtained %ld of %ld bits using %ld discriminants\n",
    3483             :                   totbits, minbits, Dcnt);
    3484           4 :     for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
    3485           2 :     Dcnt = 0;
    3486             :   }
    3487        2961 :   return gc_long(av, Dcnt);
    3488             : }
    3489             : 
    3490             : /* Select discriminant(s) to use when calculating the modular
    3491             :  * polynomial of level L and invariant inv.
    3492             :  *
    3493             :  * INPUT:
    3494             :  * - L: level of modular polynomial (must be odd)
    3495             :  * - inv: invariant of modular polynomial
    3496             :  * - L0: result of select_L0(L, inv)
    3497             :  * - minbits: height of modular polynomial
    3498             :  * - flags: see below
    3499             :  * - tab: result of scanD0(L0)
    3500             :  * - tablen: length of tab
    3501             :  *
    3502             :  * OUTPUT:
    3503             :  * - Ds: the selected discriminant(s)
    3504             :  *
    3505             :  * RETURN:
    3506             :  * - the number of Ds found
    3507             :  *
    3508             :  * The flags parameter is constructed by ORing zero or more of the
    3509             :  * following values:
    3510             :  * - MODPOLY_USE_L1: force use of second class group generator
    3511             :  * - MODPOLY_NO_AUX_L: don't use auxillary class group elements
    3512             :  * - MODPOLY_IGNORE_SPARSE_FACTOR: obtain D for which h(D) > L + 1
    3513             :  *   rather than h(D) > (L + 1)/s */
    3514             : static long
    3515        2961 : modpoly_pickD(disc_info Ds[MODPOLY_MAX_DCNT], long L, long inv,
    3516             :   long L0, long max_L1, long minbits, long flags, D_entry *tab, long tablen)
    3517             : {
    3518        2961 :   pari_sp ltop = avma, btop;
    3519             :   disc_info Dinfo;
    3520             :   pari_timer T;
    3521             :   long modinv_p1, modinv_p2; /* const after next line */
    3522        2961 :   const long modinv_deg = modinv_degree(&modinv_p1, &modinv_p2, inv);
    3523        2961 :   const long pfilter = modinv_pfilter(inv), modinv_N = modinv_level(inv);
    3524             :   long i, k, use_L1, Dcnt, D0_i, d, cost, enum_cost, best_cost, totbits;
    3525        2961 :   const double L_bits = log2(L);
    3526             : 
    3527        2961 :   if (!odd(L)) pari_err_BUG("modpoly_pickD");
    3528             : 
    3529        2961 :   timer_start(&T);
    3530        2961 :   if (flags & MODPOLY_IGNORE_SPARSE_FACTOR) d = L+2;
    3531        2814 :   else d = ceildivuu(L+1, modinv_sparse_factor(inv)) + 1;
    3532             : 
    3533             :   /* Now set level to 0 unless we will need to compute N-isogenies */
    3534        2961 :   dbg_printf(1)("Using L0=%ld for L=%ld, d=%ld, modinv_N=%ld, modinv_deg=%ld\n",
    3535             :                 L0, L, d, modinv_N, modinv_deg);
    3536             : 
    3537             :   /* We use L1 if (L0|L) == 1 or if we are forced to by flags. */
    3538        2961 :   use_L1 = (kross(L0,L) > 0 || (flags & MODPOLY_USE_L1));
    3539             : 
    3540        2961 :   Dcnt = best_cost = totbits = 0;
    3541        2961 :   dbg_printf(3)("use_L1=%ld\n", use_L1);
    3542        2961 :   dbg_printf(3)("minbits = %ld\n", minbits);
    3543             : 
    3544             :   /* Iterate over the fundamental discriminants for L0 */
    3545     1822173 :   for (D0_i = 0; D0_i < tablen; D0_i++)
    3546             :   {
    3547     1819212 :     D_entry D0_entry = tab[D0_i];
