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 - volcano.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.18.1 lcov report (development 30316-0578a48613) Lines: 340 345 98.6 %
Date: 2025-05-31 09:20:01 Functions: 28 28 100.0 %
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             : static GEN
      19      218771 : pcp_get_L(GEN G) { return gmael(G,1,1)+1; }
      20             : static GEN
      21      218771 : pcp_get_n(GEN G) { return gmael(G,1,2)+1; }
      22             : static GEN
      23      218770 : pcp_get_o(GEN G) { return gmael(G,1,3)+1; }
      24             : static long
      25      218771 : pcp_get_L0(GEN G) { return mael(G,2,1); }
      26             : static long
      27      218770 : pcp_get_k(GEN G) { return mael(G,2,2); }
      28             : static long
      29      218770 : pcp_get_enum_cnt(GEN G) { return mael(G,2,3); }
      30             : 
      31             : /* FIXME: Implement {ascend,descend}_volcano() in terms of the "new"
      32             :  * volcano traversal functions at the bottom of the file. */
      33             : 
      34             : /* Is j = 0 or 1728 (mod p)? */
      35             : INLINE int
      36      361609 : is_j_exceptional(ulong j, ulong p) { return j == 0 || j == 1728 % p; }
      37             : 
      38             : INLINE long
      39       81011 : node_degree(GEN phi, long L, ulong j, ulong p, ulong pi)
      40             : {
      41       81011 :   pari_sp av = avma;
      42       81011 :   long n = Flx_nbroots(Flm_Fl_polmodular_evalx(phi, L, j, p, pi), p);
      43       81007 :   return gc_long(av, n);
      44             : }
      45             : 
      46             : /* Given an array path = [j0, j1] of length 2, return the polynomial
      47             :  *
      48             :  *   \Phi_L(X, j1) / (X - j0)
      49             :  *
      50             :  * where \Phi_L(X, Y) is the modular polynomial of level L.  An error
      51             :  * is raised if X - j0 does not divide \Phi_L(X, j1) */
      52             : INLINE GEN
      53      142084 : nhbr_polynomial(ulong path[], GEN phi, ulong p, ulong pi, long L)
      54             : {
      55      142084 :   GEN modpol = Flm_Fl_polmodular_evalx(phi, L, path[0], p, pi);
      56             :   ulong rem;
      57      142087 :   GEN nhbr_pol = Flx_div_by_X_x(modpol, path[-1], p, &rem);
      58             :   /* If disc End(path[0]) <= L^2, it's possible for path[0] to appear among the
      59             :    * roots of nhbr_pol. This should have been obviated by earlier choices */
      60      142081 :   if (rem) pari_err_BUG("nhbr_polynomial: invalid preceding j");
      61      142081 :   return nhbr_pol;
      62             : }
      63             : 
      64             : /* Path is an array with space for at least max_len+1 * elements, whose first
      65             :  * and second elements are the beginning of the path.  I.e., the path starts
      66             :  *   (path[0], path[1])
      67             :  * If the result is less than max_len, then the last element of path is on the
      68             :  * floor.  If the result equals max_len, then it is unknown whether the last
      69             :  * element of path is on the floor or not */
      70             : static long
      71      277685 : extend_path(ulong path[], GEN phi, ulong p, ulong pi, long L, long max_len)
      72             : {
      73      277685 :   pari_sp av = avma;
      74      277685 :   long d = 1;
      75      357830 :   for ( ; d < max_len; d++)
      76             :   {
      77      102815 :     GEN nhbr_pol = nhbr_polynomial(path + d, phi, p, pi, L);
      78      102813 :     ulong nhbr = Flx_oneroot_pre(nhbr_pol, p, pi);
      79      102813 :     set_avma(av);
      80      102813 :     if (nhbr == p) break; /* no root: we are on the floor. */
      81       80145 :     path[d+1] = nhbr;
      82             :   }
      83      277683 :   return d;
      84             : }
      85             : 
      86             : /* This is Sutherland 2009 Algorithm Ascend (p12) */
      87             : ulong
      88      127181 : ascend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L,
      89             :   long depth, long steps)
      90             : {
      91      127181 :   pari_sp ltop = avma, av;
      92             :   /* path will never hold more than max_len < depth elements */
      93      127181 :   GEN path_g = cgetg(depth + 2, t_VECSMALL);
      94      127181 :   ulong *path = zv_to_ulongptr(path_g);
      95      127181 :   long max_len = depth - level;
      96      127181 :   int first_iter = 1;
      97             : 
      98      127181 :   if (steps <= 0 || max_len < 0) pari_err_BUG("ascend_volcano: bad params");
