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 - FlxX.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.18.1 lcov report (development 30145-32f0acf4da) Lines: 1199 1482 80.9 %
Date: 2025-04-18 09:18:41 Functions: 150 196 76.5 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2019  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             : /***********************************************************************/
      19             : /**                                                                   **/
      20             : /**                               FlxX                                **/
      21             : /**                                                                   **/
      22             : /***********************************************************************/
      23             : 
      24             : /* FlxX are t_POL with Flx coefficients.
      25             :  * Normally the variable ordering should be respected.*/
      26             : 
      27             : /*Similar to normalizepol, in place*/
      28             : /*FlxX_renormalize=zxX_renormalize */
      29             : GEN
      30    15238377 : FlxX_renormalize(GEN /*in place*/ x, long lx)
      31             : {
      32             :   long i;
      33    20068686 :   for (i = lx-1; i>1; i--)
      34    19289839 :     if (lgpol(gel(x,i))) break;
      35    15238364 :   stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
      36    15238846 :   setlg(x, i+1); setsigne(x, i!=1); return x;
      37             : }
      38             : 
      39             : GEN
      40      758609 : pol1_FlxX(long v, long sv)
      41             : {
      42      758609 :   GEN z = cgetg(3, t_POL);
      43      758609 :   z[1] = evalsigne(1) | evalvarn(v);
      44      758609 :   gel(z,2) = pol1_Flx(sv); return z;
      45             : }
      46             : 
      47             : GEN
      48      690500 : polx_FlxX(long v, long sv)
      49             : {
      50      690500 :   GEN z = cgetg(4, t_POL);
      51      690500 :   z[1] = evalsigne(1) | evalvarn(v);
      52      690500 :   gel(z,2) = pol0_Flx(sv);
      53      690500 :   gel(z,3) = pol1_Flx(sv); return z;
      54             : }
      55             : 
      56             : long
      57     2869415 : FlxY_degreex(GEN b)
      58             : {
      59     2869415 :   long deg = 0, i;
      60     2869415 :   if (!signe(b)) return -1;
      61    10342270 :   for (i = 2; i < lg(b); ++i)
      62     7472707 :     deg = maxss(deg, degpol(gel(b, i)));
      63     2869563 :   return deg;
      64             : }
      65             : 
      66             : /*Lift coefficient of B to constant Flx, to give a FlxY*/
      67             : GEN
      68        2498 : Fly_to_FlxY(GEN B, long sv)
      69             : {
      70        2498 :   long lb=lg(B);
      71             :   long i;
      72        2498 :   GEN b=cgetg(lb,t_POL);
      73        2497 :   b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
      74       64850 :   for (i=2; i<lb; i++)
      75       62361 :     gel(b,i) = Fl_to_Flx(B[i], sv);
      76        2489 :   return FlxX_renormalize(b, lb);
      77             : }
      78             : 
      79             : GEN
      80     2665351 : zxX_to_FlxX(GEN B, ulong p)
      81             : {
      82     2665351 :   long i, lb = lg(B);
      83     2665351 :   GEN b = cgetg(lb,t_POL);
      84     8688960 :   for (i=2; i<lb; i++)
      85     6029077 :     gel(b,i) = zx_to_Flx(gel(B,i), p);
      86     2659883 :   b[1] = B[1]; return FlxX_renormalize(b, lb);
      87             : }
      88             : 
      89             : GEN
      90     2770931 : FlxX_to_ZXX(GEN B)
      91             : {
      92     2770931 :   long i, lb = lg(B);
      93     2770931 :   GEN b = cgetg(lb,t_POL);
      94     8886123 :   for (i=2; i<lb; i++)
      95             :   {
      96     6116625 :     GEN c = gel(B,i);
      97     6116625 :     switch(lgpol(c))
      98             :     {
      99      267438 :       case 0:  c = gen_0; break;
     100      795225 :       case 1:  c = utoi(c[2]); break;
     101     5053924 :       default: c = Flx_to_ZX(c); break;
     102             :     }
     103     6114856 :     gel(b,i) = c;
     104             :   }
     105     2769498 :   b[1] = B[1]; return b;
     106             : }
     107             : 
     108             : /* Note: v is used _only_ for the t_INT. It must match
     109             :  * the variable of any t_POL coefficients. */
     110             : GEN
     111     2818163 : ZXX_to_FlxX(GEN B, ulong p, long v)
     112             : {
     113     2818163 :   long lb=lg(B);
     114             :   long i;
     115     2818163 :   GEN b=cgetg(lb,t_POL);
     116     2818263 :   b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
     117    13781484 :   for (i=2; i<lb; i++)
     118    10964872 :     switch (typ(gel(B,i)))
     119             :     {
     120     2143720 :     case t_INT:
     121     2143720 :       gel(b,i) = Z_to_Flx(gel(B,i), p, evalvarn(v));
     122     2143608 :       break;
     123     8823126 :     case t_POL:
     124     8823126 :       gel(b,i) = ZX_to_Flx(gel(B,i), p);
     125     8821587 :       break;
     126             :     }
     127     2816612 :   return FlxX_renormalize(b, lb);
     128             : }
     129             : 
     130             : GEN
     131           0 : ZXXV_to_FlxXV(GEN x, ulong p, long v)
     132           0 : { pari_APPLY_type(t_VEC, ZXX_to_FlxX(gel(x,i), p, v)) }
     133             : 
     134             : GEN
     135         512 : ZXXT_to_FlxXT(GEN x, ulong p, long v)
     136             : {
     137         512 :   if (typ(x) == t_POL)
     138         491 :     return ZXX_to_FlxX(x, p, v);
     139             :   else
     140          63 :     pari_APPLY_type(t_VEC, ZXXT_to_FlxXT(gel(x,i), p, v))
     141             : }
     142             : 
     143             : GEN
     144      319858 : FlxX_to_FlxC(GEN x, long N, long sv)
     145             : {
     146             :   long i, l;
     147             :   GEN z;
     148      319858 :   l = lg(x)-1; x++;
     149      319858 :   if (l > N+1) l = N+1; /* truncate higher degree terms */
     150      319858 :   z = cgetg(N+1,t_COL);
     151     2417645 :   for (i=1; i<l ; i++) gel(z,i) = gel(x,i);
     152     3486844 :   for (   ; i<=N; i++) gel(z,i) = pol0_Flx(sv);
     153      319858 :   return z;
     154             : }
     155             : 
     156             : /* matrix whose entries are given by the coeffs of the polynomial v in
     157             :  * two variables (considered as degree n polynomials) */
     158             : GEN
     159       57220 : FlxX_to_Flm(GEN v, long n)
     160             : {
     161       57220 :   long j, N = lg(v)-1;
     162       57220 :   GEN y = cgetg(N, t_MAT);
     163       57221 :   v++;
     164      196015 :   for (j=1; j<N; j++) gel(y,j) = Flx_to_Flv(gel(v,j), n);
     165       57217 :   return y;
     166             : }
     167             : 
     168             : GEN
     169      364633 : FlxX_to_Flx(GEN f)
     170             : {
     171      364633 :   long i, l = lg(f);
     172      364633 :   GEN V = cgetg(l, t_VECSMALL);
     173      364634 :   V[1] = ((ulong)f[1])&VARNBITS;
     174     3496703 :   for(i=2; i<l; i++)
     175     3132069 :     V[i] = lgpol(gel(f,i)) ? mael(f,i,2): 0L;
     176      364634 :   return V;
     177             : }
     178             : 
     179             : GEN
     180      221456 : Flm_to_FlxX(GEN x, long v,long w)
     181             : {
     182      221456 :   long j, lx = lg(x);
     183      221456 :   GEN y = cgetg(lx+1, t_POL);
     184      221456 :   y[1]=evalsigne(1) | v;
     185      221456 :   y++;
     186      814219 :   for (j=1; j<lx; j++) gel(y,j) = Flv_to_Flx(gel(x,j), w);
     187      221437 :   return FlxX_renormalize(--y, lx+1);
     188             : }
     189             : 
     190             : /* P(X,Y) --> P(Y,X), n is the degree in Y */
     191             : GEN
     192      181750 : FlxX_swap(GEN x, long n, long ws)
     193             : {
     194      181750 :   long j, lx = lg(x), ly = n+3;
     195      181750 :   GEN y = cgetg(ly, t_POL);
     196      181756 :   y[1] = x[1];
     197     1168622 :   for (j=2; j<ly; j++)
     198             :   {
     199             :     long k;
     200      986867 :     GEN p1 = cgetg(lx, t_VECSMALL);
     201      986866 :     p1[1] = ws;
     202    11225263 :     for (k=2; k<lx; k++)
     203    10238397 :       if (j<lg(gel(x,k)))