    3548     1819212 :     long m, n0, h0, deg, L1, H_cost, twofactor, D0 = D0_entry.D;
    3549             :     double D0_bits;
    3550     2809597 :     if (! modinv_good_disc(inv, D0)) continue;
    3551     1197068 :     dbg_printf(3)("D0=%ld\n", D0);
    3552             :     /* don't allow either modinv_p1 or modinv_p2 to ramify */
    3553     1197068 :     if (kross(D0, L) < 1
    3554      541281 :         || (modinv_p1 > 1 && kross(D0, modinv_p1) < 1)
    3555      536372 :         || (modinv_p2 > 1 && kross(D0, modinv_p2) < 1)) {
    3556      671100 :       dbg_printf(3)("Bad D0=%ld due to nonsplit L or ramified level\n", D0);
    3557      671100 :       continue;
    3558             :     }
    3559      525968 :     deg = D0_entry.h; /* class poly degree */
    3560      525968 :     h0 = ((D0_entry.m & 2) ? 2*deg : deg); /* class number */
    3561             :     /* (D0_entry.m & 1) is 1 if ord(L0) < h0 (hence = h0/2),
    3562             :      *                  is 0 if ord(L0) = h0 */
    3563      525968 :     n0 = h0 / ((D0_entry.m & 1) + 1); /* = ord(L0) */
    3564             : 
    3565             :     /* Look for L1: for each smooth prime p */
    3566      525968 :     L1 = 0;
    3567    12850616 :     for (i = 1 ; i <= SMOOTH_PRIMES; i++)
    3568             :     {
    3569    12429716 :       long p = PRIMES[i];
    3570    12429716 :       if (p <= L0) continue;
    3571             :       /* If 1 + (D0 | p) = 1, i.e. p | D0 */
    3572    11723509 :       if (((D0_entry.m >> (2*i)) & 3) == 1) {
    3573             :         /* XXX: Why (p | L) = -1?  Presumably so (L^2 v^2 D0 | p) = -1? */
    3574      379244 :         if (p <= max_L1 && modinv_N % p && kross(p,L) < 0) { L1 = p; break; }
    3575             :       }
    3576             :     }
    3577      525968 :     if (i > SMOOTH_PRIMES && (n0 < h0 || use_L1))
    3578             :     { /* Didn't find suitable L1 though we need one */
    3579      238496 :       dbg_printf(3)("Bad D0=%ld because there is no good L1\n", D0);
    3580      238496 :       continue;
    3581             :     }
    3582      287472 :     dbg_printf(3)("Good D0=%ld with L1=%ld, n0=%ld, h0=%ld, d=%ld\n",
    3583             :                   D0, L1, n0, h0, d);
    3584             : 
    3585             :     /* We're finished if we have sufficiently many discriminants that satisfy
    3586             :      * the cost requirement */
    3587      287472 :     if (totbits > minbits && best_cost && h0*(L-1) > 3*best_cost) break;
    3588             : 
    3589      287472 :     D0_bits = log2(-D0);
    3590             :     /* If L^2 D0 is too big to fit in a BIL bit integer, skip D0. */
    3591      287472 :     if (D0_bits + 2 * L_bits > (BITS_IN_LONG - 1)) continue;
    3592             : 
    3593             :     /* m is the order of L0^n0 in L^2 D0? */
    3594      287472 :     m = primeform_exp_order(L0, n0, L * L * D0, n0 * (L-1));
    3595      287472 :     if (m < (L-1)/2) {
    3596       80789 :       dbg_printf(3)("Bad D0=%ld because %ld is less than (L-1)/2=%ld\n",
    3597           0 :                     D0, m, (L - 1)/2);
    3598       80789 :       continue;
    3599             :     }
    3600             :     /* Heuristic.  Doesn't end up contributing much. */
    3601      206683 :     H_cost = 2 * deg * deg;
    3602             : 
    3603             :     /* 0xc = 0b1100, so D0_entry.m & 0xc == 1 + (D0 | 2) */
    3604      206683 :     if ((D0 & 7) == 5) /* D0 = 5 (mod 8) */
    3605        5820 :       twofactor = ((D0_entry.m & 0xc) ? 1 : 3);
    3606             :     else
    3607      200863 :       twofactor = 0;
    3608             : 
    3609      206683 :     btop = avma;
    3610             :     /* For each small prime... */