      99      127181 :   av = avma;
     100      293633 :   while (steps--)
     101             :   {
     102      127181 :     GEN nhbr_pol = first_iter? Flm_Fl_polmodular_evalx(phi, L, j, p, pi)
     103      166452 :                              : nhbr_polynomial(path+1, phi, p, pi, L);
     104      166455 :     GEN nhbrs = Flx_roots_pre(nhbr_pol, p, pi);
     105      166443 :     long nhbrs_len = lg(nhbrs)-1, i;
     106      166443 :     pari_sp btop = avma;
     107      166443 :     path[0] = j;
     108      166443 :     first_iter = 0;
     109             : 
     110      166443 :     j = nhbrs[nhbrs_len];
     111      209837 :     for (i = 1; i < nhbrs_len; i++)
     112             :     {
     113       77850 :       ulong next_j = nhbrs[i], last_j;
     114             :       long len;
     115       77850 :       if (is_j_exceptional(next_j, p))
     116             :       {
     117             :         /* Fouquet & Morain, Section 4.3, if j = 0 or 1728, then it is on the
     118             :          * surface.  So we just return it. */
     119          33 :         if (steps)
     120           0 :           pari_err_BUG("ascend_volcano: Got to the top with more steps to go!");
     121          33 :         j = next_j; break;
     122             :       }
     123       77816 :       path[1] = next_j;
     124       77816 :       len = extend_path(path, phi, p, pi, L, max_len);
     125       77817 :       last_j = path[len];
     126       77817 :       if (len == max_len
     127             :           /* Ended up on the surface */
     128       77817 :           && (is_j_exceptional(last_j, p)
     129       77817 :               || node_degree(phi, L, last_j, p, pi) > 1)) { j = next_j; break; }
     130       43392 :       set_avma(btop);
     131             :     }
     132      166441 :     path[1] = j; /* For nhbr_polynomial() at the top. */
     133             : 
     134      166441 :     max_len++; set_avma(av);
     135             :   }
     136      127181 :   return gc_long(ltop, j);
     137             : }
     138             : 
     139             : static void
     140      205934 : random_distinct_neighbours_of(ulong *nhbr1, ulong *nhbr2,
     141             :   GEN phi, ulong j, ulong p, ulong pi, long L, long must_have_two_neighbours)
     142             : {
     143      205934 :   pari_sp av = avma;
     144      205934 :   GEN modpol = Flm_Fl_polmodular_evalx(phi, L, j, p, pi);
     145             :   ulong rem;
     146      205947 :   *nhbr1 = Flx_oneroot_pre(modpol, p, pi);
     147      205938 :   if (*nhbr1 == p) pari_err_BUG("random_distinct_neighbours_of [no neighbour]");
     148      205938 :   modpol = Flx_div_by_X_x(modpol, *nhbr1, p, &rem);
     149      205927 :   *nhbr2 = Flx_oneroot_pre(modpol, p, pi);
     150      205940 :   if (must_have_two_neighbours && *nhbr2 == p)
     151           0 :     pari_err_BUG("random_distinct_neighbours_of [single neighbour]");
     152      205940 :   set_avma(av);
     153      205937 : }
     154             : 
     155             : /* This is Sutherland 2009 Algorithm Descend (p12) */
     156             : ulong
     157        2970 : descend_volcano(GEN phi, ulong j, ulong p, ulong pi,
     158             :   long level, long L, long depth, long steps)
     159             : {
     160        2970 :   pari_sp ltop = avma;
     161             :   GEN path_g;
     162             :   ulong *path;
     163             :   long max_len;
     164             : 
     165        2970 :   if (steps <= 0 || level + steps > depth) pari_err_BUG("descend_volcano");
     166        2970 :   max_len = depth - level;
     167        2970 :   path_g = cgetg(max_len + 1 + 1, t_VECSMALL);
     168        2970 :   path = zv_to_ulongptr(path_g);
     169        2970 :   path[0] = j;
     170             :   /* level = 0 means we're on the volcano surface... */
     171        2970 :   if (!level)
     172             :   {
     173             :     /* Look for any path to the floor. One of j's first three neighbours leads
     174             :      * to the floor, since at most two neighbours are on the surface. */
     175        2649 :     GEN nhbrs = Flx_roots_pre(Flm_Fl_polmodular_evalx(phi, L, j, p, pi), p, pi);
     176             :     long i;
     177        2925 :     for (i = 1; i <= 3; i++)
     178             :     {
     179             :       long len;
     180        2925 :       path[1] = nhbrs[i];
     181        2925 :       len = extend_path(path, phi, p, pi, L, max_len);
     182             :       /* If nhbrs[i] took us to the floor: */
     183        2925 :       if (len < max_len || node_degree(phi, L, path[len], p, pi) == 1) break;
