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 - Flxq_log.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.16.2 lcov report (development 29395-ef22f77854) Lines: 449 468 95.9 %
Date: 2024-06-15 09:03:40 Functions: 28 28 100.0 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2013 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_fflog
      19             : 
      20             : /* Let [ be the following order on Fp: 0 [ p-1 [ 1 [ p-2 [ 2 .. [ p\2
      21             : and [[ the lexicographic extension of [ to Fp[T]. Compute the
      22             : isomorphism (Fp[X], [[) -> (N,<) on P */
      23             : 
      24             : static long
      25      391362 : Flx_cindex(GEN P, ulong p)
      26             : {
      27      391362 :   long d = degpol(P), i;
      28      391362 :   ulong s = 0, p2 = (p-1)>>1;
      29     1778197 :   for (i = 0; i <= d; ++i)
      30             :   {
      31     1386835 :     ulong x = P[d-i+2];
      32     1386835 :     if (x<=p2) x = 2*x; else x = 1+2*(p-1-x);
      33     1386835 :     s = p*s+x;
      34             :   }
      35      391362 :   return s;
      36             : }
      37             : 
      38             : /* Compute the polynomial immediately after t for the [[ order */
      39             : 
      40             : static void
      41      423869 : Flx_cnext(GEN t, ulong p)
      42             : {
      43             :   long i;
      44      423869 :   long p2 = p>>1;
      45      540487 :   for(i=2;;i++)
      46      540487 :     if (t[i]==p2)
      47      116618 :       t[i]=0;
      48             :     else
      49             :     {
      50      423869 :       t[i] = t[i]<p2 ? p-1-t[i]: p-t[i];
      51      423869 :       break;
      52             :     }
      53      423869 : }
      54             : 
      55             : static int
      56          28 : has_deg1_auto(GEN T, ulong p, ulong pi)
      57             : {
      58          28 :   long i, n = degpol(T);
      59          28 :   GEN a = polx_Flx(get_Flx_var(T));
      60         672 :   for (i=1; i<n; i++)
      61             :   {
      62         644 :     a = Flxq_powu_pre(a, p, T, p, pi);
      63         644 :     if (degpol(a)==1) return 1;
      64             :   }
      65          28 :   return 0;
      66             : }
      67             : 
      68             : static void
      69        1057 : smallirred_Flx_next(GEN a, long p, ulong pi)
      70             : {
      71             :   do
      72             :   {
      73             :     long i;
      74        1449 :     for(i=2;;i++)
      75        1449 :       if (++a[i]==p) a[i]=0;
      76        1057 :       else break;
      77        1057 :   } while (!Flx_is_irred(a, p) || has_deg1_auto(a,p,pi) );
      78          28 : }
      79             : 
      80             : /* Avoid automorphisms of degree 1 */
      81             : static GEN
      82          28 : smallirred_Flx(long p, ulong n, long sv, ulong pi)
      83             : {
      84          28 :   GEN a = zero_zv(n+2);
      85          28 :   a[1] = sv; a[3] = 1; a[n+2] = 1;
      86          28 :   smallirred_Flx_next(a, p, pi);
      87          28 :   return a;
      88             : }
      89             : 
      90             : struct Flxq_log_rel
      91             : {
      92             :   long nbrel;
      93             :   GEN rel;
      94             :   long nb;
      95             :   long r, off, nbmax, nbexp;
      96             :   ulong nbtest;
      97             : };
      98             : 
      99             : static GEN
     100        4636 : cindex_Flx(long c, long d, ulong p, long v)
     101             : {
     102        4636 :   GEN P = cgetg(d+3, t_VECSMALL);
     103             :   long i;
     104        4636 :   P[1] = v;
     105       31599 :   for (i = 0; i <= d; ++i)
     106             :   {
     107       26963 :     ulong x = c%p;
     108       26963 :     P[i+2] = (x&1) ? p-1-(x>>1) : x>>1;
     109       26963 :     c/=p;
     110             :   }
     111        4636 :   return Flx_renormalize(P, d+3);
     112             : }
     113             : 
     114             : static GEN
     115       11005 : factorel(GEN h, ulong p)
     116             : {
     117       11005 :   GEN F = Flx_factor(h, p);
     118       11008 :   GEN F1 = gel(F, 1), F2 = gel(F, 2);
     119       11008 :   long i, l1 = lg(F1)-1;
     120       11008 :   GEN p2 = cgetg(l1+1, t_VECSMALL);
     121       11008 :   GEN e2 = cgetg(l1+1, t_VECSMALL);
     122       52011 :   for (i = 1; i <= l1; ++i)