     204     7199276 :         p1[k] = mael(x,k,j);
     205             :       else
     206     3039121 :         p1[k] = 0;
     207      986866 :     gel(y,j) = Flx_renormalize(p1,lx);
     208             :   }
     209      181755 :   return FlxX_renormalize(y,ly);
     210             : }
     211             : 
     212             : static GEN
     213     4359701 : zxX_to_Kronecker_spec(GEN P, long lp, long n)
     214             : { /* P(X) = sum Pi(Y) * X^i, return P( Y^(2n-1) ) */
     215     4359701 :   long i, j, k, l, N = (n<<1) + 1;
     216     4359701 :   GEN y = cgetg((N-2)*lp + 2, t_VECSMALL) + 2;
     217    28820270 :   for (k=i=0; i<lp; i++)
     218             :   {
     219    28783883 :     GEN c = gel(P,i);
     220    28783883 :     l = lg(c);
     221    28783883 :     if (l-3 >= n)
     222           0 :       pari_err_BUG("zxX_to_Kronecker, P is not reduced mod Q");
     223   168688772 :     for (j=2; j < l; j++) y[k++] = c[j];
     224    28783847 :     if (i == lp-1) break;
     225   219122349 :     for (   ; j < N; j++) y[k++] = 0;
     226             :   }
     227     4359634 :   y -= 2;
     228     4359634 :   y[1] = 0; setlg(y, k+2); return y;
     229             : }
     230             : 
     231             : GEN
     232     3773434 : zxX_to_Kronecker(GEN P, GEN Q)
     233             : {
     234     3773434 :   GEN z = zxX_to_Kronecker_spec(P+2, lg(P)-2, degpol(Q));
     235     3773445 :   z[1] = P[1]; return z;
     236             : }
     237             : 
     238             : GEN
     239      348540 : FlxX_add(GEN x, GEN y, ulong p)
     240             : {
     241             :   long i,lz;
     242             :   GEN z;
     243      348540 :   long lx=lg(x);
     244      348540 :   long ly=lg(y);
     245      348540 :   if (ly>lx) swapspec(x,y, lx,ly);
     246      348540 :   lz = lx; z = cgetg(lz, t_POL); z[1]=x[1];
     247     3922222 :   for (i=2; i<ly; i++) gel(z,i) = Flx_add(gel(x,i), gel(y,i), p);
     248     2148291 :   for (   ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
     249      348525 :   return FlxX_renormalize(z, lz);
     250             : }
     251             : 
     252             : GEN
     253         245 : FlxX_Flx_add(GEN y, GEN x, ulong p)
     254             : {
     255         245 :   long i, lz = lg(y);
     256             :   GEN z;
     257         245 :   if (signe(y) == 0) return scalarpol(x, varn(y));
     258         245 :   z = cgetg(lz,t_POL); z[1] = y[1];
     259         245 :   gel(z,2) = Flx_add(gel(y,2), x, p);
     260         245 :   if (lz == 3) z = FlxX_renormalize(z,lz);
     261             :   else
     262        1071 :     for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
     263         245 :   return z;
     264             : }
     265             : 
     266             : GEN
     267       11662 : FlxX_Flx_sub(GEN y, GEN x, ulong p)
     268             : {
     269       11662 :   long i, lz = lg(y);
     270             :   GEN z;
     271       11662 :   if (signe(y) == 0) return scalarpol(x, varn(y));
     272       11662 :   z = cgetg(lz,t_POL); z[1] = y[1];
     273       11662 :   gel(z,2) = Flx_sub(gel(y,2), x, p);
     274       11662 :   if (lz == 3) z = FlxX_renormalize(z,lz);
     275             :   else
     276       84532 :     for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
     277       11662 :   return z;
     278             : }
     279             : 
     280             : GEN
     281        2657 : FlxX_neg(GEN x, ulong p)
     282             : {
     283        2657 :   long i, lx=lg(x);
     284        2657 :   GEN z = cgetg(lx, t_POL);
     285        2657 :   z[1]=x[1];
     286       45554 :   for (i=2; i<lx; i++) gel(z,i) = Flx_neg(gel(x,i), p);
     287        2657 :   return z;
     288             : }
     289             : 
     290             : GEN
     291         761 : FlxX_Fl_mul(GEN x, ulong y, ulong p)
     292             : {
     293         761 :   long i, lx=lg(x);
     294         761 :   GEN z = cgetg(lx, t_POL);
     295         761 :   z[1]=x[1];
     296        3667 :   for (i=2; i<lx; i++) gel(z,i) = Flx_Fl_mul(gel(x,i), y, p);
     297         761 :   return FlxX_renormalize(z, lx);
     298             : }
     299             : 
     300             : GEN
     301           0 : FlxX_triple(GEN x, ulong p)
     302             : {
     303           0 :   long i, lx=lg(x);
     304           0 :   GEN z = cgetg(lx, t_POL);
     305           0 :   z[1]=x[1];
     306           0 :   for (i=2; i<lx; i++) gel(z,i) = Flx_triple(gel(x,i), p);
     307           0 :   return FlxX_renormalize(z, lx);
     308             : }
     309             : 
     310             : GEN
     311         761 : FlxX_double(GEN x, ulong p)
     312             : {
     313         761 :   long i, lx=lg(x);
     314         761 :   GEN z = cgetg(lx, t_POL);
     315         761 :   z[1]=x[1];
     316        6088 :   for (i=2; i<lx; i++) gel(z,i) = Flx_double(gel(x,i), p);
     317         761 :   return FlxX_renormalize(z, lx);
     318             : }
     319             : 
     320             : GEN
     321       84241 : FlxX_deriv(GEN z, ulong p)
     322             : {
     323       84241 :   long i,l = lg(z)-1;
     324             :   GEN x;
     325       84241 :   if (l < 2) l = 2;
     326       84241 :   x = cgetg(l, t_POL); x[1] = z[1];
     327      903912 :   for (i=2; i<l; i++) gel(x,i) = Flx_mulu(gel(z,i+1), (ulong) i-1, p);
     328       84242 :   return FlxX_renormalize(x,l);
     329             : }
     330             : 
     331             : GEN
     332           0 : FlxX_translate1(GEN P, long p, long n)
     333             : {
     334             :   GEN Q;
     335           0 :   long i, l, ws, lP = lgpol(P);
     336           0 :   if (!lP) return gcopy(P);
     337           0 :   ws = mael(P,2,1);
     338           0 :   Q = FlxX_swap(P, n, ws);
     339           0 :   l = lg(Q);
     340           0 :   for (i=2; i<l; i++) gel(Q, i) = Flx_translate1(gel(Q, i), p);
     341           0 :   return FlxX_swap(Q, lP, ws);
     342             : }
     343             : 
     344             : GEN
     345           0 : zlxX_translate1(GEN P, long p, long e, long n)
     346             : {
     347             :   GEN Q;
     348           0 :   long i, l, ws, lP = lgpol(P);
     349           0 :   if (!lP) return gcopy(P);
     350           0 :   ws = mael(P,2,1);
     351           0 :   Q = FlxX_swap(P, n, ws);
     352           0 :   l = lg(Q);
     353           0 :   for (i=2; i<l; i++) gel(Q, i) = zlx_translate1(gel(Q, i), p, e);
     354           0 :   return FlxX_swap(Q, lP, ws);
     355             : }
     356             : 
     357             : static GEN
     358      110317 : FlxX_subspec(GEN x, GEN y, ulong p, long lx, long ly)
     359             : {
     360             :   long i,lz;
     361             :   GEN z;
     362             : 
     363      110317 :   if (ly <= lx)
     364             :   {
     365      110317 :     lz = lx+2; z = cgetg(lz, t_POL);
     366     3346614 :     for (i=0; i<ly; i++) gel(z,i+2) = Flx_sub(gel(x,i),gel(y,i),p);
     367      112124 :     for (   ; i<lx; i++) gel(z,i+2) = Flx_copy(gel(x,i));
     368             :   }
     369             :   else
     370             :   {
     371           0 :     lz = ly+2; z = cgetg(lz, t_POL);
     372           0 :     for (i=0; i<lx; i++) gel(z,i+2) = Flx_sub(gel(x,i),gel(y,i),p);
     373           0 :     for (   ; i<ly; i++) gel(z,i+2) = Flx_neg(gel(y,i),p);
     374             :   }
     375      110317 :   z[1] = 0; return FlxX_renormalize(z, lz);
     376             : }
     377             : 
     378             : GEN
     379      623866 : FlxX_sub(GEN x, GEN y, ulong p)
     380             : {
     381             :   long lx,ly,i,lz;
     382             :   GEN z;
     383      623866 :   lx = lg(x); ly = lg(y);
     384      623866 :   lz=maxss(lx,ly);
     385      623866 :   z = cgetg(lz,t_POL);
     386      623864 :   if (lx >= ly)
     387             :   {
     388      109985 :     z[1] = x[1];
     389      635507 :     for (i=2; i<ly; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
     390      388611 :     for (   ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
     391      109985 :     if (lx==ly) z = FlxX_renormalize(z, lz);
     392             :   }
     393             :   else
     394             :   {
     395      513879 :     z[1] = y[1];
     396     1294806 :     for (i=2; i<lx; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
     397     1381470 :     for (   ; i<ly; i++) gel(z,i) = Flx_neg(gel(y,i),p);