     184             :     }
     185        2648 :     if (i > 3) pari_err_BUG("descend_volcano [2]");
     186             :   }
     187             :   else
     188             :   {
     189             :     ulong nhbr1, nhbr2;
     190             :     long len;
     191         321 :     random_distinct_neighbours_of(&nhbr1, &nhbr2, phi, j, p, pi, L, 1);
     192         321 :     path[1] = nhbr1;
     193         321 :     len = extend_path(path, phi, p, pi, L, max_len);
     194             :     /* If last j isn't on the floor */
     195         321 :     if (len == max_len   /* Ended up on the surface. */
     196         321 :         && (is_j_exceptional(path[len], p)
     197         269 :             || node_degree(phi, L, path[len], p, pi) != 1)) {
     198             :       /* The other neighbour leads to the floor */
     199         139 :       path[1] = nhbr2;
     200         139 :       (void) extend_path(path, phi, p, pi, L, steps);
     201             :     }
     202             :   }
     203        2969 :   return gc_ulong(ltop, path[steps]);
     204             : }
     205             : 
     206             : long
     207      205629 : j_level_in_volcano(
     208             :   GEN phi, ulong j, ulong p, ulong pi, long L, long depth)
     209             : {
     210      205629 :   pari_sp av = avma;
     211             :   GEN chunk;
     212             :   ulong *path1, *path2;
     213             :   long lvl;
     214             : 
     215             :   /* Fouquet & Morain, Section 4.3, if j = 0 or 1728 then it is on the
     216             :    * surface.  Also, if the volcano depth is zero then j has level 0 */
     217      205629 :   if (depth == 0 || is_j_exceptional(j, p)) return 0;
     218             : 
     219      205615 :   chunk = new_chunk(2 * (depth + 1));
     220      205612 :   path1 = (ulong *) &chunk[0];
     221      205612 :   path2 = (ulong *) &chunk[depth + 1];
     222      205612 :   path1[0] = path2[0] = j;
     223      205612 :   random_distinct_neighbours_of(&path1[1], &path2[1], phi, j, p, pi, L, 0);
     224      205629 :   if (path2[1] == p)
     225      107381 :     lvl = depth; /* Only one neighbour => j is on the floor => level = depth */
     226             :   else
     227             :   {
     228       98248 :     long path1_len = extend_path(path1, phi, p, pi, L, depth);
     229       98246 :     long path2_len = extend_path(path2, phi, p, pi, L, path1_len);
     230       98247 :     lvl = depth - path2_len;
     231             :   }
     232      205628 :   return gc_long(av, lvl);
     233             : }
     234             : 
     235             : INLINE GEN
     236    32226869 : Flx_remove_root(GEN f, ulong a, ulong p)
     237             : {
     238             :   ulong r;
     239    32226869 :   GEN g = Flx_div_by_X_x(f, a, p, &r);
     240    32106451 :   if (r) pari_err_BUG("Flx_remove_root");
     241    32108311 :   return g;
     242             : }
     243             : 
     244             : INLINE GEN
     245    24302699 : get_nbrs(GEN phi, long L, ulong J, const ulong *xJ, ulong p, ulong pi)
     246             : {
     247    24302699 :   pari_sp av = avma;
     248    24302699 :   GEN f = Flm_Fl_polmodular_evalx(phi, L, J, p, pi);
     249    24302094 :   if (xJ) f = Flx_remove_root(f, *xJ, p);
     250    24230488 :   return gc_upto(av, Flx_roots_pre(f, p, pi));
     251             : }
     252             : 
     253             : /* Return a path of length n along the surface of an L-volcano of height h
     254             :  * starting from surface node j0.  Assumes (D|L) = 1 where D = disc End(j0).
     255             :  *
     256             :  * Actually, if j0's endomorphism ring is a suborder, we return the
     257             :  * corresponding shorter path. W must hold space for n + h nodes.
     258             :  *
     259             :  * TODO: have two versions of this function: one that assumes J has the correct
     260             :  * endomorphism ring (hence avoiding several branches in the inner loop) and a
     261             :  * second that does not and accordingly checks for repetitions */
     262             : static long
     263      214368 : surface_path(
     264             :   ulong W[],
     265             :   long n, GEN phi, long L, long h, ulong J, const ulong *nJ, ulong p, ulong pi)
     266             : {
     267      214368 :   pari_sp av = avma, bv;
     268             :   GEN T, v;
     269             :   long j, k, w, x;
     270             :   ulong W0;
     271             : 
     272      214368 :   W[0] = W0 = J;
     273      214368 :   if (n == 1) return 1;
     274             : 