     123             :   {
     124       41003 :     p2[i] = Flx_cindex(gel(F1, i), p);
     125       41003 :     e2[i] = F2[i];
     126             :   }
     127       11008 :   return mkmat2(p2, e2);
     128             : }
     129             : 
     130             : static long
     131       74256 : Flx_addifsmooth3(pari_sp *av, struct Flxq_log_rel *r, GEN h, long u, long v, long w, ulong p)
     132             : {
     133       74256 :   long off = r->off;
     134       74256 :   r->nbtest++;
     135       74256 :   if (Flx_is_smooth(h, r->r, p))
     136             :   {
     137        5670 :     GEN z = factorel(h, p);
     138        5670 :     if (v<0)
     139        1225 :       z = mkmat2(vecsmall_append(gel(z,1),off+u),vecsmall_append(gel(z,2),-1));
     140             :     else
     141       13335 :       z = famatsmall_reduce(mkmat2(
     142        4445 :             vecsmall_concat(gel(z,1),mkvecsmall3(off+u,off+v,off+w)),
     143        4445 :             vecsmall_concat(gel(z,2),mkvecsmall3(-1,-1,-1))));
     144        5670 :     gel(r->rel,++r->nbrel) = gerepilecopy(*av,z);
     145        5670 :     if (DEBUGLEVEL && (r->nbrel&511UL)==0)
     146           0 :       err_printf("%ld%% ",r->nbrel*100/r->nbexp);
     147        5670 :     *av = avma;
     148       68586 :   } else set_avma(*av);
     149       74256 :   return r->nbrel==r->nb || r->nbrel==r->nbmax;
     150             : }
     151             : 
     152             : static void
     153      423911 : Flx_renormalize_inplace(GEN x, long lx)
     154             : {
     155             :   long i;
     156     4701614 :   for (i = lx-1; i>1; i--)
     157     4698989 :     if (x[i]) break;
     158      423911 :   setlg(x, i+1);
     159      424071 : }
     160             : 
     161             : /*
     162             :    Let T*X^e=C^3-R
     163             :    a+b+c = 0
     164             :    (C+a)*(C+b)*(C+c) = C^3+ (a*b+a*c+b*c)*C+a*b*c
     165             :    = R + (a*b+a*c+b*c)*C+a*b*c
     166             :    = R + (a*b-c^2)*C+a*b*c
     167             :  */
     168             : static void
     169          14 : Flxq_log_cubic(struct Flxq_log_rel *r, GEN C, GEN R, ulong p, ulong pi)
     170             : {
     171          14 :   long l = lg(C);
     172          14 :   GEN a = zero_zv(l); /*We allocate one extra word to catch overflow*/
     173          14 :   GEN b = zero_zv(l);
     174          14 :   pari_sp av = avma;
     175             :   long i,j,k;
     176        2800 :   for(i=0; ; i++, Flx_cnext(a, p))
     177             :   {
     178        2800 :     Flx_renormalize_inplace(a, l+1);
     179        2800 :     r->nb++;
     180        2800 :     if (Flx_addifsmooth3(&av, r, Flx_add(a, C, p), i, -1, -1, p)) return;
     181       29400 :     for(j=2; j<=l; j++) b[j] = 0;
     182      353129 :     for(j=0; j<=i; j++, Flx_cnext(b, p))
     183             :     {
     184             :       GEN h,c;
     185             :       GEN pab,pabc,pabc2;
     186      350343 :       Flx_renormalize_inplace(b, l+1);
     187      350343 :       c = Flx_neg(Flx_add(a,b,p),p);
     188      350343 :       k = Flx_cindex(c, p);
     189      350343 :       if (k > j) continue;
     190       71456 :       pab  = Flx_mul_pre(a, b, p, pi);
     191       71456 :       pabc = Flx_mul_pre(pab,c,p,pi);
     192       71456 :       pabc2= Flx_sub(pab,Flx_sqr_pre(c,p,pi),p);
     193       71456 :       h = Flx_add(R,Flx_add(Flx_mul_pre(C,pabc2,p,pi),pabc,p), p);
     194       71456 :       h = Flx_normalize(h, p);
     195       71456 :       if (Flx_addifsmooth3(&av, r, h, i, j, k, p)) return;
     196             :     }
     197             :   }
     198             : }
     199             : 
     200             : static GEN
     201          74 : Flxq_log_find_rel(GEN b, long r, GEN T, ulong p, ulong pi, GEN *g, long *e)
     202             : {
     203          74 :   pari_sp av = avma;
     204             :   while (1)
     205        3848 :   {
     206             :     GEN M, z;
     207        3922 :     *g = Flxq_mul_pre(*g, b, T, p, pi); (*e)++;
     208        3922 :     M = Flx_halfgcd_all_pre(*g,T,p,pi,&z,NULL);
     209        3922 :     if (Flx_is_smooth_pre(gcoeff(M,1,1), r, p, pi)
     210         499 :      && Flx_is_smooth_pre(z, r, p, pi))
     211             :     {
     212          74 :       GEN F = factorel(z, p);
     213          74 :       GEN G = factorel(gcoeff(M,1,1), p);
     214          74 :       GEN rel = mkmat2(vecsmall_concat(gel(F, 1),gel(G, 1)),