     398             :   }
     399      623807 :   if (!lgpol(z)) { set_avma((pari_sp)(z + lz)); z = pol_0(varn(x)); }
     400      623843 :   return z;
     401             : }
     402             : 
     403             : GEN
     404           0 : FlxX_Flx_mul(GEN P, GEN U, ulong p)
     405             : {
     406           0 :   long i, lP = lg(P);
     407           0 :   GEN res = cgetg(lP,t_POL);
     408           0 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     409           0 :   res[1] = P[1];
     410           0 :   for(i=2; i<lP; i++) gel(res,i) = Flx_mul_pre(U,gel(P,i), p, pi);
     411           0 :   return FlxX_renormalize(res, lP);
     412             : }
     413             : 
     414             : GEN
     415     5577869 : FlxY_evalx_pre(GEN Q, ulong x, ulong p, ulong pi)
     416             : {
     417     5577869 :   long i, lb = lg(Q);
     418             :   GEN z;
     419     5577869 :   z = cgetg(lb,t_VECSMALL); z[1] = evalvarn(varn(Q));
     420    75833005 :   for (i=2; i<lb; i++) z[i] = Flx_eval_pre(gel(Q,i), x, p, pi);
     421     5579678 :   return Flx_renormalize(z, lb);
     422             : }
     423             : GEN
     424         231 : FlxY_evalx(GEN Q, ulong x, ulong p)
     425         231 : { return FlxY_evalx_pre(Q, x, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     426             : 
     427             : GEN
     428           0 : FlxY_Flx_translate(GEN P, GEN c, ulong p)
     429             : {
     430           0 :   pari_sp av = avma;
     431           0 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     432             :   GEN Q;
     433             :   long i, k, n;
     434             : 
     435           0 :   if (!signe(P) || gequal0(c)) return RgX_copy(P);
     436           0 :   Q = leafcopy(P); n = degpol(P);
     437           0 :   for (i=1; i<=n; i++)
     438             :   {
     439           0 :     for (k=n-i; k<n; k++)
     440           0 :       gel(Q,2+k) = Flx_add(gel(Q,2+k), Flx_mul_pre(gel(Q,2+k+1), c, p, pi), p);
     441           0 :     if (gc_needed(av,2))
     442             :     {
     443           0 :       if(DEBUGMEM>1)
     444           0 :         pari_warn(warnmem,"FlxY_Flx_translate, i = %ld/%ld", i,n);
     445           0 :       Q = gc_GEN(av, Q);
     446             :     }
     447             :   }
     448           0 :   return gc_GEN(av, Q);
     449             : }
     450             : 
     451             : /* allow pi = 0 */
     452             : GEN
     453    10084850 : FlxY_evalx_powers_pre(GEN pol, GEN ypowers, ulong p, ulong pi)
     454             : {
     455    10084850 :   long i, len = lg(pol);
     456    10084850 :   GEN res = cgetg(len, t_VECSMALL);
     457    10083013 :   res[1] = pol[1] & VARNBITS;
     458    34199906 :   for (i = 2; i < len; ++i)
     459    24100706 :     res[i] = Flx_eval_powers_pre(gel(pol, i), ypowers, p, pi);
     460    10099200 :   return Flx_renormalize(res, len);
     461             : }
     462             : 
     463             : /* allow pi = 0 */
     464             : ulong
     465     6761603 : FlxY_eval_powers_pre(GEN pol, GEN ypowers, GEN xpowers, ulong p, ulong pi)
     466             : {
     467     6761603 :   pari_sp av = avma;
     468     6761603 :   GEN t = FlxY_evalx_powers_pre(pol, ypowers, p, pi);
     469     6760517 :   return gc_ulong(av, Flx_eval_powers_pre(t, xpowers, p, pi));
     470             : }
     471             : 
     472             : GEN
     473      136362 : FlxY_FlxqV_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
     474             : {
     475      136362 :   long i, lP = lg(P);
     476      136362 :   GEN res = cgetg(lP,t_POL);
     477      136362 :   res[1] = P[1];
     478      930268 :   for(i=2; i<lP; i++)
     479      793906 :     gel(res,i) = Flx_FlxqV_eval_pre(gel(P,i), x, T, p, pi);
     480      136362 :   return FlxX_renormalize(res, lP);
     481             : }
     482             : GEN
     483           0 : FlxY_FlxqV_evalx(GEN P, GEN x, GEN T, ulong p)
     484           0 : { return FlxY_FlxqV_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     485             : 
     486             : GEN
     487           0 : FlxY_Flxq_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
     488             : {
     489           0 :   pari_sp av = avma;
     490           0 :   long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(P),1);
     491           0 :   GEN xp = Flxq_powers_pre(x, n, T, p, pi);
     492           0 :   return gerepileupto(av, FlxY_FlxqV_evalx_pre(P, xp, T, p, pi));
     493             : }
     494             : GEN
     495           0 : FlxY_Flxq_evalx(GEN P, GEN x, GEN T, ulong p)
     496           0 : { return FlxY_Flxq_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     497             : 
     498             : GEN
     499        7467 : FlxY_Flx_div(GEN x, GEN y, ulong p)
     500             : {
     501             :   long i, l;
     502             :   GEN z;
     503        7467 :   if (degpol(y) == 0)
     504             :   {
     505        5530 :     ulong t = uel(y,2);
     506        5530 :     if (t == 1) return x;
     507           0 :     t = Fl_inv(t, p);
     508           0 :     z = cgetg_copy(x, &l); z[1] = x[1];
     509           0 :     for (i=2; i<l; i++) gel(z,i) = Flx_Fl_mul(gel(x,i),t,p);
     510             :   }
     511             :   else
     512             :   {
     513        1936 :     ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     514        1936 :     z = cgetg_copy(x, &l); z[1] = x[1];
     515        3874 :     for (i=2; i<l; i++) gel(z,i) = Flx_div_pre(gel(x,i),y,p,pi);
     516             :   }
     517        1937 :   return z;
     518             : }
     519             : 
     520             : GEN
     521       71625 : FlxX_shift(GEN a, long n, long vs)
     522             : {
     523       71625 :   long i, l = lg(a);
     524             :   GEN  b;
     525       71625 :   if (l == 2 || !n) return a;
     526       64631 :   l += n;
     527       64631 :   if (n < 0)
     528             :   {
     529       35774 :     if (l <= 2) return pol_0(varn(a));
     530       29404 :     b = cgetg(l, t_POL); b[1] = a[1];
     531       29404 :     a -= n;
     532      612668 :     for (i=2; i<l; i++) gel(b,i) = gel(a,i);
     533             :   } else {
     534       28857 :     b = cgetg(l, t_POL); b[1] = a[1];
     535       28857 :     a -= n; n += 2;
     536      507050 :     for (i=2; i<n; i++) gel(b,i) = pol0_Flx(vs);
     537      365801 :     for (   ; i<l; i++) gel(b,i) = gel(a,i);
     538             :   }
     539       58261 :   return b;
     540             : }
     541             : 
     542             : GEN
     543       13194 : FlxX_blocks(GEN P, long n, long m, long vs)
     544             : {
     545       13194 :   GEN z = cgetg(m+1,t_VEC);
     546       13194 :   long i,j, k=2, l = lg(P);
     547       39585 :   for(i=1; i<=m; i++)
     548             :   {
     549       26389 :     GEN zi = cgetg(n+2,t_POL);
     550       26387 :     zi[1] = P[1];
     551       26387 :     gel(z,i) = zi;
     552      160472 :     for(j=2; j<n+2; j++)
     553      134172 :       gel(zi, j) = k==l ? pol0_Flx(vs) : gel(P,k++);
     554       26300 :     zi = FlxX_renormalize(zi, n+2);
     555             :   }
     556       13196 :   return z;
     557             : }
     558             : 
     559             : static GEN
     560      235489 : FlxX_recipspec(GEN x, long l, long n, long vs)
     561             : {
     562             :   long i;
     563      235489 :   GEN z = cgetg(n+2,t_POL);
     564      235489 :   z[1] = 0; z += 2;
     565     5279930 :   for(i=0; i<l; i++)
     566     5044441 :     gel(z,n-i-1) = Flx_copy(gel(x,i));
     567      242331 :   for(   ; i<n; i++)
     568        6842 :     gel(z,n-i-1) = pol0_Flx(vs);
     569      235489 :   return FlxX_renormalize(z-2,n+2);
     570             : }
     571             : 
     572             : GEN
     573        2432 : FlxX_invLaplace(GEN x, ulong p)
     574             : {
     575        2432 :   long i, d = degpol(x);
     576             :   GEN y;
     577             :   ulong t;
     578        2432 :   if (d <= 1) return gcopy(x);
     579        2425 :   t = Fl_inv(factorial_Fl(d, p), p);
     580        2425 :   y = cgetg(d+3, t_POL);
     581        2425 :   y[1] = x[1];
     582       47642 :   for (i=d; i>=2; i--)
     583             :   {
     584       45217 :     gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