    3611      718859 :     for (i = 0; i <= SMOOTH_PRIMES; i++) {
    3612             :       long h1, h2, D1, D2, n1, n2, dl1, dl20, dl21, p, q, j;
    3613             :       double p_bits;
    3614      718754 :       set_avma(btop);
    3615             :       /* i = 0 corresponds to 1, which we do not want to skip! (i.e. DK = D) */
    3616      718754 :       if (i) {
    3617     1014218 :         if (modinv_odd_conductor(inv) && i == 1) continue;
    3618      502575 :         p = PRIMES[i];
    3619             :         /* Don't allow large factors in the conductor. */
    3620      615330 :         if (p > max_L1) break;
    3621      408752 :         if (p == L0 || p == L1 || p == L || p == modinv_p1 || p == modinv_p2)
    3622      139311 :           continue;
    3623      269441 :         p_bits = log2(p);
    3624             :         /* h1 is the class number of D1 = q^2 D0, where q = p^j (j defined in the loop below) */
    3625      269441 :         h1 = h0 * (p - ((D0_entry.m >> (2*i)) & 0x3) + 1);
    3626             :         /* q is the smallest power of p such that h1 >= d ~ "L + 1". */
    3627      272116 :         for (j = 1, q = p; h1 < d; j++, q *= p, h1 *= p)
    3628             :           ;
    3629      269441 :         D1 = q * q * D0;
    3630             :         /* can't have D1 = 0 mod 16 and hope to get any primes congruent to 3 mod 4 */
    3631      269441 :         if ((pfilter & IQ_FILTER_1MOD4) && !(D1 & 0xF)) continue;
    3632             :       } else {
    3633             :         /* i = 0, corresponds to "p = 1". */
    3634      206683 :         h1 = h0;
    3635      206683 :         D1 = D0;
    3636      206683 :         p = q = j = 1;
    3637      206683 :         p_bits = 0;
    3638             :       }
    3639             :       /* include a factor of 4 if D1 is 5 mod 8 */
    3640             :       /* XXX: No idea why he does this. */
    3641      476054 :       if (twofactor && (q & 1)) {
    3642       14550 :         if (modinv_odd_conductor(inv)) continue;
    3643         518 :         D1 *= 4;
    3644         518 :         h1 *= twofactor;
    3645             :       }
    3646             :       /* heuristic early abort; we may miss good D1's, but this saves time */
    3647      462022 :       if (totbits > minbits && best_cost && h1*(L-1) > 2.2*best_cost) continue;
    3648             : 
    3649             :       /* log2(D0 * (p^j)^2 * L^2 * twofactor) > (BIL - 1) -- params too big. */
    3650      902496 :       if (D0_bits + 2*j*p_bits + 2*L_bits
    3651      451248 :           + (twofactor && (q & 1) ? 2.0 : 0.0) > (BITS_IN_LONG-1)) continue;
    3652             : 
    3653      449556 :       if (! check_generators(&n1, NULL, D1, h1, n0, d, L0, L1)) continue;
    3654             : 
    3655      432021 :       if (n1 >= h1) dl1 = -1; /* fill it in later */
    3656      194673 :       else if ((dl1 = primeform_discrete_log(L0, L, n1, D1)) < 0) continue;
    3657      313414 :       dbg_printf(3)("Good D0=%ld, D1=%ld with q=%ld, L1=%ld, n1=%ld, h1=%ld\n",
    3658             :                     D0, D1, q, L1, n1, h1);
    3659      313414 :       if (modinv_deg && orientation_ambiguity(D1, L0, modinv_p1, modinv_p2, modinv_N))
    3660        1487 :         continue;
    3661             : 
    3662      311927 :       D2 = L * L * D1;
    3663      311927 :       h2 = h1 * (L-1);
    3664             :       /* m is the order of L0^n1 in cl(D2) */
    3665      311927 :       if (!check_generators(&n2, &m, D2, h2, n1, d*(L-1), L0, L1)) continue;
    3666             : 
    3667             :       /* This restriction on m is not necessary, but simplifies life later */
    3668      296408 :       if (m < (L-1)/2 || (!L1 && m < L-1)) {