     215          74 :           vecsmall_concat(gel(F, 2),zv_neg(gel(G, 2))));
     216          74 :       return gc_all(av,2,&rel,g);
     217             :     }
     218        3848 :     if (gc_needed(av,2))
     219             :     {
     220           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flxq_log_find_rel");
     221           0 :       *g = gerepilecopy(av, *g);
     222             :     }
     223             :   }
     224             : }
     225             : 
     226             : /* Generalised Odlyzko formulae ( EUROCRYPT '84, LNCS 209, pp. 224-314, 1985. ) */
     227             : /* Return the number of monic, k smooth, degree n polynomials for k=1..r */
     228             : static GEN
     229        2233 : smoothness_vec(ulong p, long r, long n)
     230             : {
     231             :   long i,j,k;
     232        2233 :   GEN R = cgetg(r+1, t_VEC), pp = utoipos(p);
     233        2233 :   GEN V = cgetg(n+1, t_VEC);
     234       20496 :   for (j = 1; j <= n; ++j)
     235       18263 :     gel(V, j) =  binomialuu(p+j-1,j);
     236        2233 :   gel(R, 1) = gel(V, n);
     237        5341 :   for (k = 2; k <= r; ++k)
     238             :   {
     239        3108 :     GEN W = cgetg(n+1, t_VEC);
     240        3108 :     GEN Ik = ffnbirred(pp, k);
     241       36029 :     for (j = 1; j <= n; ++j)
     242             :     {
     243       32921 :       long l = j/k;
     244       32921 :       GEN s = gen_0;
     245       32921 :       pari_sp av2 = avma;
     246       32921 :       if (l*k == j)
     247             :       {
     248       10801 :         s = binomial(addiu(Ik,l-1), l);
     249       10801 :         l--;
     250             :       }
     251      119847 :       for (i = 0; i <= l; ++i)
     252       86926 :         s = addii(s, mulii(gel(V, j-k*i), binomial(addis(Ik,i-1), i)));
     253       32921 :       gel(W, j) = gerepileuptoint(av2, s);
     254             :     }
     255        3108 :     V = W;
     256        3108 :     gel(R, k) = gel(V, n);
     257             :   }
     258        2233 :   return R;
     259             : }
     260             : 
     261             : /* Solve N^2*pr/6 + N*prC = N+fb
     262             :    N^2*pr/6 + N*(prC-1) -fb = 0
     263             :  */
     264             : 
     265             : static GEN
     266        1729 : smooth_cost(GEN fb, GEN pr, GEN prC)
     267             : {
     268        1729 :   GEN a = gdivgu(pr,6);
     269        1729 :   GEN b = gsubgs(prC,1);
     270        1729 :   GEN c = gneg(fb);
     271        1729 :   GEN vD = gsqrt(gsub(gsqr(b),gmul2n(gmul(a,c),2)),BIGDEFAULTPREC);
     272        1729 :   return ceil_safe(gdiv(gsub(vD,b),gmul2n(a,1)));
     273             : }
     274             : 
     275             : /* Return best choice of r.
     276             :    We loop over d until there is sufficiently many triples (a,b,c) (a+b+c=0)
     277             :    of degree <=d with respect to the probability of smoothness of (a*b-c^2)*C
     278             :  */
     279             : 
     280             : static GEN
     281         315 : smooth_best(long p, long n, long *pt_r, long *pt_nb)
     282             : {
     283         315 :   pari_sp av = avma, av2;
     284         315 :   GEN bestc = NULL, pp = utoipos(p);
     285         315 :   long bestr = 0, bestFB = 0;
     286         315 :   long r,d, dC = (n+2)/3;
     287         819 :   for (r = 1; r < dC; ++r)
     288             :   {
     289         504 :     GEN fb = ffsumnbirred(pp, r);
     290         504 :     GEN smoothC = smoothness_vec(p,r,dC);
     291         504 :     GEN prC = gdiv(gel(smoothC,r), powuu(p,dC));
     292         504 :     ulong rels = 0;
     293         504 :     av2 = avma;
     294        2023 :     for(d=0; d<dC && rels < ULONG_MAX; d++)
     295             :     {
     296             :       GEN c;
     297        1729 :       long dt = dC+2*d;
     298        1729 :       GEN smooth = smoothness_vec(p,r,dt);
     299        1729 :       GEN pr = gdiv(gel(smooth,r), powuu(p,dt));
     300        1729 :       GEN FB = addii(fb,powuu(p,d));
     301        1729 :       GEN N = smooth_cost(subiu(FB,rels),pr,prC);
     302        1729 :       GEN Nmax = powuu(p,d+1);
     303        1729 :       if (gcmp(N,Nmax) >= 0)
     304             :       {
     305        1519 :         rels = itou_or_0(addui(rels, gceil(gmul(gdivgu(sqri(Nmax),6),pr))));
     306        1519 :         if (!rels) rels = ULONG_MAX;
     307        1519 :         set_avma(av2);
     308        1519 :         continue;
     309             :       }