     585       45219 :     t = Fl_mul(t, i, p);
     586             :   }
     587        2425 :   gel(y,3) = Flx_copy(gel(x,3));
     588        2425 :   gel(y,2) = Flx_copy(gel(x,2));
     589        2425 :   return FlxX_renormalize(y, d+3);
     590             : }
     591             : 
     592             : GEN
     593        1216 : FlxX_Laplace(GEN x, ulong p)
     594             : {
     595        1216 :   long i, d = degpol(x);
     596        1216 :   ulong t = 1;
     597             :   GEN y;
     598        1216 :   if (d <= 1) return gcopy(x);
     599        1216 :   y = cgetg(d+3, t_POL);
     600        1216 :   y[1] = x[1];
     601        1216 :   gel(y,2) = Flx_copy(gel(x,2));
     602        1216 :   gel(y,3) = Flx_copy(gel(x,3));
     603       23850 :   for (i=2; i<=d; i++)
     604             :   {
     605       22634 :     t = Fl_mul(t, i%p, p);
     606       22634 :     gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
     607             :   }
     608        1216 :   return FlxX_renormalize(y, d+3);
     609             : }
     610             : 
     611             : /***********************************************************************/
     612             : /**                                                                   **/
     613             : /**                               FlxXV                               **/
     614             : /**                                                                   **/
     615             : /***********************************************************************/
     616             : 
     617             : GEN
     618           0 : FlxXC_sub(GEN x, GEN y, ulong p)
     619           0 : { pari_APPLY_same(FlxX_sub(gel(x, i), gel(y,i), p)) }
     620             : 
     621             : static GEN
     622      138362 : FlxXV_to_FlxM_lg(GEN x, long m, long n, long sv)
     623             : {
     624             :   long i;
     625      138362 :   GEN y = cgetg(n+1, t_MAT);
     626      458220 :   for (i=1; i<=n; i++) gel(y,i) = FlxX_to_FlxC(gel(x,i), m, sv);
     627      138362 :   return y;
     628             : }
     629             : 
     630             : GEN
     631           0 : FlxXV_to_FlxM(GEN v, long n, long sv)
     632           0 : { return FlxXV_to_FlxM_lg(v, n, lg(v)-1, sv); }
     633             : 
     634             : GEN
     635       12460 : FlxXC_to_ZXXC(GEN x)
     636       62416 : { pari_APPLY_type(t_COL, FlxX_to_ZXX(gel(x,i))) }
     637             : 
     638             : GEN
     639           0 : FlxXM_to_ZXXM(GEN x)
     640           0 : { pari_APPLY_same(FlxXC_to_ZXXC(gel(x,i))) }
     641             : 
     642             : /***********************************************************************/
     643             : /**                                                                   **/
     644             : /**                               FlxqX                               **/
     645             : /**                                                                   **/
     646             : /***********************************************************************/
     647             : 
     648             : static GEN
     649     3602700 : get_FlxqX_red(GEN T, GEN *B)
     650             : {
     651     3602700 :   if (typ(T)!=t_VEC) { *B=NULL; return T; }
     652      141825 :   *B = gel(T,1); return gel(T,2);
     653             : }
     654             : 
     655             : GEN
     656      151976 : RgX_to_FlxqX(GEN x, GEN T, ulong p)
     657             : {
     658      151976 :   long i, l = lg(x);
     659      151976 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     660     2326256 :   for (i = 2; i < l; i++)
     661     2174284 :     gel(z,i) = Rg_to_Flxq(gel(x,i), T, p);
     662      151972 :   return FlxX_renormalize(z, l);
     663             : }
     664             : 
     665             : /* FlxqX are t_POL with Flxq coefficients.
     666             :  * Normally the variable ordering should be respected.*/
     667             : 
     668             : GEN
     669         590 : random_FlxqX(long d1, long v, GEN T, ulong p)
     670             : {
     671         590 :   long dT = get_Flx_degree(T), vT = get_Flx_var(T);
     672         590 :   long i, d = d1+2;
     673         590 :   GEN y = cgetg(d,t_POL); y[1] = evalsigne(1) | evalvarn(v);
     674        3124 :   for (i=2; i<d; i++) gel(y,i) = random_Flx(dT, vT, p);
     675         590 :   return FlxX_renormalize(y,d);
     676             : }
     677             : 
     678             : /*Not stack clean*/
     679             : GEN
     680     2356806 : Kronecker_to_FlxqX_pre(GEN z, GEN T, ulong p, ulong pi)
     681             : {
     682     2356806 :   long i,j,lx,l, N = (get_Flx_degree(T)<<1) + 1;
     683     2356807 :   GEN x, t = cgetg(N,t_VECSMALL);
     684     2356804 :   t[1] = get_Flx_var(T);
     685     2356804 :   l = lg(z); lx = (l-2) / (N-2);
     686     2356804 :   x = cgetg(lx+3,t_POL);
     687     2356807 :   x[1] = z[1];
     688    28859458 :   for (i=2; i<lx+2; i++)
     689             :   {
     690   370677990 :     for (j=2; j<N; j++) t[j] = z[j];
     691    26502676 :     z += (N-2);
     692    26502676 :     gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
     693             :   }
     694     2356782 :   N = (l-2) % (N-2) + 2;
     695     7565689 :   for (j=2; j<N; j++) t[j] = z[j];
     696     2356782 :   gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
     697     2356745 :   return FlxX_renormalize(x, i+1);
     698             : }
     699             : GEN
     700           0 : Kronecker_to_FlxqX(GEN z, GEN T, ulong p)
     701           0 : { return Kronecker_to_FlxqX_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     702             : 
     703             : GEN
     704     1264699 : FlxqX_red_pre(GEN z, GEN T, ulong p, ulong pi)
     705             : {
     706             :   GEN res;
     707     1264699 :   long i, l = lg(z);
     708     1264699 :   res = cgetg(l,t_POL); res[1] = z[1];
     709    13067506 :   for(i=2;i<l;i++) gel(res,i) = Flx_rem_pre(gel(z,i),T,p,pi);
     710     1264660 :   return FlxX_renormalize(res,l);
     711             : }
     712             : GEN
     713           0 : FlxqX_red(GEN z, GEN T, ulong p)
     714           0 : { return FlxqX_red_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     715             : 
     716             : static GEN
     717      293138 : FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, ulong pi, long lx, long ly)
     718             : {
     719      293138 :   pari_sp av = avma;
     720             :   GEN z,kx,ky;
     721      293138 :   long dT =  get_Flx_degree(T);
     722      293138 :   kx= zxX_to_Kronecker_spec(x,lx,dT);
     723      293138 :   ky= zxX_to_Kronecker_spec(y,ly,dT);
     724      293138 :   z = Flx_mul_pre(ky, kx, p, pi);
     725      293138 :   z = Kronecker_to_FlxqX_pre(z,T,p,pi);
     726      293138 :   return gerepileupto(av, z);
     727             : }
     728             : 
     729             : GEN
     730     1709735 : FlxqX_mul_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
     731             : {
     732     1709735 :   pari_sp av = avma;
     733     1709735 :   GEN z, kx, ky, Tm = get_Flx_mod(T);
     734     1709730 :   kx= zxX_to_Kronecker(x, Tm);
     735     1709743 :   ky= zxX_to_Kronecker(y, Tm);
     736     1709739 :   z = Flx_mul_pre(ky, kx, p, pi);
     737     1709696 :   z = Kronecker_to_FlxqX_pre(z, T, p, pi);
     738     1709649 :   return gerepileupto(av, z);
     739             : }
     740             : GEN
     741       63586 : FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
     742       63586 : { return FlxqX_mul_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     743             : 
     744             : GEN
     745      353989 : FlxqX_sqr_pre(GEN x, GEN T, ulong p, ulong pi)
     746             : {
     747      353989 :   pari_sp av = avma;
     748             :   GEN z,kx;
     749      353989 :   kx= zxX_to_Kronecker(x,get_Flx_mod(T));
     750      353987 :   z = Flx_sqr_pre(kx, p, pi);
     751      353988 :   z = Kronecker_to_FlxqX_pre(z,T,p,pi);
     752      353986 :   return gerepileupto(av, z);
     753             : }
     754             : GEN
     755        1218 : FlxqX_sqr(GEN x, GEN T, ulong p)
     756        1218 : { return FlxqX_sqr_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     757             : 
     758             : GEN
     759      155138 : FlxqX_Flxq_mul_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