     275      214368 :   T = cgetg(h+2, t_VEC); bv = avma;
     276      214368 :   v = get_nbrs(phi, L, J, nJ, p, pi);
     277             :   /* Insert known neighbour first */
     278      214365 :   if (nJ) v = gc_upto(bv, vecsmall_prepend(v, *nJ));
     279      214365 :   gel(T,1) = v; k = lg(v)-1;
     280             : 
     281      214365 :   switch (k) {
     282           0 :   case 0: pari_err_BUG("surface_path"); /* We must always have neighbours */
     283        8851 :   case 1:
     284             :     /* If volcano is not flat, then we must have more than one neighbour */
     285        8851 :     if (h) pari_err_BUG("surface_path");
     286        8851 :     W[1] = uel(v, 1);
     287        8851 :     set_avma(av);
     288             :     /* Check for bad endo ring */
     289        8851 :     if (W[1] == W[0]) return 1;
     290        8664 :     return 2;
     291       25054 :   case 2:
     292             :     /* If L=2 the only way we can have 2 neighbours is if we have a double root
     293             :      * which can only happen for |D| <= 16 (Thm 2.2 of Fouquet-Morain)
     294             :      * and if it does we must have a 2-cycle. Happens for D=-15. */
     295       25054 :     if (L == 2)
     296             :     { /* The double root is the neighbour on the surface, with exactly one
     297             :        * neighbour other than J; the other neighbour of J has either 0 or 2
     298             :        * neighbours that are not J */
     299          84 :       GEN u = get_nbrs(phi, L, uel(v, 1), &J, p, pi);
     300          84 :       long n = lg(u)-1 - !!vecsmall_isin(u, J);
     301          84 :       W[1] = n == 1 ? uel(v,1) : uel(v,2);
     302          84 :       return gc_long(av, 2);
     303             :     }
     304             :     /* Volcano is not flat but found only 2 neighbours for the surface node J */
     305       24970 :     if (h) pari_err_BUG("surface_path");
     306             : 
     307       24970 :     W[1] = uel(v,1); /* TODO: Can we use the other root uel(v,2) somehow? */
     308     4397915 :     for (w = 2; w < n; w++)
     309             :     {
     310     4373529 :       v = get_nbrs(phi, L, W[w-1], &W[w-2], p, pi);
     311             :       /* A flat volcano must have exactly one non-previous neighbour */
     312     4373516 :       if (lg(v) != 2) pari_err_BUG("surface_path");
     313     4373516 :       W[w] = uel(v, 1);
     314             :       /* Detect cycle in case J doesn't have the right endo ring. */
     315     4373516 :       set_avma(av); if (W[w] == W0) return w;
     316             :     }
     317       24386 :     return gc_long(av, n);
     318             :   }
     319      180460 :   if (!h) pari_err_BUG("surface_path"); /* Can't have a flat volcano if k > 2 */
     320             : 
     321             :   /* At this point, each surface node has L+1 distinct neighbours, 2 of which
     322             :    * are on the surface */
     323      180460 :   w = 1;
     324     6426432 :   for (x = 0;; x++)
     325             :   {
     326             :     /* Get next neighbour of last known surface node to attempt to
     327             :      * extend the path. */
     328     6426432 :     W[w] = umael(T, ((w-1) % h) + 1, x + 1);
     329             : 
     330             :     /* Detect cycle in case the given J didn't have the right endo ring */
     331     6426432 :     if (W[w] == W0) return gc_long(av,w);
     332             : 
     333             :     /* If we have to test the last neighbour, we know it's on the
     334             :      * surface, and if we're done there's no need to extend. */
     335     6426401 :     if (x == k-1 && w == n-1) return gc_long(av,n);
     336             : 
     337             :     /* Walk forward until we hit the floor or finish. */
     338             :     /* NB: We don't keep the stack clean here; usage is in the order of Lh,
     339             :      * i.e. L roots for each level of the volcano of height h. */
     340     6307088 :     for (j = w;;)
     341    13223285 :     {
     342             :       long m;
     343             :       /* We must get 0 or L neighbours here. */
     344    19530373 :       v = get_nbrs(phi, L, W[j], &W[j-1], p, pi);
     345    19484380 :       m = lg(v)-1;
     346    19484380 :       if (!m) {
     347             :         /* We hit the floor: save the neighbours of W[w-1] and dump the rest */
     348     6245582 :         GEN nbrs = gel(T, ((w-1) % h) + 1);
     349     6245582 :         gel(T, ((w-1) % h) + 1) = gc_upto(bv, nbrs);
     350     6245972 :         break;
     351             :       }
     352    13238798 :       if (m != L) pari_err_BUG("surface_path");