     310         210 :       c = gdivgu(addii(powuu(p,2*d),sqri(N)),6);
     311         210 :       FB = addii(FB,N);
     312         210 :       if ((!bestc || gcmp(gmul2n(c,r), gmul2n(bestc,bestr)) < 0))
     313             :       {
     314         133 :         if (DEBUGLEVEL)
     315           0 :           err_printf("r=%ld d=%ld fb=%Ps early rels=%lu P=%.5Pe -> C=%.5Pe \n",
     316             :                       r, dt, FB, rels, pr, c);
     317         133 :         bestc = c;
     318         133 :         bestr = r;
     319         133 :         bestFB = itos_or_0(FB);
     320             :       }
     321         210 :       break;
     322             :     }
     323             :   }
     324         315 :   *pt_r=bestr;
     325         315 :   *pt_nb=bestFB;
     326         315 :   return bestc ? gerepileupto(av, gceil(bestc)): NULL;
     327             : }
     328             : 
     329             : static GEN
     330          28 : check_kernel(long r, GEN M, long nbi, long nbrow, GEN T, ulong p, ulong pi, GEN m)
     331             : {
     332          28 :   pari_sp av = avma;
     333          28 :   long N = 3*upowuu(p, r);
     334          28 :   GEN K = FpMs_leftkernel_elt(M, nbrow, m);
     335          28 :   long i, f=0, tbs;
     336          28 :   long lm = lgefint(m), u=1;
     337             :   GEN tab, g;
     338          28 :   GEN q = powuu(p,degpol(T));
     339          28 :   GEN idx = diviiexact(subiu(q,1),m);
     340             :   pari_timer ti;
     341          28 :   if (DEBUGLEVEL) timer_start(&ti);
     342         224 :   while (signe(gel(K,u))==0)
     343         196 :     u++;
     344          28 :   K = FpC_Fp_mul(K, Fp_inv(gel(K, u), m), m);
     345          28 :   g = Flxq_pow_pre(cindex_Flx(u, r, p, T[1]), idx, T, p, pi);
     346          28 :   tbs = maxss(1, expu(nbi/expi(m)));
     347          28 :   tab = Flxq_pow_init_pre(g, q, tbs, T, p, pi);
     348          28 :   setlg(K, N);
     349       46662 :   for (i=1; i<N; i++)
     350             :   {
     351       46634 :     GEN k = gel(K,i);
     352       46634 :     pari_sp av = avma;
     353       51026 :     long t = signe(k) && Flx_equal(Flxq_pow_table_pre(tab, k, T, p, pi),
     354        4392 :                                    Flxq_pow_pre(cindex_Flx(i,r,p,T[1]), idx, T, p, pi));
     355       46634 :     set_avma(av);
     356       46634 :     if (!t)
     357       42242 :       gel(K,i) = cgetineg(lm);
     358             :     else
     359        4392 :       f++;
     360             :   }
     361          28 :   if (DEBUGLEVEL) timer_printf(&ti,"found %ld/%ld logs", f, nbi);
     362          28 :   if (f < maxss(3,maxss(p/2,nbi/p))) return NULL; /* Not enough logs found */
     363          28 :   return gerepilecopy(av, K);
     364             : }
     365             : 
     366             : static GEN
     367          28 : Flxq_log_rec(GEN W, GEN a, long r, GEN T, ulong p, ulong pi, GEN m)
     368             : {
     369          28 :   long AV = 0, u = 1;
     370          28 :   GEN g = a, b;
     371             :   pari_timer ti;
     372         280 :   while (!equali1(gel(W,u)))
     373         252 :    u++;
     374          28 :   b = cindex_Flx(u, r, p, T[1]);
     375             :   while(1)
     376          17 :   {
     377             :     long i, l;
     378             :     GEN V, F, E, Ao;
     379          45 :     timer_start(&ti);
     380          45 :     V = Flxq_log_find_rel(b, r, T, p, pi, &g, &AV);
     381          45 :     if (DEBUGLEVEL>1) timer_printf(&ti,"%ld-smooth element",r);
     382          45 :     F = gel(V,1); E = gel(V,2);
     383          45 :     l = lg(F);
     384          45 :     Ao = gen_0;
     385         339 :     for(i=1; i<l; i++)
     386             :     {
     387         311 :       GEN R = gel(W,F[i]);
     388         311 :       if (signe(R)<=0)
     389          17 :         break;
     390         294 :       Ao = Fp_add(Ao, mulis(R, E[i]), m);
     391             :     }
     392          45 :     if (i==l) return subis(Ao,AV);
     393             :   }
     394             : }
     395             : 
     396             : static int
     397         301 : Flxq_log_use_index_cubic(GEN m, GEN T0, ulong p)
     398             : {
     399         301 :   pari_sp av = avma;
     400         301 :   long n = get_Flx_degree(T0), r, nb;
     401         301 :   GEN cost = smooth_best(p, n, &r, &nb);
     402         301 :   GEN cost_rho = sqrti(shifti(m,2));
     403         301 :   int use = (cost && gcmp(cost,cost_rho)<0);