    3669      145871 :         dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
    3670             :                       "order of L0^n1 in cl(D2) is too small\n", D2, D1, D0, n2, h2, L1);
    3671      145871 :         continue;
    3672             :       }
    3673      150537 :       dl20 = n1;
    3674      150537 :       dl21 = 0;
    3675      150537 :       if (m < L-1) {
    3676       73534 :         GEN Q1 = qform_primeform2(L, D1), Q2, X;
    3677       73534 :         if (!Q1) pari_err_BUG("modpoly_pickD");
    3678       73534 :         Q2 = primeform_u(stoi(D2), L1);
    3679       73534 :         Q2 = qfbcomp(Q1, Q2); /* we know this element has order L-1 */
    3680       73534 :         Q1 = primeform_u(stoi(D2), L0);
    3681       73534 :         k = ((n2 & 1) ? 2*n2 : n2)/(L-1);
    3682       73534 :         Q1 = gpowgs(Q1, k);
    3683       73534 :         X = qfi_Shanks(Q2, Q1, L-1);
    3684       73534 :         if (!X) {
    3685       11488 :           dbg_printf(3)("Bad D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
    3686             :               "form of norm L^2 not generated by L0 and L1\n",
    3687             :               D2, D1, D0, n2, h2, L1);
    3688       11488 :           continue;
    3689             :         }
    3690       62046 :         dl20 = itos(X) * k;
    3691       62046 :         dl21 = 1;
    3692             :       }
    3693      139049 :       if (! (m < L-1 || n2 < d*(L-1)) && n1 >= d && ! use_L1)
    3694       76511 :         L1 = 0;  /* we don't need L1 */
    3695             : 
    3696      139049 :       if (!L1 && use_L1) {
    3697           0 :         dbg_printf(3)("not using D2=%ld for D1=%ld, D0=%ld, with n2=%ld, h2=%ld, L1=%ld, "
    3698             :                    "because we don't need L1 but must use it\n",
    3699             :                    D2, D1, D0, n2, h2, L1);
    3700           0 :         continue;
    3701             :       }
    3702             :       /* don't allow zero dl21 with L1 for the moment, since
    3703             :        * modpoly doesn't handle it - we may change this in the future */
    3704      139049 :       if (L1 && ! dl21) continue;
    3705      138557 :       dbg_printf(3)("Good D0=%ld, D1=%ld, D2=%ld with s=%ld^%ld, L1=%ld, dl2=%ld, n2=%ld, h2=%ld\n",
    3706             :                  D0, D1, D2, p, j, L1, dl20, n2, h2);
    3707             : 
    3708             :       /* This estimate is heuristic and fiddling with the
    3709             :        * parameters 5 and 0.25 can change things quite a bit. */
    3710      138557 :       enum_cost = n2 * (5 * L0 * L0 + 0.25 * L1 * L1);
    3711      138557 :       cost = enum_cost + H_cost;
    3712      138557 :       if (best_cost && cost > 2.2*best_cost) break;
    3713       33823 :       if (best_cost && cost >= 0.99*best_cost) continue;
    3714             : 
    3715        8612 :       Dinfo.GENcode0 = evaltyp(t_VECSMALL)|_evallg(13);
    3716        8612 :       Dinfo.inv = inv;
    3717        8612 :       Dinfo.L = L;
    3718        8612 :       Dinfo.D0 = D0;
    3719        8612 :       Dinfo.D1 = D1;
    3720        8612 :       Dinfo.L0 = L0;
    3721        8612 :       Dinfo.L1 = L1;
    3722        8612 :       Dinfo.n1 = n1;
    3723        8612 :       Dinfo.n2 = n2;
    3724        8612 :       Dinfo.dl1 = dl1;
    3725        8612 :       Dinfo.dl2_0 = dl20;
    3726        8612 :       Dinfo.dl2_1 = dl21;
    3727        8612 :       Dinfo.cost = cost;
    3728             : 
    3729        8612 :       if (!modpoly_pickD_primes(NULL, NULL, 0, NULL, 0, &Dinfo.bits, minbits, &Dinfo))
    3730          58 :         continue;
    3731        8554 :       dbg_printf(2)("Best D2=%ld, D1=%ld, D0=%ld with s=%ld^%ld, L1=%ld, "