     353             : 
     354    13284404 :       gel(T, (j % h) + 1) = v;
     355             : 
     356    13284404 :       W[++j] = uel(v, 1);
     357             :       /* If we have our path by h nodes, we know W[w] is on the surface */
     358    13284404 :       if (j == w + h) {
     359    12294997 :         ++w;
     360             :         /* Detect cycle in case the given J didn't have the right endo ring */
     361    12294997 :         if (W[w] == W0) return gc_long(av,w);
     362    12266883 :         x = 0; k = L;
     363             :       }
     364    13256290 :       if (w == n) return gc_long(av,w);
     365             :     }
     366             :   }
     367             : }
     368             : 
     369             : long
     370      148491 : next_surface_nbr(
     371             :   ulong *nJ,
     372             :   GEN phi, long L, long h, ulong J, const ulong *pJ, ulong p, ulong pi)
     373             : {
     374      148491 :   pari_sp av = avma, bv;
     375             :   GEN S;
     376             :   ulong *P;
     377             :   long i, k;
     378             : 
     379      148491 :   S = get_nbrs(phi, L, J, pJ, p, pi); k = lg(S)-1;
     380             :   /* If there is a double root and pJ is set, then k will be zero. */
     381      148495 :   if (!k) return gc_long(av,0);
     382      148495 :   if (k == 1 || ( ! pJ && k == 2)) { *nJ = uel(S, 1); return gc_long(av,1); }
     383       24218 :   if (!h) pari_err_BUG("next_surface_nbr");
     384             : 
     385       24218 :   P = (ulong *) new_chunk(h + 1); bv = avma;
     386       24218 :   P[0] = J;
     387       52062 :   for (i = 0; i < k; i++)
     388             :   {
     389             :     long j;
     390       52062 :     P[1] = uel(S, i + 1);
     391       81387 :     for (j = 1; j <= h; j++)
     392             :     {
     393       57169 :       GEN T = get_nbrs(phi, L, P[j], &P[j - 1], p, pi);
     394       57170 :       if (lg(T) == 1) break;
     395       29325 :       P[j + 1] = uel(T, 1);
     396             :     }
     397       52063 :     if (j < h) pari_err_BUG("next_surface_nbr");
     398       52063 :     set_avma(bv); if (j > h) break;
     399             :   }
     400             :   /* TODO: We could save one get_nbrs call by iterating from i up to k-1 and
     401             :    * assume that the last (kth) nbr is the one we want. For now we're careful
     402             :    * and check that this last nbr really is on the surface */
     403       24218 :   if (i == k) pari_err_BUG("next_surf_nbr");
     404       24218 :   *nJ = uel(S, i+1); return gc_long(av,1);
     405             : }
     406             : 
     407             : /* Return the number of distinct neighbours (1 or 2) */
     408             : INLINE long
     409      238750 : common_nbr(ulong *nbr,
     410             :   ulong J1, GEN Phi1, long L1,
     411             :   ulong J2, GEN Phi2, long L2, ulong p, ulong pi)
     412             : {
     413      238750 :   pari_sp av = avma;
     414             :   GEN d, f, g, r;
     415             :   long rlen;
     416             : 
     417      238750 :   g = Flm_Fl_polmodular_evalx(Phi1, L1, J1, p, pi);
     418      238767 :   f = Flm_Fl_polmodular_evalx(Phi2, L2, J2, p, pi);
     419      238759 :   d = Flx_gcd(f, g, p);
     420      238643 :   if (degpol(d) == 1) { *nbr = Flx_deg1_root(d, p); return gc_long(av,1); }
     421        1280 :   if (degpol(d) != 2) pari_err_BUG("common_neighbour");
     422        1280 :   r = Flx_roots_pre(d, p, pi);
     423        1280 :   rlen = lg(r)-1;
     424        1280 :   if (!rlen) pari_err_BUG("common_neighbour");
     425             :   /* rlen is 1 or 2 depending on whether the root is unique or not. */
     426        1280 :   nbr[0] = uel(r, 1);
     427        1280 :   nbr[1] = uel(r, rlen); return gc_long(av,rlen);
     428             : }
     429             : 
     430             : /* Return gcd(Phi1(X,J1)/(X - J0), Phi2(X,J2)). Not stack clean. */
     431             : INLINE GEN
     432       44083 : common_nbr_pred_poly(
     433             :   ulong J1, GEN Phi1, long L1,
     434             :   ulong J2, GEN Phi2, long L2, ulong J0, ulong p, ulong pi)
     435             : {
     436             :   GEN f, g;
     437             : 
     438       44083 :   g = Flm_Fl_polmodular_evalx(Phi1, L1, J1, p, pi);
     439       44084 :   g = Flx_remove_root(g, J0, p);
     440       44085 :   f = Flm_Fl_polmodular_evalx(Phi2, L2, J2, p, pi);
     441       44079 :   return Flx_gcd(f, g, p);
     442             : }
     443             : 
     444             : /* Find common neighbour of J1 and J2, where J0 is an L1 predecessor of J1.