     760             : {
     761      155138 :   long i, lP = lg(P);
     762      155138 :   GEN res = cgetg(lP,t_POL);
     763      155139 :   res[1] = P[1];
     764      554361 :   for(i=2; i<lP; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
     765      155112 :   return FlxX_renormalize(res, lP);
     766             : }
     767             : GEN
     768           0 : FlxqX_Flxq_mul(GEN P, GEN U, GEN T, ulong p)
     769           0 : { return FlxqX_Flxq_mul_pre(P, U, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     770             : 
     771             : GEN
     772      647912 : FlxqX_Flxq_mul_to_monic_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
     773             : {
     774      647912 :   long i, lP = lg(P);
     775      647912 :   GEN res = cgetg(lP,t_POL);
     776      647903 :   res[1] = P[1];
     777     3487089 :   for(i=2; i<lP-1; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
     778      647519 :   gel(res,lP-1) = pol1_Flx(get_Flx_var(T));
     779      647914 :   return FlxX_renormalize(res, lP);
     780             : }
     781             : GEN
     782           0 : FlxqX_Flxq_mul_to_monic(GEN P, GEN U, GEN T, ulong p)
     783             : {
     784           0 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     785           0 :   return FlxqX_Flxq_mul_to_monic_pre(P, U, T, p, pi);
     786             : }
     787             : 
     788             : GEN
     789      190041 : FlxqX_normalize_pre(GEN z, GEN T, ulong p, ulong pi)
     790             : {
     791      190041 :   GEN p1 = leading_coeff(z);
     792      190041 :   if (!lgpol(z) || (!degpol(p1) && p1[1] == 1)) return z;
     793      190020 :   return FlxqX_Flxq_mul_to_monic_pre(z, Flxq_inv_pre(p1,T,p,pi), T,p,pi);
     794             : }
     795             : GEN
     796         133 : FlxqX_normalize(GEN z, GEN T, ulong p)
     797         133 : { return FlxqX_normalize_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     798             : 
     799             : struct _FlxqXQ {
     800             :   GEN T, S;
     801             :   ulong p, pi;
     802             : };
     803             : 
     804      538530 : static GEN _FlxqX_mul(void *data,GEN a,GEN b)
     805             : {
     806      538530 :   struct _FlxqXQ *d=(struct _FlxqXQ*)data;
     807      538530 :   return FlxqX_mul_pre(a,b,d->T,d->p,d->pi);
     808             : }
     809       10283 : static GEN _FlxqX_sqr(void *data,GEN a)
     810             : {
     811       10283 :   struct _FlxqXQ *d=(struct _FlxqXQ*)data;
     812       10283 :   return FlxqX_sqr_pre(a,d->T,d->p,d->pi);
     813             : }
     814             : 
     815             : GEN
     816       10248 : FlxqX_powu_pre(GEN V, ulong n, GEN T, ulong p, ulong pi)
     817             : {
     818       10248 :   struct _FlxqXQ d; d.p = p; d.pi = pi; d.T = T;
     819       10248 :   return gen_powu(V, n, (void*)&d, &_FlxqX_sqr, &_FlxqX_mul);
     820             : }
     821             : GEN
     822           0 : FlxqX_powu(GEN V, ulong n, GEN T, ulong p)
     823           0 : { return FlxqX_powu_pre(V, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     824             : 
     825             : /* x and y in Z[Y][X]. Assume T irreducible mod p */
     826             : static GEN
     827     3150584 : FlxqX_divrem_basecase(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pr)
     828             : {
     829             :   long vx, dx, dy, dz, i, j, sx, lr;
     830             : 
     831             :   pari_sp av0, av, tetpil;
     832             :   GEN z,p1,rem,lead;
     833             : 
     834     3150584 :   if (!signe(y)) pari_err_INV("FlxqX_divrem",y);
     835     3150584 :   vx=varn(x); dy=degpol(y); dx=degpol(x);
     836     3150597 :   if (dx < dy)
     837             :   {
     838       21604 :     if (pr)
     839             :     {
     840       21352 :       av0 = avma; x = FlxqX_red_pre(x, T, p, pi);
     841       21352 :       if (pr == ONLY_DIVIDES) { set_avma(av0); return signe(x)? NULL: pol_0(vx); }
     842       21352 :       if (pr == ONLY_REM) return x;
     843       21352 :       *pr = x;
     844             :     }
     845       21604 :     return pol_0(vx);
     846             :   }
     847     3128993 :   lead = leading_coeff(y);
     848     3129002 :   if (!dy) /* y is constant */
     849             :   {
     850      326429 :     if (pr && pr != ONLY_DIVIDES)
     851             :     {
     852      321754 :       if (pr == ONLY_REM) return pol_0(vx);
     853      133819 :       *pr = pol_0(vx);
     854             :     }
     855      138494 :     if (Flx_equal1(lead)) return gcopy(x);
     856      134295 :     av0 = avma; x = FlxqX_Flxq_mul_pre(x,Flxq_inv(lead,T,p),T,p,pi);
     857      134292 :     return gerepileupto(av0,x);
     858             :   }
     859     2802573 :   av0 = avma; dz = dx-dy;
     860     2802573 :   lead = Flx_equal1(lead)? NULL: gclone(Flxq_inv_pre(lead,T,p,pi));
     861     2802603 :   set_avma(av0);
     862     2802592 :   z = cgetg(dz+3,t_POL); z[1] = x[1];
     863     2802602 :   x += 2; y += 2; z += 2;
     864             : 
     865     2802602 :   p1 = gel(x,dx); av = avma;
     866     2802602 :   gel(z,dz) = lead? gerepileupto(av, Flxq_mul_pre(p1,lead, T,p,pi)): gcopy(p1);
     867     6460793 :   for (i=dx-1; i>=dy; i--)
     868             :   {
     869     3658128 :     av=avma; p1=gel(x,i);
     870    11904490 :     for (j=i-dy+1; j<=i && j<=dz; j++)
     871     8246612 :       p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
     872     3657878 :     if (lead) p1 = Flx_mul_pre(p1, lead,p,pi);
     873     3657881 :     tetpil=avma; gel(z,i-dy) = gerepile(av,tetpil,Flx_rem_pre(p1,T,p,pi));
     874             :   }
     875     2802665 :   if (!pr) { guncloneNULL(lead); return z-2; }
     876             : 
     877     2608606 :   rem = (GEN)avma; av = (pari_sp)new_chunk(dx+3);
     878     2918722 :   for (sx=0; ; i--)
     879             :   {
     880     2918722 :     p1 = gel(x,i);
     881     8630731 :     for (j=0; j<=i && j<=dz; j++)
     882     5712413 :       p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
     883     2918318 :     tetpil=avma; p1 = Flx_rem_pre(p1, T,p,pi); if (lgpol(p1)) { sx = 1; break; }
     884      383994 :     if (!i) break;
     885      310081 :     set_avma(av);
     886             :   }
     887     2608274 :   if (pr == ONLY_DIVIDES)
     888             :   {
     889           0 :     guncloneNULL(lead);
     890           0 :     if (sx) return gc_NULL(av0);
     891           0 :     return gc_const((pari_sp)rem, z-2);
     892             :   }
     893     2608274 :   lr=i+3; rem -= lr;
     894     2608274 :   rem[0] = evaltyp(t_POL) | _evallg(lr);
     895     2608274 :   rem[1] = z[-1];
     896     2608274 :   p1 = gerepile((pari_sp)rem,tetpil,p1);
     897     2608576 :   rem += 2; gel(rem,i) = p1;
     898    16310941 :   for (i--; i>=0; i--)
     899             :   {
     900    13702352 :     av=avma; p1 = gel(x,i);
     901    44718662 :     for (j=0; j<=i && j<=dz; j++)
     902    31024004 :       p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi), p);
     903    13694658 :     tetpil=avma; gel(rem,i) = gerepile(av,tetpil, Flx_rem_pre(p1, T,p,pi));
     904             :   }
     905     2608589 :   rem -= 2;
     906     2608589 :   guncloneNULL(lead);
     907     2608601 :   if (!sx) (void)FlxX_renormalize(rem, lr);
     908     2608607 :   if (pr == ONLY_REM) return gerepileupto(av0,rem);
     909     1221211 :   *pr = rem; return z-2;
     910             : }
     911             : 
     912             : static GEN
     913        1419 : FlxqX_invBarrett_basecase(GEN T, GEN Q, ulong p, ulong pi)
     914             : {
     915        1419 :   long i, l=lg(T)-1, lr = l-1, k;
     916        1419 :   long sv=Q[1];
     917        1419 :   GEN r=cgetg(lr,t_POL); r[1]=T[1];
     918        1419 :   gel(r,2) = pol1_Flx(sv);
     919       16396 :   for (i=3;i<lr;i++)
     920             :   {
     921       14977 :     pari_sp ltop=avma;
     922       14977 :     GEN u = Flx_neg(gel(T,l-i+2),p);
     923      108758 :     for (k=3;k<i;k++)
     924       93781 :       u = Flx_sub(u, Flxq_mul_pre(gel(T,l-i+k), gel(r,k), Q, p, pi), p);
     925       14977 :     gel(r,i) = gerepileupto(ltop, u);
     926             :   }
     927        1419 :   r = FlxX_renormalize(r,lr);
     928        1419 :   return r;
     929             : }
     930             : 
     931             : /* Return new lgpol */
     932             : static long