    3732             :                  "n1=%ld, n2=%ld, cost ratio %.2f, bits=%ld\n",
    3733             :                  D2, D1, D0, p, j, L1, n1, n2,
    3734           0 :                  (double)cost/(d*(L-1)), Dinfo.bits);
    3735             :       /* Insert Dinfo into the Ds array.  Ds is sorted by ascending cost. */
    3736       45860 :       for (j = 0; j < Dcnt; j++)
    3737       42888 :         if (Dinfo.cost < Ds[j].cost) break;
    3738        8554 :       if (n2 > MAX_VOLCANO_FLOOR_SIZE && n2*(L1 ? 2 : 1) > 1.2* (d*(L-1)) ) {
    3739           0 :         dbg_printf(3)("Not using D1=%ld, D2=%ld for space reasons\n", D1, D2);
    3740           0 :         continue;
    3741             :       }
    3742        8554 :       if (j == Dcnt && Dcnt == MODPOLY_MAX_DCNT)
    3743           0 :         continue;
    3744        8554 :       totbits += Dinfo.bits;
    3745        8554 :       if (Dcnt == MODPOLY_MAX_DCNT) totbits -= Ds[Dcnt-1].bits;
    3746        8554 :       if (Dcnt < MODPOLY_MAX_DCNT) Dcnt++;
    3747        8554 :       if (n2 > MAX_VOLCANO_FLOOR_SIZE)
    3748           0 :         dbg_printf(3)("totbits=%ld, minbits=%ld\n", totbits, minbits);
    3749       18995 :       for (k = Dcnt-1; k > j; k--) Ds[k] = Ds[k-1];
    3750        8554 :       Ds[k] = Dinfo;
    3751        8554 :       best_cost = (totbits > minbits)? Ds[Dcnt-1].cost: 0;
    3752             :       /* if we were able to use D1 with s = 1, there is no point in
    3753             :        * using any larger D1 for the same D0 */
    3754        8554 :       if (!i) break;
    3755             :     } /* END FOR over small primes */
    3756             :   } /* END WHILE over D0's */
    3757        2961 :   dbg_printf(2)("  checked %ld of %ld fundamental discriminants to find suitable "
    3758             :                 "discriminant (Dcnt = %ld)\n", D0_i, tablen, Dcnt);
    3759        2961 :   if ( ! Dcnt) {
    3760           0 :     dbg_printf(1)("failed completely for L=%ld\n", L);
    3761           0 :     return 0;
    3762             :   }
    3763             : 
    3764        2961 :   Dcnt = calc_primes_for_discriminants(Ds, Dcnt, L, minbits);
    3765             : 
    3766             :   /* fill in any missing dl1's */
    3767        5939 :   for (i = 0 ; i < Dcnt; i++)
    3768        2978 :     if (Ds[i].dl1 < 0 &&
    3769        2933 :        (Ds[i].dl1 = primeform_discrete_log(L0, L, Ds[i].n1, Ds[i].D1)) < 0)
    3770           0 :         pari_err_BUG("modpoly_pickD");
    3771        2961 :   if (DEBUGLEVEL > 1+3) {
    3772           0 :     err_printf("Selected %ld discriminants using %ld msecs\n", Dcnt, timer_delay(&T));
    3773           0 :     for (i = 0 ; i < Dcnt ; i++)
    3774             :     {
    3775           0 :       GEN H = classno(stoi(Ds[i].D0));
    3776           0 :       long h0 = itos(H);
    3777           0 :       err_printf ("    D0=%ld, h(D0)=%ld, D=%ld, L0=%ld, L1=%ld, "
    3778             :           "cost ratio=%.2f, enum ratio=%.2f,",
    3779           0 :           Ds[i].D0, h0, Ds[i].D1, Ds[i].L0, Ds[i].L1,
    3780           0 :           (double)Ds[i].cost/(d*(L-1)),
    3781           0 :           (double)(Ds[i].n2*(Ds[i].L1 ? 2 : 1))/(d*(L-1)));
    3782           0 :       err_printf (" %ld primes, %ld bits\n", Ds[i].nprimes, Ds[i].bits);
    3783             :     }
    3784             :   }
    3785        2961 :   return gc_long(ltop, Dcnt);
    3786             : }
    3787             : 
    3788             : static int
    3789    14196534 : _qsort_cmp(const void *a, const void *b)
    3790             : {
    3791    14196534 :   D_entry *x = (D_entry *)a, *y = (D_entry *)b;
    3792             :   long u, v;
    3793             : 