     404         301 :   set_avma(av);
     405         301 :   return use;
     406             : }
     407             : 
     408             : static GEN
     409          14 : Flxq_log_index_cubic(GEN a0, GEN b0, GEN m, GEN T0, ulong p)
     410             : {
     411          14 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     412          14 :   long n = get_Flx_degree(T0), r, nb;
     413          14 :   pari_sp av = avma;
     414             :   struct Flxq_log_rel rel;
     415             :   long nbi;
     416             :   GEN W, M, S, T, a, b, Ao, Bo, e, C, R;
     417             :   pari_timer ti;
     418          14 :   GEN cost = smooth_best(p, n, &r, &nb);
     419          14 :   GEN cost_rho = sqrti(shifti(m,2));
     420          14 :   if (!cost || gcmp(cost,cost_rho)>=0) return gc_NULL(av);
     421          14 :   nbi = itos(ffsumnbirred(stoi(p), r));
     422          14 :   if (DEBUGLEVEL)
     423             :   {
     424           0 :     err_printf("Size FB=%ld, looking for %ld relations, %Ps tests needed\n", nbi, nb,cost);
     425           0 :     timer_start(&ti);
     426             :   }
     427          14 :   T = smallirred_Flx(p,n,get_Flx_var(T0), pi);
     428             :   for(;;)
     429             :   {
     430          14 :     S = Flx_ffisom(T0,T,p);
     431          14 :     a = Flx_Flxq_eval_pre(a0, S, T, p, pi);
     432          14 :     b = Flx_Flxq_eval_pre(b0, S, T, p, pi);
     433          14 :     C = Flx_shift(pol1_Flx(get_Flx_var(T)), (n+2)/3);
     434          14 :     R = Flxq_powu_pre(C,3,T,p,pi);
     435          14 :     if (DEBUGLEVEL)
     436           0 :       timer_printf(&ti," model change: %Ps",Flx_to_ZX(T));
     437          14 :     rel.nbmax=2*nb;
     438          14 :     M = cgetg(rel.nbmax+1, t_VEC);
     439          14 :     rel.rel = M;
     440          14 :     rel.nbrel = 0; rel.r = r; rel.off = 3*upowuu(p,r);
     441          14 :     rel.nb = nbi; rel.nbexp = nb; rel.nbtest=0;
     442          14 :     Flxq_log_cubic(&rel, C, R, p, pi);
     443          14 :     setlg(M,1+rel.nbrel);
     444          14 :     if (DEBUGLEVEL)
     445             :     {
     446           0 :       err_printf("\n");
     447           0 :       timer_printf(&ti," %ld relations, %ld generators (%ld tests)",rel.nbrel,rel.nb,rel.nbtest);
     448             :     }
     449          14 :     W = check_kernel(r, M, nbi, rel.off + rel.nb - nbi, T, p, pi, m);
     450          14 :     if (W) break;
     451           0 :     if (DEBUGLEVEL) timer_start(&ti);
     452           0 :     smallirred_Flx_next(T,p, pi);
     453             :   }
     454          14 :   if (DEBUGLEVEL) timer_start(&ti);
     455          14 :   Ao = Flxq_log_rec(W, a, r, T, p, pi, m);
     456          14 :   if (DEBUGLEVEL) timer_printf(&ti,"smooth element");
     457          14 :   Bo = Flxq_log_rec(W, b, r, T, p, pi, m);
     458          14 :   if (DEBUGLEVEL) timer_printf(&ti,"smooth generator");
     459          14 :   e = Fp_div(Ao, Bo, m);
     460          14 :   if (!Flx_equal(Flxq_pow_pre(b0, e, T0, p, pi), a0)) pari_err_BUG("Flxq_log");
     461          14 :   return gerepileupto(av, e);
     462             : }
     463             : 
     464       20833 : INLINE GEN Flx_frob(GEN u, ulong p) { return Flx_inflate(u, p); }
     465             : 
     466             : static GEN
     467       32413 : rel_Coppersmith(long r, GEN u, GEN v, long h, GEN R, long d, ulong p, ulong pi)
     468             : {
     469             :   GEN a, b, F, G, M;
     470       32413 :   if (degpol(Flx_gcd_pre(u,v,p,pi))) return NULL;
     471       32363 :   a = Flx_add(Flx_shift(u, h), v, p);
     472       32476 :   if (lgpol(a)==0 || !Flx_is_smooth_pre(a, r, p, pi)) return NULL;
     473        8392 :   b = Flx_add(Flx_mul_pre(R, Flx_frob(u, p), p, pi),
     474             :               Flx_shift(Flx_frob(v, p),d), p);
     475        8435 :   if (!Flx_is_smooth_pre(b, r, p, pi)) return NULL;
     476        2524 :   F = factorel(a, p); G = factorel(b, p);
     477        5052 :   M = mkmat2(vecsmall_concat(gel(F, 1), vecsmall_append(gel(G, 1), 2*p)),
     478        5052 :              vecsmall_concat(zv_z_mul(gel(F, 2),p), vecsmall_append(zv_neg(gel(G, 2)),d)));
     479        2526 :   return famatsmall_reduce(M);
     480             : }
     481             : 
     482             : GEN
     483        1357 : Flxq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R)
     484             : {
     485        1357 :   long r = V[1], h = V[2], d = V[3], p = V[4], pi = V[5], dT = V[6];