     933      328043 : FlxX_lgrenormalizespec(GEN x, long lx)
     934             : {
     935             :   long i;
     936      359738 :   for (i = lx-1; i>=0; i--)
     937      359738 :     if (lgpol(gel(x,i))) break;
     938      328043 :   return i+1;
     939             : }
     940             : 
     941             : static GEN
     942        6711 : FlxqX_invBarrett_Newton(GEN S, GEN T, ulong p, ulong pi)
     943             : {
     944        6711 :   pari_sp av = avma;
     945        6711 :   long nold, lx, lz, lq, l = degpol(S), i, lQ;
     946        6711 :   GEN q, y, z, x = cgetg(l+2, t_POL) + 2;
     947        6711 :   long dT = get_Flx_degree(T), vT = get_Flx_var(T);
     948        6711 :   ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
     949      273213 :   for (i=0;i<l;i++) gel(x,i) = pol0_Flx(vT);
     950        6711 :   q = FlxX_recipspec(S+2,l+1,l+1,dT);
     951        6711 :   lQ = lgpol(q); q+=2;
     952             :   /* We work on _spec_ FlxX's, all the l[xzq] below are lgpol's */
     953             : 
     954             :   /* initialize */
     955        6711 :   gel(x,0) = Flxq_inv_pre(gel(q,0),T, p, pi);
     956        6711 :   if (lQ>1 && degpol(gel(q,1)) >= dT)
     957           0 :     gel(q,1) = Flx_rem_pre(gel(q,1), T, p, pi);
     958        6711 :   if (lQ>1 && lgpol(gel(q,1)))
     959        5686 :   {
     960        5686 :     GEN u = gel(q, 1);
     961        5686 :     if (!Flx_equal1(gel(x,0)))
     962           7 :       u = Flxq_mul_pre(u, Flxq_sqr_pre(gel(x,0), T,p,pi), T,p,pi);
     963        5686 :     gel(x,1) = Flx_neg(u, p); lx = 2;
     964             :   }
     965             :   else
     966        1025 :     lx = 1;
     967        6711 :   nold = 1;
     968       43278 :   for (; mask > 1; )
     969             :   { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
     970       36567 :     long i, lnew, nnew = nold << 1;
     971             : 
     972       36567 :     if (mask & 1) nnew--;
     973       36567 :     mask >>= 1;
     974             : 
     975       36567 :     lnew = nnew + 1;
     976       36567 :     lq = FlxX_lgrenormalizespec(q, minss(lQ,lnew));
     977       36567 :     z = FlxqX_mulspec(x, q, T,p,pi, lx, lq); /* FIXME: high product */
     978       36567 :     lz = lgpol(z); if (lz > lnew) lz = lnew;
     979       36567 :     z += 2;
     980             :     /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
     981       74746 :     for (i = nold; i < lz; i++) if (lgpol(gel(z,i))) break;
     982       36567 :     nold = nnew;
     983       36567 :     if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
     984             : 
     985             :     /* z + i represents (x*q - 1) / t^i */
     986       35664 :     lz = FlxX_lgrenormalizespec (z+i, lz-i);
     987       35664 :     z = FlxqX_mulspec(x, z+i, T,p,pi, lx, lz); /* FIXME: low product */
     988       35664 :     lz = lgpol(z); z += 2;
     989       35664 :     if (lz > lnew-i) lz = FlxX_lgrenormalizespec(z, lnew-i);
     990             : 
     991       35664 :     lx = lz+ i;
     992       35664 :     y  = x + i; /* x -= z * t^i, in place */
     993      278801 :     for (i = 0; i < lz; i++) gel(y,i) = Flx_neg(gel(z,i), p);
     994             :   }
     995        6711 :   x -= 2; setlg(x, lx + 2); x[1] = S[1];
     996        6711 :   return gc_GEN(av, x);
     997             : }
     998             : 
     999             : GEN
    1000        8130 : FlxqX_invBarrett_pre(GEN T, GEN Q, ulong p, ulong pi)
    1001             : {
    1002        8130 :   pari_sp ltop=avma;
    1003        8130 :   long l=lg(T), v = varn(T);
    1004             :   GEN r;
    1005        8130 :   GEN c = gel(T,l-1);
    1006        8130 :   if (l<5) return pol_0(v);
    1007        8130 :   if (l<=FlxqX_INVBARRETT_LIMIT)
    1008             :   {
    1009        1419 :     if (!Flx_equal1(c))
    1010             :     {
    1011           0 :       GEN ci = Flxq_inv_pre(c,Q,p,pi);
    1012           0 :       T = FlxqX_Flxq_mul_pre(T, ci, Q, p, pi);
    1013           0 :       r = FlxqX_invBarrett_basecase(T,Q,p,pi);
    1014           0 :       r = FlxqX_Flxq_mul_pre(r,ci,Q,p,pi);
    1015             :     } else
    1016        1419 :       r = FlxqX_invBarrett_basecase(T,Q,p,pi);
    1017             :   } else
    1018        6711 :     r = FlxqX_invBarrett_Newton(T,Q,p,pi);
    1019        8130 :   return gerepileupto(ltop, r);
    1020             : }
    1021             : GEN
    1022          76 : FlxqX_invBarrett(GEN T, GEN Q, ulong p)
    1023          76 : { return FlxqX_invBarrett_pre(T, Q, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1024             : 
    1025             : GEN
    1026      491659 : FlxqX_get_red_pre(GEN S, GEN T, ulong p, ulong pi)
    1027             : {
    1028      491659 :   if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
    1029        6674 :     retmkvec2(FlxqX_invBarrett_pre(S, T, p, pi), S);
    1030      484985 :   return S;
    1031             : }
    1032             : GEN
    1033         371 : FlxqX_get_red(GEN S, GEN T, ulong p)
    1034             : {
    1035         371 :   if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
    1036          76 :     retmkvec2(FlxqX_invBarrett(S, T, p), S);
    1037         295 :   return S;
    1038             : }
    1039             : 
    1040             : /* Compute x mod S where 2 <= degpol(S) <= l+1 <= 2*(degpol(S)-1)
    1041             :  *  * and mg is the Barrett inverse of S. */
    1042             : static GEN
    1043      110590 : FlxqX_divrem_Barrettspec(GEN x, long l, GEN mg, GEN S, GEN T, ulong p,
    1044             :   ulong pi, GEN *pr)
    1045             : {
    1046             :   GEN q, r;
    1047      110590 :   long lt = degpol(S); /*We discard the leading term*/
    1048             :   long ld, lm, lT, lmg;
    1049      110590 :   ld = l-lt;
    1050      110590 :   lm = minss(ld, lgpol(mg));
    1051      110590 :   lT  = FlxX_lgrenormalizespec(S+2,lt);
    1052      110590 :   lmg = FlxX_lgrenormalizespec(mg+2,lm);
    1053      110590 :   q = FlxX_recipspec(x+lt,ld,ld,0);               /* = rec(x)     lq<=ld*/
    1054      110590 :   q = FlxqX_mulspec(q+2,mg+2,T,p,pi,lgpol(q),lmg); /* = rec(x)*mg lq<=ld+lm*/
    1055      110590 :   q = FlxX_recipspec(q+2,minss(ld,lgpol(q)),ld,0); /* = rec(rec(x)*mg) lq<=ld*/
    1056      110590 :   if (!pr) return q;
    1057      110317 :   r = FlxqX_mulspec(q+2,S+2,T,p,pi,lgpol(q),lT);  /* = q*pol   lr<=ld+lt*/
    1058      110317 :   r = FlxX_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* = x - r   lr<=lt */
    1059      110317 :   if (pr == ONLY_REM) return r;
    1060        7688 :   *pr = r; return q;
    1061             : }
    1062             : 
    1063             : static GEN
    1064      103701 : FlxqX_divrem_Barrett(GEN x, GEN mg, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
    1065             : {
    1066      103701 :   GEN q = NULL, r = FlxqX_red_pre(x, T, p, pi);
    1067      103701 :   long l = lgpol(r), lt = degpol(S), lm = 2*lt-1, v = varn(S);
    1068             :   long i;
    1069      103701 :   if (l <= lt)
    1070             :   {
    1071           0 :     if (pr == ONLY_REM) return r;
    1072           0 :     if (pr == ONLY_DIVIDES) return signe(r)? NULL: pol_0(v);
    1073           0 :     if (pr) *pr = r;
    1074           0 :     return pol_0(v);
    1075             :   }
    1076      103701 :   if (lt <= 1)
    1077           0 :     return FlxqX_divrem_basecase(x,S,T,p,pi,pr);
    1078      103701 :   if (pr != ONLY_REM && l>lm)
    1079             :   {
    1080         764 :     long vT = get_Flx_var(T);
    1081         764 :     q = cgetg(l-lt+2, t_POL); q[1] = S[1];
    1082       56948 :     for (i=0;i<l-lt;i++) gel(q+2,i) = pol0_Flx(vT);
    1083             :   }
    1084      110672 :   while (l>lm)
    1085             :   {
    1086        6971 :     GEN zr, zq = FlxqX_divrem_Barrettspec(r+2+l-lm,lm,mg,S,T,p,pi,&zr);
    1087        6971 :     long lz = lgpol(zr);
    1088        6971 :     if (pr != ONLY_REM)
    1089             :     {
    1090        2582 :       long lq = lgpol(zq);
    1091       50816 :       for(i=0; i<lq; i++) gel(q+2+l-lm,i) = gel(zq,2+i);
    1092             :     }
    1093       72514 :     for(i=0; i<lz; i++) gel(r+2+l-lm,i) = gel(zr,2+i);
    1094        6971 :     l = l-lm+lz;
    1095             :   }
    1096      103701 :   if (pr == ONLY_REM)
    1097             :   {
    1098      102629 :     if (l > lt)