    3794             :   /* u and v are the class numbers of x and y */
    3795    14196534 :   u = x->h * (!!(x->m & 2) + 1);
    3796    14196534 :   v = y->h * (!!(y->m & 2) + 1);
    3797             :   /* Sort by class number */
    3798    14196534 :   if (u < v) return -1;
    3799     9876825 :   if (u > v) return 1;
    3800             :   /* Sort by discriminant (which is < 0, hence the sign reversal) */
    3801     2964072 :   if (x->D > y->D) return -1;
    3802           0 :   if (x->D < y->D) return 1;
    3803           0 :   return 0;
    3804             : }
    3805             : 
    3806             : /* Build a table containing fundamental D, |D| <= maxD whose class groups
    3807             :  * - are cyclic generated by an element of norm L0
    3808             :  * - have class number at most maxh
    3809             :  * The table is ordered using _qsort_cmp above, which ranks the discriminants
    3810             :  * by class number, then by absolute discriminant.
    3811             :  *
    3812             :  * INPUT:
    3813             :  * - maxd: largest allowed discriminant
    3814             :  * - maxh: largest allowed class number
    3815             :  * - L0: norm of class group generator (2, 3, 5, or 7)
    3816             :  *
    3817             :  * OUTPUT:
    3818             :  * - tablelen: length of return value
    3819             :  *
    3820             :  * RETURN:
    3821             :  * - array of {D, h(D), kronecker symbols for small p} */
    3822             : static D_entry *
    3823        2961 : scanD0(long *tablelen, long *minD, long maxD, long maxh, long L0)
    3824             : {
    3825             :   pari_sp av;
    3826             :   D_entry *tab;
    3827             :   long i, lF, cnt;
    3828             :   GEN F;
    3829             : 
    3830             :   /* NB: As seen in the loop below, the real class number of D can be */
    3831             :   /* 2*maxh if cl(D) is cyclic. */
    3832        2961 :   tab = (D_entry *) stack_malloc((maxD/4)*sizeof(*tab)); /* Overestimate */
    3833        2961 :   F = vecfactorsquarefreeu_coprime(*minD, maxD, mkvecsmall(2));
    3834        2961 :   lF = lg(F);
    3835    29595195 :   for (av = avma, cnt = 0, i = 1; i < lF; i++, set_avma(av))
    3836             :   {
    3837    29592234 :     GEN DD, ordL, f, q = gel(F,i);
    3838             :     long j, k, n, h, L1, d, D;
    3839             :     ulong m;
    3840             : 
    3841    29592234 :     if (!q) continue; /* not square-free */
    3842             :     /* restrict to possibly cyclic class groups */
    3843    12000917 :     k = lg(q) - 1; if (k > 2) continue;
    3844     9350358 :     d = i + *minD - 1; /* q = prime divisors of d */
    3845     9350358 :     if ((d & 3) == 1) continue;
    3846     4704775 :     D = -d; /* d = 3 (mod 4), D = 1 mod 4 fundamental */
    3847     4704775 :     if (kross(D, L0) < 1) continue;
    3848             : 
    3849             :     /* L1 initially the first factor of d if small enough, otherwise ignored */
    3850     2258780 :     L1 = (k > 1 && q[1] <= MAX_L1)? q[1]: 0;
    3851             : 
    3852             :     /* Check if h(D) is too big */
    3853     2258780 :     h = hclassno6u(d) / 6;
    3854     2258780 :     if (h > 2*maxh || (!L1 && h > maxh)) continue;
    3855             : 
    3856             :     /* Check if ord(f) is not big enough to generate at least half the
    3857             :      * class group (where f is the L0-primeform). */
    3858     2119527 :     DD = stoi(D);
    3859     2119527 :     f = primeform_u(DD, L0);
    3860     2119527 :     ordL = qfi_order(qfbred_i(f), stoi(h));
    3861     2119527 :     n = itos(ordL);