     445             :  * Return 1 if successful, 0 if not. */
     446             : INLINE int
     447       43028 : common_nbr_pred(ulong *nbr,
     448             :   ulong J1, GEN Phi1, long L1,
     449             :   ulong J2, GEN Phi2, long L2, ulong J0, ulong p, ulong pi)
     450             : {
     451       43028 :   pari_sp av = avma;
     452       43028 :   GEN d = common_nbr_pred_poly(J1, Phi1, L1, J2, Phi2, L2, J0, p, pi);
     453       43012 :   int res = (degpol(d) == 1);
     454       43010 :   if (res) *nbr = Flx_deg1_root(d, p);
     455       43022 :   return gc_bool(av,res);
     456             : }
     457             : 
     458             : INLINE long
     459        1055 : common_nbr_verify(ulong *nbr,
     460             :   ulong J1, GEN Phi1, long L1,
     461             :   ulong J2, GEN Phi2, long L2, ulong J0, ulong p, ulong pi)
     462             : {
     463        1055 :   pari_sp av = avma;
     464        1055 :   GEN d = common_nbr_pred_poly(J1, Phi1, L1, J2, Phi2, L2, J0, p, pi);
     465             : 
     466        1054 :   if (!degpol(d)) return gc_long(av,0);
     467         359 :   if (degpol(d) > 1) pari_err_BUG("common_neighbour_verify");
     468         359 :   *nbr = Flx_deg1_root(d, p);
     469         359 :   return gc_long(av,1);
     470             : }
     471             : 
     472             : INLINE ulong
     473         534 : Flm_Fl_polmodular_evalxy(GEN Phi, long L, ulong x, ulong y, ulong p, ulong pi)
     474             : {
     475         534 :   pari_sp av = avma;
     476         534 :   GEN f = Flm_Fl_polmodular_evalx(Phi, L, x, p, pi);
     477         534 :   return gc_ulong(av, Flx_eval_pre(f, y, p, pi));
     478             : }
     479             : 
     480             : /* Find a common L1-neighbor of J1 and L2-neighbor of J2, given J0 an
     481             :  * L2-neighbor of J1 and an L1-neighbor of J2. Return 1 if successful, 0
     482             :  * otherwise. Will only fail if initial J-invariant had the wrong endo ring */
     483             : INLINE int
     484       37332 : common_nbr_corner(ulong *nbr,
     485             :   ulong J1, GEN Phi1, long L1, long h1,
     486             :   ulong J2, GEN Phi2, long L2, ulong J0, ulong p, ulong pi)
     487             : {
     488             :   ulong nbrs[2];
     489       37332 :   if (common_nbr(nbrs, J1,Phi1,L1, J2,Phi2,L2, p, pi) == 2)
     490             :   {
     491             :     ulong nJ1, nJ2;
     492         690 :     if (!next_surface_nbr(&nJ2, Phi1, L1, h1, J2, &J0, p, pi) ||
     493         395 :         !next_surface_nbr(&nJ1, Phi1, L1, h1, nbrs[0], &J1, p, pi)) return 0;
     494             : 
     495         345 :     if (Flm_Fl_polmodular_evalxy(Phi2, L2, nJ1, nJ2, p, pi))
     496         156 :       nbrs[0] = nbrs[1];
     497         378 :     else if (!next_surface_nbr(&nJ1, Phi1, L1, h1, nbrs[1], &J1, p, pi) ||
     498         239 :              !Flm_Fl_polmodular_evalxy(Phi2, L2, nJ1, nJ2, p, pi)) return 0;
     499             :   }
     500       37281 :   *nbr = nbrs[0]; return 1;
     501             : }
     502             : 
     503             : /* Enumerate a surface L1-cycle using gcds with Phi_L2, where c_L2=c_L1^e and
     504             :  * |c_L1|=n, where c_a is the class of the pos def reduced primeform <a,b,c>.
     505             :  * Assumes n > e > 1 and roots[0],...,roots[e-1] are already present in W */
     506             : static long
     507       93285 : surface_gcd_cycle(
     508             :   ulong W[], ulong V[], long n,
     509             :   GEN Phi1, long L1, GEN Phi2, long L2, long e, ulong p, ulong pi)
     510             : {
     511       93285 :   pari_sp av = avma;
     512             :   long i1, i2, j1, j2;
     513             : 
     514       93285 :   i1 = j2 = 0;
     515       93285 :   i2 = j1 = e - 1;
     516             :   /* If W != V we assume V actually points to an L2-isogenous parallel L1-path.
     517             :    * e should be 2 in this case */
     518       93285 :   if (W != V) { i1 = j1+1; i2 = n-1; }
     519             :   do {
     520             :     ulong t0, t1, t2, h10, h11, h20, h21;
     521             :     long k;
     522             :     GEN f, g, h1, h2;
     523             : 
     524     4123090 :     f = Flm_Fl_polmodular_evalx(Phi2, L2, V[i1], p, pi);
     525     4121195 :     g = Flm_Fl_polmodular_evalx(Phi1, L1, W[j1], p, pi);
     526     4120368 :     g = Flx_remove_root(g, W[j1 - 1], p);
     527     4111391 :     h1 = Flx_gcd(f, g, p);
     528     4101373 :     if (degpol(h1) != 1) break; /* Error */
     529     4101716 :     h11 = Flx_coeff(h1, 1);
     530     4102160 :     h10 = Flx_coeff(h1, 0); set_avma(av);
     531             : 
     532     4102345 :     f = Flm_Fl_polmodular_evalx(Phi2, L2, V[i2], p, pi);
     533     4121603 :     g = Flm_Fl_polmodular_evalx(Phi1, L1, W[j2], p, pi);
     534     4120899 :     k = j2 + 1;
     535     4120899 :     if (k == n) k = 0;
     536     4120899 :     g = Flx_remove_root(g, W[k], p);
     537     4112732 :     h2 = Flx_gcd(f, g, p);
     538     4102961 :     if (degpol(h2) != 1) break; /* Error */
     539     4103281 :     h21 = Flx_coeff(h2, 1);
     540     4103771 :     h20 = Flx_coeff(h2, 0); set_avma(av);
     541             : 
     542     4103976 :     i1++; i2--; if (i2 < 0) i2 = n-1;
     543     4103976 :     j1++; j2--; if (j2 < 0) j2 = n-1;
     544             : 
     545     4103976 :     t0 = Fl_mul_pre(h11, h21, p, pi);
     546     4123411 :     t1 = Fl_inv(t0, p);
     547     4126455 :     t0 = Fl_mul_pre(t1, h21, p, pi);
     548     4124455 :     t2 = Fl_mul_pre(t0, h10, p, pi);
     549     4123752 :     W[j1] = Fl_neg(t2, p);
     550     4123288 :     t0 = Fl_mul_pre(t1, h11, p, pi);
     551     4124492 :     t2 = Fl_mul_pre(t0, h20, p, pi);
     552     4123579 :     W[j2] = Fl_neg(t2, p);
     553     4122942 :   } while (j2 > j1 + 1);
     554             :   /* Usually the loop exits when j2 = j1 + 1, in which case we return n.