     486        1357 :   pari_sp ltop = avma;
     487        1357 :   GEN v = zero_zv(dT+2);
     488        1355 :   GEN L = cgetg(2*i+1, t_VEC);
     489        1355 :   pari_sp av = avma;
     490             :   long j;
     491        1355 :   long nbtest=0, rel = 1;
     492        1355 :   ulong lu = Flx_lead(u), lv;
     493       70719 :   for (j=1; j<=i; j++)
     494             :   {
     495             :     GEN z;
     496       69362 :     Flx_cnext(v, p);
     497       69378 :     Flx_renormalize_inplace(v, dT+2);
     498       69536 :     lv = Flx_lead(v);
     499       69520 :     set_avma(av);
     500       69510 :     if (lu != 1 && lv != 1) continue;
     501       40185 :     if (degpol(Flx_gcd_pre(u, v, p, pi))!=0) continue;
     502       27004 :     if (lu==1)
     503             :     {
     504       15026 :       z = rel_Coppersmith(r, u, v, h, R, d, p, pi);
     505       15048 :       nbtest++;
     506       15048 :       if (z) { gel(L, rel++) = z; av = avma; }
     507             :     }
     508       27026 :     if (i==j) continue;
     509       26941 :     if (lv==1)
     510             :     {
     511       17388 :       z = rel_Coppersmith(r, v, u, h, R, d, p, pi);
     512       17445 :       nbtest++;
     513       17445 :       if (z) { gel(L, rel++) = z; av = avma; }
     514             :     }
     515             :   }
     516        1357 :   setlg(L,rel);
     517        1357 :   return gerepilecopy(ltop, mkvec2(stoi(nbtest), L));
     518             : }
     519             : 
     520             : static GEN
     521          14 : Flxq_log_Coppersmith(long nbrel, long r, GEN T, ulong p, ulong pi)
     522             : {
     523             :   pari_sp av;
     524          14 :   long dT = degpol(T);
     525          14 :   long h = dT/p, d = dT-(h*p);
     526          14 :   GEN R = Flx_sub(Flx_shift(pol1_Flx(T[1]), dT), T, p);
     527          14 :   GEN u = zero_zv(dT+2);
     528             :   GEN done;
     529          14 :   long nbtest = 0, rel = 0;
     530          14 :   GEN M = cgetg(nbrel+1, t_VEC);
     531          14 :   long i = 1;
     532          14 :   GEN worker = snm_closure(is_entry("_Flxq_log_Coppersmith_worker"),
     533             :                mkvec2(mkvecsmalln(6, r,h,d,p,pi,dT), R));
     534             :   struct pari_mt pt;
     535          14 :   long running, pending = 0, stop=0;
     536          14 :   if (DEBUGLEVEL) err_printf("Coppersmith (R = %ld): ",degpol(R));
     537          14 :   mt_queue_start(&pt, worker);
     538          14 :   av = avma;
     539        1401 :   while ((running = !stop) || pending)
     540             :   {
     541             :     GEN L;
     542             :     long l, j;
     543        1387 :     Flx_cnext(u, p);
     544        1387 :     Flx_renormalize_inplace(u, dT+2);
     545        1387 :     mt_queue_submit(&pt, 0, running ? mkvec2(u, stoi(i)): NULL);
     546        1387 :     done = mt_queue_get(&pt, NULL, &pending);
     547        1387 :     if (!done) continue;
     548        1357 :     L = gel(done, 2); nbtest += itos(gel(done,1));
     549        1357 :     l = lg(L);
     550        1357 :     if (l > 1)
     551             :     {
     552        3393 :       for (j=1; j<l; j++)
     553             :       {
     554        2469 :         if (rel>nbrel) break;
     555        2429 :         gel(M,++rel) = gel(L,j);
     556        2429 :         if (DEBUGLEVEL && (rel&511UL)==0)
     557           0 :           err_printf("%ld%%[%ld] ",rel*100/nbrel,i);
     558             :       }
     559         964 :       av = avma;
     560             :     }
     561         393 :     else set_avma(av);
     562        1357 :     if (rel>nbrel) stop = 1;
     563        1357 :     i++;
     564             :   }
     565          14 :   mt_queue_end(&pt);
     566          14 :   if (DEBUGLEVEL) err_printf(": %ld tests\n", nbtest);
     567          14 :   return M;
     568             : }
     569             : 
     570             : static GEN Flxq_log_Coppersmith_d(GEN W, GEN g, long r, GEN T, ulong p, ulong pi, GEN mo);
     571             : 
     572             : static GEN
     573          69 : Flxq_log_from_rel(GEN W, GEN rel, long r, GEN T, ulong p, ulong pi, GEN m)
     574             : {
     575          69 :   pari_sp av = avma;
     576          69 :   GEN F = gel(rel,1), E = gel(rel,2), o = gen_0;
     577          69 :   long i, l = lg(F);
     578         515 :   for(i=1; i<l; i++)
     579             :   {
     580         446 :     GEN R = gel(W, F[i]);