    3862     2119527 :     if (n < h/2 || (!L1 && n < h)) continue;
    3863             : 
    3864             :     /* If f is big enough, great! Otherwise, for each potential L1,
    3865             :      * do a discrete log to see if it is NOT in the subgroup generated
    3866             :      * by L0; stop as soon as such is found. */
    3867     1819212 :     for (j = 1;; j++) {
    3868     2056818 :       if (n == h || (L1 && !qfi_Shanks(primeform_u(DD, L1), f, n))) {
    3869     1725885 :         dbg_printf(2)("D0=%ld good with L1=%ld\n", D, L1);
    3870     1725885 :         break;
    3871             :       }
    3872      330933 :       if (!L1) break;
    3873      237606 :       L1 = (j <= k && k > 1 && q[j] <= MAX_L1 ? q[j] : 0);
    3874             :     }
    3875             :     /* The first bit of m is set iff f generates a proper subgroup of cl(D)
    3876             :      * (hence implying that we need L1). */
    3877     1819212 :     m = (n < h ? 1 : 0);
    3878             :     /* bits j and j+1 give the 2-bit number 1 + (D|p) where p = prime(j) */
    3879    54129024 :     for (j = 1 ; j <= SMOOTH_PRIMES; j++)
    3880             :     {
    3881    52309812 :       ulong x = (ulong) (1 + kross(D, PRIMES[j]));
    3882    52309812 :       m |= x << (2*j);
    3883             :     }
    3884             : 
    3885             :     /* Insert d, h and m into the table */
    3886     1819212 :     tab[cnt].D = D;
    3887     1819212 :     tab[cnt].h = h;
    3888     1819212 :     tab[cnt].m = m; cnt++;
    3889             :   }
    3890             : 
    3891             :   /* Sort the table */
    3892        2961 :   qsort(tab, cnt, sizeof(*tab), _qsort_cmp);
    3893        2961 :   *tablelen = cnt;
    3894        2961 :   *minD = maxD + 3 - (maxD & 3); /* smallest d >= maxD, d = 3 (mod 4) */
    3895        2961 :   return tab;
    3896             : }
    3897             : 
    3898             : /* Populate Ds with discriminants (and attached data) that can be
    3899             :  * used to calculate the modular polynomial of level L and invariant
    3900             :  * inv.  Return the number of discriminants found. */
    3901             : static long
    3902        2959 : discriminant_with_classno_at_least(disc_info bestD[MODPOLY_MAX_DCNT],
    3903             :   long L, long inv, GEN Q, long ignore_sparse)
    3904             : {
    3905             :   enum { SMALL_L_BOUND = 101 };
    3906        2959 :   long max_max_D = 160000 * (inv ? 2 : 1);
    3907             :   long minD, maxD, maxh, L0, max_L1, minbits, Dcnt, flags, s, d, i, tablen;
    3908             :   D_entry *tab;
    3909        2959 :   double eps, cost, best_eps = -1.0, best_cost = -1.0;
    3910             :   disc_info Ds[MODPOLY_MAX_DCNT];
    3911        2959 :   long best_cnt = 0;
    3912             :   pari_timer T;
    3913        2959 :   timer_start(&T);
    3914             : 
    3915        2959 :   s = modinv_sparse_factor(inv);
    3916        2959 :   d = ceildivuu(L+1, s) + 1;
    3917             : 
    3918             :   /* maxD of 10000 allows us to get a satisfactory discriminant in
    3919             :    * under 250ms in most cases. */
    3920        2959 :   maxD = 10000;
    3921             :   /* Allow the class number to overshoot L by 50%.  Must be at least
    3922             :    * 1.1*L, and higher values don't seem to provide much benefit,
    3923             :    * except when L is small, in which case it's necessary to get any
    3924             :    * discriminant at all in some cases. */
    3925        2959 :   maxh = (L / s < SMALL_L_BOUND) ? 10 * L : 1.5 * L;
    3926             : 
    3927        2959 :   flags = ignore_sparse ? MODPOLY_IGNORE_SPARSE_FACTOR : 0;