     555             :    * If we break early because of an error, then (j2 - (j1+1)) > 0 is the
     556             :    * number of elements we haven't calculated yet, and we return n minus that
     557             :    * quantity */
     558       93137 :   return gc_long(av, n - j2 + j1 + 1);
     559             : }
     560             : 
     561             : static long
     562        1212 : surface_gcd_path(
     563             :   ulong W[], ulong V[], long n,
     564             :   GEN Phi1, long L1, GEN Phi2, long L2, long e, ulong p, ulong pi)
     565             : {
     566        1212 :   pari_sp av = avma;
     567             :   long i, j;
     568             : 
     569        1212 :   i = 0; j = e;
     570             :   /* If W != V then assume V actually points to a L2-isogenous
     571             :    * parallel L1-path.  e should be 2 in this case */
     572        1212 :   if (W != V) i = j;
     573        4946 :   while (j < n)
     574             :   {
     575             :     GEN f, g, d;
     576             : 
     577        3734 :     f = Flm_Fl_polmodular_evalx(Phi2, L2, V[i], p, pi);
     578        3734 :     g = Flm_Fl_polmodular_evalx(Phi1, L1, W[j - 1], p, pi);
     579        3734 :     g = Flx_remove_root(g, W[j - 2], p);
     580        3733 :     d = Flx_gcd(f, g, p);
     581        3732 :     if (degpol(d) != 1) break; /* Error */
     582        3732 :     W[j] = Flx_deg1_root(d, p);
     583        3734 :     i++; j++; set_avma(av);
     584             :   }
     585        1212 :   return gc_long(av, j);
     586             : }
     587             : 
     588             : /* Given a path V of length n on an L1-volcano, and W[0] L2-isogenous to V[0],
     589             :  * extends the path W to length n on an L1-volcano, with W[i] L2-isogenous
     590             :  * to V[i]. Uses gcds unless L2 is too large to make it helpful. Always uses
     591             :  * GCD to get W[1] to ensure consistent orientation.
     592             :  *
     593             :  * Returns the new length of W. This will almost always be n, but could be
     594             :  * lower if V was started with a J-invariant with bad endomorphism ring */
     595             : INLINE long
     596      201431 : surface_parallel_path(
     597             :   ulong W[], ulong V[], long n,
     598             :   GEN Phi1, long L1, GEN Phi2, long L2, ulong p, ulong pi, long cycle)
     599             : {
     600             :   ulong W2, nbrs[2];
     601      201431 :   if (common_nbr(nbrs, W[0], Phi1, L1, V[1], Phi2, L2, p, pi) == 2)
     602             :   {
     603         739 :     if (n <= 2) return 1; /* Error: Two choices with n = 2; ambiguous */
     604         739 :     if (!common_nbr_verify(&W2,nbrs[0], Phi1,L1,V[2], Phi2,L2,W[0], p,pi))
     605         423 :       nbrs[0] = nbrs[1]; /* nbrs[1] must be the correct choice */
     606         316 :     else if (common_nbr_verify(&W2,nbrs[1], Phi1,L1,V[2], Phi2,L2,W[0], p,pi))
     607          43 :       return 1; /* Error: Both paths extend successfully */
     608             :   }
     609      201390 :   W[1] = nbrs[0];
     610      201390 :   if (n <= 2) return n;
     611       93286 :   return cycle? surface_gcd_cycle(W, V, n, Phi1, L1, Phi2, L2, 2, p, pi)
     612      187795 :               : surface_gcd_path (W, V, n, Phi1, L1, Phi2, L2, 2, p, pi);
     613             : }
     614             : 
     615             : GEN
     616      218772 : enum_roots(ulong J0, norm_eqn_t ne, GEN fdb, GEN G, GEN vshape)
     617             : { /* MAX_HEIGHT >= max_{p,n} val_p(n) where p and n are ulongs */
     618             :   enum { MAX_HEIGHT = BITS_IN_LONG };
     619      218772 :   pari_sp av, ltop = avma;
     620      218772 :   long s = !!pcp_get_L0(G);
     621      218771 :   long *n = pcp_get_n(G)+s, *L = pcp_get_L(G)+s, *o = pcp_get_o(G)+s, k = pcp_get_k(G)-s;
     622      218770 :   long i, t, vlen, *e, *h, *off, *poff, *M, N = pcp_get_enum_cnt(G);
     623      218770 :   ulong p = ne->p, pi = ne->pi, *roots;