     581         446 :     if (signe(R)==0) /* Already failed */
     582           0 :       return NULL;
     583         446 :     else if (signe(R)<0) /* Not yet tested */
     584             :     {
     585          16 :       setsigne(gel(W,F[i]),0);
     586          16 :       R = Flxq_log_Coppersmith_d(W, cindex_Flx(F[i],r,p,T[1]), r, T, p, pi, m);
     587          16 :       if (!R) return NULL;
     588             :     }
     589         446 :     o = Fp_add(o, mulis(R, E[i]), m);
     590             :   }
     591          69 :   return gerepileuptoint(av, o);
     592             : }
     593             : 
     594             : static GEN
     595          70 : Flxq_log_Coppersmith_d(GEN W, GEN g, long r, GEN T, ulong p, ulong pi, GEN mo)
     596             : {
     597          70 :   pari_sp av = avma, av2;
     598          70 :   long dg = degpol(g), k = r-1, m = maxss((dg-k)/2,0);
     599          70 :   long i, j, l = dg-m, N;
     600          70 :   GEN v = cgetg(k+m+1,t_MAT);
     601          70 :   long dT = degpol(T);
     602          70 :   long h = dT/p, d = dT-h*p;
     603          70 :   GEN R = Flx_rem_pre(Flx_shift(pol1_Flx(T[1]), dT), T, p, pi);
     604          70 :   GEN z = Flx_rem_pre(Flx_shift(pol1_Flx(T[1]), h), g, p, pi);
     605         470 :   for(i=1; i<=k+m; i++)
     606             :   {
     607         400 :     gel(v,i) = Flx_to_Flv(Flx_shift(z,-l),m);
     608         400 :     z = Flx_rem_pre(Flx_shift(z,1),g,p,pi);
     609             :   }
     610          70 :   v = Flm_ker(v,p);
     611         405 :   for(i=1; i<=k; i++)
     612         335 :     gel(v,i) = Flv_to_Flx(gel(v,i),T[1]);
     613          70 :   N = upowuu(p,k);
     614          70 :   av2 = avma;
     615        1993 :   for (i=1; i<N; i++)
     616             :   {
     617             :     GEN p0,q,qh,a,b;
     618        1992 :     ulong el = i;
     619        1992 :     set_avma(av2);
     620        1992 :     q = pol0_Flx(T[1]);
     621       11684 :     for (j=1; j<=k; j++)
     622             :     {
     623        9692 :       ulong r = el % p;
     624        9692 :       el /= p;
     625        9692 :       if (r) q = Flx_add(q, Flx_Fl_mul(gel(v,j), r, p), p);
     626             :     }
     627        1992 :     qh = Flx_shift(q, h);
     628        1992 :     p0 = Flx_rem_pre(qh, g, p, pi);
     629        1992 :     b = Flx_sub(Flx_mul_pre(R, Flx_frob(q, p), p, pi),
     630             :                 Flx_shift(Flx_frob(p0, p), d), p);
     631        1992 :     if (lgpol(b)==0 || !Flx_is_smooth_pre(b, r, p, pi)) continue;
     632         165 :     a = Flx_div_pre(Flx_sub(qh, p0, p), g, p, pi);
     633         165 :     if (degpol(Flx_gcd_pre(a, q, p, pi)) && degpol(Flx_gcd_pre(a, p0, p, pi)))
     634          48 :       continue;
     635         117 :     if (!(lgpol(a)==0 || !Flx_is_smooth_pre(a, r, p, pi)))
     636             :     {
     637          69 :       GEN F = factorel(b, p);
     638          69 :       GEN G = factorel(a, p);
     639          69 :       GEN FG = vecsmall_concat(vecsmall_append(gel(F, 1), 2*p), gel(G, 1));
     640          69 :       GEN E  = vecsmall_concat(vecsmall_append(gel(F, 2), -d),
     641          69 :           zv_z_mul(gel(G, 2),-p));
     642          69 :       GEN R  = famatsmall_reduce(mkmat2(FG, E));
     643          69 :       GEN l  = Flxq_log_from_rel(W, R, r, T, p, pi, mo);
     644          69 :       if (!l) continue;
     645          69 :       l = Fp_divu(l,p,mo);
     646          69 :       if (dg <= r)
     647             :       {
     648          16 :         long idx = Flx_cindex(g, p);
     649          16 :         affii(l, gel(W, idx));
     650          16 :         if (DEBUGLEVEL>1) err_printf("Found %lu\n", idx);
     651             :       }
     652          69 :       return gerepileuptoint(av, l);
     653             :     }
     654             :   }
     655           1 :   set_avma(av);
     656           1 :   return NULL;
     657             : }
     658             : 
     659             : static GEN
     660          28 : Flxq_log_Coppersmith_rec(GEN W, long r2, GEN a, long r, GEN T, ulong p, ulong pi, GEN m)
     661             : {
     662          28 :   GEN b = polx_Flx(T[1]);
     663          28 :   long AV = 0;
     664          28 :   GEN g = a, bad = pol0_Flx(T[1]);
     665             :   pari_timer ti;
     666             :   while(1)
     667           1 :   {
     668             :     long i, l;
     669             :     GEN V, F, E, Ao;
     670          29 :     timer_start(&ti);