    1099      102629 :       r = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,ONLY_REM);
    1100             :     else
    1101           0 :       r = FlxX_renormalize(r, l+2);
    1102      102629 :     setvarn(r, v); return r;
    1103             :   }
    1104        1072 :   if (l > lt)
    1105             :   {
    1106         990 :     GEN zq = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,pr? &r: NULL);
    1107         990 :     if (!q) q = zq;
    1108             :     else
    1109             :     {
    1110         682 :       long lq = lgpol(zq);
    1111        6048 :       for(i=0; i<lq; i++) gel(q+2,i) = gel(zq,2+i);
    1112             :     }
    1113             :   }
    1114          82 :   else if (pr)
    1115          82 :     r = FlxX_renormalize(r, l+2);
    1116        1072 :   setvarn(q, v); q = FlxX_renormalize(q, lg(q));
    1117        1072 :   if (pr == ONLY_DIVIDES) return signe(r)? NULL: q;
    1118        1072 :   if (pr) { setvarn(r, v); *pr = r; }
    1119        1072 :   return q;
    1120             : }
    1121             : 
    1122             : GEN
    1123     1576269 : FlxqX_divrem_pre(GEN x, GEN S, GEN T, ulong p, long pi, GEN *pr)
    1124             : {
    1125             :   GEN B, y;
    1126             :   long dy, dx, d;
    1127     1576269 :   if (pr==ONLY_REM) return FlxqX_rem_pre(x, S, T, p, pi);
    1128     1576269 :   y = get_FlxqX_red(S, &B);
    1129     1576263 :   dy = degpol(y); dx = degpol(x); d = dx-dy;
    1130     1576219 :   if (!B && d+3 < FlxqX_DIVREM_BARRETT_LIMIT)
    1131     1575147 :     return FlxqX_divrem_basecase(x,y,T,p,pi,pr);
    1132             :   else
    1133             :   {
    1134        1072 :     pari_sp av = avma;
    1135        1072 :     GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
    1136        1072 :     GEN q = FlxqX_divrem_Barrett(x,mg,y,T,p,pi,pr);
    1137        1072 :     if (!q) return gc_NULL(av);
    1138        1072 :     if (!pr || pr==ONLY_DIVIDES) return gc_GEN(av, q);
    1139         799 :     return gc_all(av, 2, &q, pr);
    1140             :   }
    1141             : }
    1142             : GEN
    1143     1073724 : FlxqX_divrem(GEN x, GEN S, GEN T, ulong p, GEN *pr)
    1144             : {
    1145     1073724 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1146     1073724 :   return FlxqX_divrem_pre(x, S, T, p, pi, pr);
    1147             : }
    1148             : 
    1149             : GEN
    1150     2025925 : FlxqX_rem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
    1151             : {
    1152     2025925 :   GEN B, y = get_FlxqX_red(S, &B);
    1153     2025923 :   long dy = degpol(y), dx = degpol(x), d = dx-dy;
    1154     2025919 :   if (d < 0) return FlxqX_red_pre(x, T, p, pi);
    1155     1677968 :   if (!B && d+3 < FlxqX_REM_BARRETT_LIMIT)
    1156     1575339 :     return FlxqX_divrem_basecase(x,y, T, p, pi, ONLY_REM);
    1157             :   else
    1158             :   {
    1159      102629 :     pari_sp av=avma;
    1160      102629 :     GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
    1161      102629 :     GEN r = FlxqX_divrem_Barrett(x, mg, y, T, p, pi, ONLY_REM);
    1162      102629 :     return gerepileupto(av, r);
    1163             :   }
    1164             : }
    1165             : GEN
    1166        5949 : FlxqX_rem(GEN x, GEN S, GEN T, ulong p)
    1167        5949 : { return FlxqX_rem_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1168             : 
    1169             : /* x + y*z mod p */
    1170             : INLINE GEN
    1171      103656 : Flxq_addmul_pre(GEN x, GEN y, GEN z, GEN T, ulong p, ulong pi)
    1172             : {
    1173             :   pari_sp av;
    1174      103656 :   if (!lgpol(y) || !lgpol(z)) return Flx_rem_pre(x, T, p, pi);
    1175      102125 :   if (!lgpol(x)) return Flxq_mul_pre(z, y, T, p, pi);
    1176      102021 :   av = avma;
    1177      102021 :   return gerepileupto(av, Flx_add(x, Flxq_mul_pre(y, z, T, p, pi), p));
    1178             : }
    1179             : 
    1180             : GEN
    1181       51828 : FlxqX_div_by_X_x_pre(GEN a, GEN x, GEN T, ulong p, ulong pi, GEN *r)
    1182             : {
    1183       51828 :   long l = lg(a), i;
    1184             :   GEN z;
    1185       51828 :   if (l <= 3)
    1186             :   {
    1187           0 :     if (r) *r = l == 2? pol0_Flx(get_Flx_var(T)): Flx_copy(gel(a,2));
    1188           0 :     return pol_0(varn(a));
    1189             :   }
    1190       51828 :   l--; z = cgetg(l, t_POL); z[1] = a[1];
    1191       51828 :   gel(z, l-1) = gel(a,l);
    1192      155484 :   for (i=l-2; i>1; i--) /* z[i] = a[i+1] + x*z[i+1] */
    1193      103656 :     gel(z, i) = Flxq_addmul_pre(gel(a,i+1), x, gel(z,i+1), T, p, pi);
    1194       51828 :   if (r) *r = Flxq_addmul_pre(gel(a,2), x, gel(z,2), T, p, pi);
    1195       51828 :   return z;
    1196             : }
    1197             : 
    1198             : GEN
    1199       51828 : FlxqX_div_by_X_x(GEN a, GEN x, GEN T, ulong p, GEN *r)
    1200       51828 : { return FlxqX_div_by_X_x_pre(a, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), r); }
    1201             : 
    1202             : static GEN
    1203       13530 : FlxqX_addmulmul(GEN u, GEN v, GEN x, GEN y, GEN T, ulong p, ulong pi)
    1204             : {
    1205       13530 :   return FlxX_add(FlxqX_mul_pre(u, x, T, p, pi),
    1206             :                   FlxqX_mul_pre(v, y, T, p, pi), p);
    1207             : }
    1208             : 
    1209             : static GEN
    1210        6626 : FlxqXM_FlxqX_mul2(GEN M, GEN x, GEN y, GEN T, ulong p, ulong pi)
    1211             : {
    1212        6626 :   GEN res = cgetg(3, t_COL);
    1213        6626 :   gel(res, 1) = FlxqX_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, T, p, pi);
    1214        6626 :   gel(res, 2) = FlxqX_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, T, p, pi);
    1215        6626 :   return res;
    1216             : }
    1217             : 
    1218             : static GEN
    1219        3276 : FlxqXM_mul2(GEN A, GEN B, GEN T, ulong p, ulong pi)
    1220             : {
    1221        3276 :   GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
    1222        3276 :   GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
    1223        3276 :   GEN M1 = FlxqX_mul_pre(FlxX_add(A11,A22, p), FlxX_add(B11,B22, p), T, p, pi);
    1224        3276 :   GEN M2 = FlxqX_mul_pre(FlxX_add(A21,A22, p), B11, T, p, pi);
    1225        3276 :   GEN M3 = FlxqX_mul_pre(A11, FlxX_sub(B12,B22, p), T, p, pi);
    1226        3276 :   GEN M4 = FlxqX_mul_pre(A22, FlxX_sub(B21,B11, p), T, p, pi);
    1227        3276 :   GEN M5 = FlxqX_mul_pre(FlxX_add(A11,A12, p), B22, T, p, pi);
    1228        3276 :   GEN M6 = FlxqX_mul_pre(FlxX_sub(A21,A11, p), FlxX_add(B11,B12, p), T, p, pi);
    1229        3276 :   GEN M7 = FlxqX_mul_pre(FlxX_sub(A12,A22, p), FlxX_add(B21,B22, p), T, p, pi);
    1230        3276 :   GEN T1 = FlxX_add(M1,M4, p), T2 = FlxX_sub(M7,M5, p);
    1231        3276 :   GEN T3 = FlxX_sub(M1,M2, p), T4 = FlxX_add(M3,M6, p);
    1232        3276 :   retmkmat22(FlxX_add(T1,T2, p), FlxX_add(M3,M5, p),
    1233             :              FlxX_add(M2,M4, p), FlxX_add(T3,T4, p));
    1234             : }
    1235             : 
    1236             : /* Return [0,1;1,-q]*M */
    1237             : static GEN
    1238        3276 : FlxqX_FlxqXM_qmul(GEN q, GEN M, GEN T, ulong p, ulong pi)
    1239             : {
    1240        3276 :   GEN u = FlxqX_mul_pre(gcoeff(M,2,1), q, T,p,pi);
    1241        3276 :   GEN v = FlxqX_mul_pre(gcoeff(M,2,2), q, T,p,pi);
    1242        3276 :   retmkmat22(gcoeff(M,2,1), gcoeff(M,2,2),
    1243             :     FlxX_sub(gcoeff(M,1,1), u, p), FlxX_sub(gcoeff(M,1,2), v, p));
    1244             : }
    1245             : 
    1246             : static GEN
    1247          16 : matid2_FlxXM(long v, long sv)
    1248          16 : { retmkmat22(pol1_FlxX(v, sv),pol_0(v),pol_0(v),pol1_FlxX(v, sv)); }
    1249             : 
    1250             : static GEN
    1251           0 : matJ2_FlxXM(long v, long sv)
    1252           0 : { retmkmat22(pol_0(v),pol1_FlxX(v, sv),pol1_FlxX(v, sv),pol_0(v)); }
    1253             : 
    1254             : struct FlxqX_res
    1255             : {
    1256             :    GEN res, lc;
    1257             :    long deg0, deg1, off;
    1258             : };
    1259             : 
    1260             : INLINE void
    1261           0 : FlxqX_halfres_update(long da, long db, long dr, GEN T, ulong p, ulong pi, struct FlxqX_res *res)
    1262             : {