     624             :   GEN Phi, vp, ve, roots_;
     625             : 
     626      218770 :   if (!k) return mkvecsmall(J0);
     627             : 
     628      214370 :   roots_ = cgetg(N + MAX_HEIGHT, t_VECSMALL);
     629      214371 :   roots = zv_to_ulongptr(roots_);
     630      214371 :   av = avma;
     631             : 
     632      214371 :   if (!vshape) vshape = factoru(ne->v);
     633      214369 :   vp = gel(vshape, 1); vlen = lg(vp)-1;
     634      214369 :   ve = gel(vshape, 2);
     635             : 
     636      214369 :   Phi = new_chunk(k);
     637      214370 :   e = new_chunk(k);
     638      214370 :   off = new_chunk(k);
     639      214370 :   poff = new_chunk(k);
     640             :   /* TODO: Surely we can work these out ahead of time? */
     641             :   /* h[i] is the valuation of p[i] in v */
     642      214370 :   h = new_chunk(k);
     643      495810 :   for (i = 0; i < k; ++i) {
     644      281442 :     h[i] = 0;
     645      417753 :     for (t = 1; t <= vlen; ++t)
     646      325771 :       if (vp[t] == L[i]) { h[i] = uel(ve, t); break; }
     647      281442 :     e[i] = 0;
     648      281442 :     off[i] = 0;
     649      281442 :     gel(Phi, i) = polmodular_db_getp(fdb, L[i], p);
     650             :   }
     651             : 
     652      214368 :   t = surface_path(roots, n[0], gel(Phi, 0), L[0], h[0], J0, NULL, p, pi);
     653      214366 :   if (t < n[0]) return gc_NULL(ltop); /* J0 has bad endo ring */
     654      213621 :   if (k == 1) { setlg(roots_, t + 1); return gc_const(av,roots_); }
     655             : 
     656       54416 :   M = new_chunk(k);
     657      120196 :   for (M[0] = 1, i = 1; i < k; ++i) M[i] = M[i-1] * n[i-1];
     658       54416 :   i = 1;
     659      255810 :   while (i < k) {
     660             :     long j, t0;
     661      228200 :     for (j = i + 1; j < k && ! e[j]; ++j);
     662      201535 :     if (j < k) {
     663       80358 :       if (e[i]) {
     664       43023 :         if (! common_nbr_pred(
     665       43028 :               &roots[t], roots[off[i]], gel(Phi,i), L[i],
     666       43028 :               roots[t - M[j]], gel(Phi, j), L[j], roots[poff[i]], p, pi)) {
     667           0 :           break; /* J0 has bad endo ring */
     668             :         }
     669       37330 :       } else if ( ! common_nbr_corner(
     670       37330 :             &roots[t], roots[off[i]], gel(Phi,i), L[i], h[i],
     671       37330 :             roots[t - M[j]], gel(Phi, j), L[j], roots[poff[j]], p, pi)) {
     672          50 :         break; /* J0 has bad endo ring */
     673             :       }
     674      186842 :     } else if ( ! next_surface_nbr(
     675      121177 :           &roots[t], gel(Phi,i), L[i], h[i],
     676      186837 :           roots[off[i]], e[i] ? &roots[poff[i]] : NULL, p, pi))
     677           0 :       break; /* J0 has bad endo ring */
     678      201485 :     if (roots[t] == roots[0]) break; /* J0 has bad endo ring */
     679             : 
     680      201437 :     poff[i] = off[i];
     681      201437 :     off[i] = t;
     682      201437 :     e[i]++;
     683      238770 :     for (j = i-1; j; --j) { e[j] = 0; off[j] = off[j+1]; }
     684             : 
     685      201437 :     t0 = surface_parallel_path(&roots[t], &roots[poff[i]], n[0],
     686      201437 :         gel(Phi, 0), L[0], gel(Phi, i), L[i], p, pi, n[0] == o[0]);
     687      201437 :     if (t0 < n[0]) break; /* J0 has bad endo ring */
     688             : 
     689             :     /* TODO: Do I need to check if any of the new roots is a repeat in
     690             :      * the case where J0 has bad endo ring? */
     691      201394 :     t += n[0];
     692      304195 :     for (i = 1; i < k && e[i] == n[i]-1; i++);
     693             :   }
     694       54416 :   if (t != N) return gc_NULL(ltop); /* J0 has wrong endo ring */
     695       54275 :   setlg(roots_, t + 1); return gc_const(av,roots_);
     696             : }

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