     671          29 :     V = Flxq_log_find_rel(b, r2, T, p, pi, &g, &AV);
     672          29 :     if (DEBUGLEVEL>1) timer_printf(&ti,"%ld-smooth element",r2);
     673          29 :     F = gel(V,1); E = gel(V,2);
     674          29 :     l = lg(F);
     675          29 :     Ao = gen_0;
     676         200 :     for(i=1; i<l; i++)
     677             :     {
     678         172 :       GEN Fi = cindex_Flx(F[i], r2, p, T[1]);
     679             :       GEN R;
     680         172 :       if (degpol(Fi) <= r)
     681             :       {
     682         118 :         if (signe(gel(W,F[i]))==0)
     683           0 :           break;
     684         118 :         else if (signe(gel(W,F[i]))<0)
     685             :         {
     686           0 :           setsigne(gel(W,F[i]),0);
     687           0 :           R = Flxq_log_Coppersmith_d(W,Fi,r,T,p,pi,m);
     688             :         } else
     689         118 :           R = gel(W,F[i]);
     690             :       }
     691             :       else
     692             :       {
     693          54 :         if (Flx_equal(Fi,bad)) break;
     694          54 :         R = Flxq_log_Coppersmith_d(W,Fi,r,T,p,pi,m);
     695          54 :         if (!R) bad = Fi;
     696             :       }
     697         172 :       if (!R) break;
     698         171 :       Ao = Fp_add(Ao, mulis(R, E[i]), m);
     699             :     }
     700          29 :     if (i==l) return subis(Ao,AV);
     701             :   }
     702             : }
     703             : 
     704             : static GEN
     705          14 : Flxq_log_index_Coppersmith(GEN a0, GEN b0, GEN m, GEN T0, ulong p)
     706             : {
     707          14 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     708          14 :   pari_sp av = avma;
     709          14 :   GEN  M, S, a, b, Ao=NULL, Bo=NULL, W, e;
     710             :   pari_timer ti;
     711          14 :   double rf = p ==3 ? 1.2 : .9;
     712          14 :   long n = degpol(T0), r = (long) sqrt(n*rf);
     713             :   GEN T;
     714          14 :   long r2 = 3*r/2;
     715          14 :   long nbi = itos(ffsumnbirred(utoipos(p), r)), nbrel=nbi*5/4;
     716          14 :   if (DEBUGLEVEL)
     717             :   {
     718           0 :     err_printf("Coppersmith: Parameters r=%ld r2=%ld\n", r,r2);
     719           0 :     err_printf("Coppersmith: Size FB=%ld rel. needed=%ld\n", nbi, nbrel);
     720           0 :     timer_start(&ti);
     721             :   }
     722          14 :   T = smallirred_Flx(p,n,get_Flx_var(T0), pi);
     723          14 :   S = Flx_ffisom(T0,T,p);
     724          14 :   a = Flx_Flxq_eval_pre(a0, S, T, p, pi);
     725          14 :   b = Flx_Flxq_eval_pre(b0, S, T, p, pi);
     726          14 :   if (DEBUGLEVEL) timer_printf(&ti,"model change");
     727          14 :   M = Flxq_log_Coppersmith(nbrel, r, T, p, pi);
     728          14 :   if (DEBUGLEVEL) timer_printf(&ti,"relations");
     729          14 :   W = check_kernel(r, M, nbi, 3*upowuu(p,r), T, p, pi, m);
     730          14 :   timer_start(&ti);
     731          14 :   Ao = Flxq_log_Coppersmith_rec(W, r2, a, r, T, p, pi, m);
     732          14 :   if (DEBUGLEVEL) timer_printf(&ti,"smooth element");
     733          14 :   Bo = Flxq_log_Coppersmith_rec(W, r2, b, r, T, p, pi, m);
     734          14 :   if (DEBUGLEVEL) timer_printf(&ti,"smooth generator");
     735          14 :   e = Fp_div(Ao, Bo, m);
     736          14 :   if (!Flx_equal(Flxq_pow_pre(b0,e,T0,p,pi), a0)) pari_err_BUG("Flxq_log");
     737          14 :   return gerepileupto(av, e);
     738             : }
     739             : 
     740             : GEN
     741          28 : Flxq_log_index(GEN a, GEN b, GEN m, GEN T, ulong p)
     742             : {
     743          28 :   long d = get_Flx_degree(T);
     744          28 :   if (p==3 || (p==5 && d>41))
     745          14 :     return Flxq_log_index_Coppersmith(a, b, m, T, p);
     746          14 :   else    return Flxq_log_index_cubic(a, b, m, T, p);
     747             : }
     748             : 
     749             : int
     750      164525 : Flxq_log_use_index(GEN m, GEN T, ulong p)
     751             : {
     752      164525 :   long d = get_Flx_degree(T);
     753      164525 :   if (p==3 || (p==5 && d>41))
     754       24283 :     return 1;
     755      140242 :   else if (d<=4 || d==6)
     756      139941 :     return 0;
     757             :   else
     758         301 :     return Flxq_log_use_index_cubic(m, T, p);
     759             : }

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