    3928        2959 :   L0 = select_L0(L, inv, 0);
    3929        2959 :   max_L1 = L / 2 + 2;    /* for L=11 we need L1=7 for j */
    3930        2959 :   minbits = modpoly_height_bound(L, inv);
    3931        2959 :   if (Q) minbits += expi(Q);
    3932        2959 :   minD = 7;
    3933             : 
    3934        5918 :   while ( ! best_cnt) {
    3935        2961 :     while (maxD <= max_max_D) {
    3936             :       /* TODO: Find a way to re-use tab when we need multiple modpolys */
    3937        2961 :       tab = scanD0(&tablen, &minD, maxD, maxh, L0);
    3938        2961 :       dbg_printf(1)("Found %ld potential fundamental discriminants\n", tablen);
    3939             : 
    3940        2961 :       Dcnt = modpoly_pickD(Ds, L, inv, L0, max_L1, minbits, flags, tab, tablen);
    3941        2961 :       eps = 0.0;
    3942        2961 :       cost = 0.0;
    3943             : 
    3944        2961 :       if (Dcnt) {
    3945        2959 :         long n1 = 0;
    3946        5937 :         for (i = 0; i < Dcnt; i++) {
    3947        2978 :           n1 = maxss(n1, Ds[i].n1);
    3948        2978 :           cost += Ds[i].cost;
    3949             :         }
    3950        2959 :         eps = (n1 * s - L) / (double)L;
    3951             : 
    3952        2959 :         if (best_cost < 0.0 || cost < best_cost) {
    3953        2959 :           if (best_cnt)
    3954           0 :             for (i = 0; i < best_cnt; i++) killblock((GEN)bestD[i].primes);
    3955        2959 :           (void) memcpy(bestD, Ds, Dcnt * sizeof(disc_info));
    3956        2959 :           best_cost = cost;
    3957        2959 :           best_cnt = Dcnt;
    3958        2959 :           best_eps = eps;
    3959             :           /* We're satisfied if n1 is within 5% of L. */
    3960        2959 :           if (L / s <= SMALL_L_BOUND || eps < 0.05) break;
    3961             :         } else {
    3962           0 :           for (i = 0; i < Dcnt; i++) killblock((GEN)Ds[i].primes);
    3963             :         }
    3964             :       } else {
    3965           2 :         if (log2(maxD) > BITS_IN_LONG - 2 * (log2(L) + 2))
    3966             :         {
    3967           0 :           char *err = stack_sprintf("modular polynomial of level %ld and invariant %ld",L,inv);
    3968           0 :           pari_err(e_ARCH, err);
    3969             :         }
    3970             :       }
    3971           2 :       maxD *= 2;
    3972           2 :       minD += 4;
    3973           2 :       dbg_printf(0)("  Doubling discriminant search space (closest: %.1f%%, cost ratio: %.1f)...\n", eps*100, cost/(double)(d*(L-1)));
    3974             :     }
    3975        2959 :     max_max_D *= 2;
    3976             :   }
    3977             : 
    3978        2959 :   if (DEBUGLEVEL > 3) {
    3979           0 :     pari_sp av = avma;
    3980           0 :     err_printf("Found discriminant(s):\n");
    3981           0 :     for (i = 0; i < best_cnt; ++i) {
    3982           0 :       long h = itos(classno(stoi(bestD[i].D1)));
    3983           0 :       set_avma(av);
    3984           0 :       err_printf("  D = %ld, h = %ld, u = %ld, L0 = %ld, L1 = %ld, n1 = %ld, n2 = %ld, cost = %ld\n",
    3985           0 :           bestD[i].D1, h, usqrt(bestD[i].D1 / bestD[i].D0), bestD[i].L0,
    3986           0 :           bestD[i].L1, bestD[i].n1, bestD[i].n2, bestD[i].cost);
    3987             :     }
    3988           0 :     err_printf("(off target by %.1f%%, cost ratio: %.1f)\n",
    3989           0 :                best_eps*100, best_cost/(double)(d*(L-1)));
    3990             :   }
    3991        2959 :   return best_cnt;
    3992             : }

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