    1263           0 :   if (dr >= 0)
    1264             :   {
    1265           0 :     if (!Flx_equal1(res->lc))
    1266             :     {
    1267           0 :       res->lc  = Flxq_powu_pre(res->lc, da - dr, T, p, pi);
    1268           0 :       res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
    1269             :     }
    1270           0 :     if (both_odd(da + res->off, db + res->off))
    1271           0 :       res->res = Flx_neg(res->res, p);
    1272             :   } else
    1273             :   {
    1274           0 :     if (db == 0)
    1275             :     {
    1276           0 :       if (!Flx_equal1(res->lc))
    1277             :       {
    1278           0 :           res->lc  = Flxq_powu_pre(res->lc, da, T, p, pi);
    1279           0 :           res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
    1280             :       }
    1281             :     } else
    1282           0 :       res->res = pol0_Flx(get_Flx_var(T));
    1283             :   }
    1284           0 : }
    1285             : 
    1286             : static GEN
    1287        4035 : FlxqX_halfres_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb, struct FlxqX_res *res)
    1288             : {
    1289        4035 :   pari_sp av=avma;
    1290             :   GEN u,u1,v,v1, M;
    1291        4035 :   long vx = varn(a), vT = get_Flx_var(T), n = lgpol(a)>>1;
    1292        4035 :   u1 = v = pol_0(vx);
    1293        4035 :   u = v1 = pol1_FlxX(vx, vT);
    1294       22321 :   while (lgpol(b)>n)
    1295             :   {
    1296             :     GEN r, q;
    1297       18286 :     q = FlxqX_divrem(a,b, T, p, &r);
    1298       18286 :     if (res)
    1299             :     {
    1300           0 :       long da = degpol(a), db = degpol(b), dr = degpol(r);
    1301           0 :       res->lc = gel(b,db+2);
    1302           0 :       if (dr >= n)
    1303           0 :         FlxqX_halfres_update(da, db, dr, T, p, pi, res);
    1304             :       else
    1305             :       {
    1306           0 :         res->deg0 = da;
    1307           0 :         res->deg1 = db;
    1308             :       }
    1309             :     }
    1310       18286 :     a = b; b = r; swap(u,u1); swap(v,v1);
    1311       18286 :     u1 = FlxX_sub(u1, FlxqX_mul_pre(u, q, T, p, pi), p);
    1312       18286 :     v1 = FlxX_sub(v1, FlxqX_mul_pre(v, q, T, p, pi), p);
    1313       18286 :     if (gc_needed(av,2))
    1314             :     {
    1315           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_halfgcd (d = %ld)",degpol(b));
    1316           0 :       if (res)
    1317           0 :         gerepileall(av, 8, &a,&b,&u1,&v1,&u,&v,&res->res,&res->lc);
    1318             :       else
    1319           0 :         gerepileall(av, 6, &a,&b,&u1,&v1,&u,&v);
    1320             :     }
    1321             :   }
    1322        4035 :   M = mkmat22(u,v,u1,v1); *pa = a; *pb = b;
    1323           0 :   return res ? gc_all(av, 5, &M, pa, pb, &res->res, &res->lc)
    1324        4035 :              : gc_all(av, 3, &M, pa, pb);
    1325             : }
    1326             : 
    1327             : static GEN FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res);
    1328             : 
    1329             : static GEN
    1330        3366 : FlxqX_halfres_split(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
    1331             : {
    1332        3366 :   pari_sp av = avma;
    1333             :   GEN Q, R, S, V1, V2;
    1334             :   GEN x1, y1, r, q;
    1335        3366 :   long l = lgpol(x), n = l>>1, k, vT = get_Flx_var(T);
    1336        3366 :   if (lgpol(y) <= n)
    1337          16 :     { *a = RgX_copy(x); *b = RgX_copy(y); return matid2_FlxXM(varn(x), vT); }
    1338        3350 :   if (res)
    1339             :   {
    1340           0 :      res->lc = leading_coeff(y);
    1341           0 :      res->deg0 -= n;
    1342           0 :      res->deg1 -= n;
    1343           0 :      res->off += n;
    1344             :   }
    1345        3350 :   R = FlxqX_halfres_i(FlxX_shift(x,-n, vT),FlxX_shift(y,-n, vT), T, p, pi, a, b, res);
    1346        3350 :   if (res)
    1347             :   {
    1348           0 :     res->off -= n;
    1349           0 :     res->deg0 += n;
    1350           0 :     res->deg1 += n;
    1351             :   }
    1352        3350 :   V1 = FlxqXM_FlxqX_mul2(R, Flxn_red(x,n), Flxn_red(y,n), T, p, pi);
    1353        3350 :   x1 = FlxX_add(FlxX_shift(*a,n,vT), gel(V1,1), p);
    1354        3350 :   y1 = FlxX_add(FlxX_shift(*b,n,vT), gel(V1,2), p);
    1355        3350 :   if (lgpol(y1) <= n)
    1356             :   {
    1357          74 :     *a = x1; *b = y1;
    1358           0 :     return res ? gc_all(av, 5, &R, a, b, &res->res, &res->lc)
    1359          74 :                : gc_all(av, 3, &R, a, b);
    1360             :   }
    1361        3276 :   k = 2*n-degpol(y1);
    1362        3276 :   q = FlxqX_divrem(x1, y1, T, p, &r);
    1363        3276 :   if (res)
    1364             :   {
    1365           0 :     long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
    1366           0 :     if (dy1 < degpol(y))
    1367           0 :       FlxqX_halfres_update(res->deg0, res->deg1, dy1, T, p, pi, res);
    1368           0 :     res->lc = leading_coeff(y1);
    1369           0 :     res->deg0 = dx1;
    1370           0 :     res->deg1 = dy1;
    1371           0 :     if (dr >= n)
    1372             :     {
    1373           0 :       FlxqX_halfres_update(dx1, dy1, dr, T, p, pi, res);
    1374           0 :       res->deg0 = dy1;
    1375           0 :       res->deg1 = dr;
    1376             :     }
    1377           0 :     res->deg0 -= k;
    1378           0 :     res->deg1 -= k;
    1379           0 :     res->off += k;
    1380             :   }
    1381        3276 :   S = FlxqX_halfres_i(FlxX_shift(y1,-k, vT), FlxX_shift(r,-k, vT), T, p, pi, a, b, res);
    1382        3276 :   if (res)
    1383             :   {
    1384           0 :     res->deg0 += k;
    1385           0 :     res->deg1 += k;
    1386           0 :     res->off -= k;
    1387             :   }
    1388        3276 :   Q = FlxqXM_mul2(S, FlxqX_FlxqXM_qmul(q, R, T, p, pi), T, p, pi);
    1389        3276 :   V2 = FlxqXM_FlxqX_mul2(S, FlxXn_red(y1,k), FlxXn_red(r,k), T, p, pi);
    1390        3276 :   *a = FlxX_add(FlxX_shift(*a,k,vT), gel(V2,1), p);
    1391        3276 :   *b = FlxX_add(FlxX_shift(*b,k,vT), gel(V2,2), p);
    1392           0 :   return res ? gc_all(av, 5, &Q, a, b, &res->res, &res->lc)
    1393        3276 :              : gc_all(av, 3, &Q, a, b);
    1394             : }
    1395             : 
    1396             : static GEN
    1397        7401 : FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
    1398             : {
    1399        7401 :   if (lgpol(x) < FlxqX_HALFGCD_LIMIT)
    1400        4035 :     return FlxqX_halfres_basecase(x, y, T, p, pi, a, b, res);
    1401        3366 :   return FlxqX_halfres_split(x, y, T, p, pi, a, b, res);
    1402             : }
    1403             : 
    1404             : static GEN
    1405         775 : FlxqX_halfgcd_all_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb)
    1406             : {
    1407             :   GEN a, b;
    1408         775 :   GEN R = FlxqX_halfres_i(x, y, T, p, pi, &a, &b, NULL);
    1409         775 :   if (pa) *pa = a;
    1410         775 :   if (pb) *pb = b;
    1411         775 :   return R;
    1412             : }
    1413             : 
    1414             : /* Return M in GL_2(Fp[X]/(T)[Y]) such that:
    1415             : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
    1416             : */
    1417             : 
    1418             : GEN
    1419         775 : FlxqX_halfgcd_all_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b)
    1420             : {
    1421         775 :   pari_sp av = avma;
    1422             :   GEN R,q,r;
    1423         775 :   if (!signe(x))
    1424             :   {
    1425           0 :     if (a) *a = RgX_copy(y);
    1426           0 :     if (b) *b = RgX_copy(x);
    1427           0 :     return matJ2_FlxXM(varn(x),get_Flx_var(T));
    1428             :   }
    1429         775 :   if (degpol(y)<degpol(x)) return FlxqX_halfgcd_all_i(x, y, T, p, pi, a, b);
    1430         180 :   q = FlxqX_divrem_pre(y, x, T, p, pi, &r);
    1431         180 :   R = FlxqX_halfgcd_all_i(x, r, T, p, pi, a, b);
    1432         180 :   gcoeff(R,1,1) = FlxX_sub(gcoeff(R,1,1),
    1433         180 :                            FlxqX_mul_pre(q, gcoeff(R,1,2), T, p, pi), p);
    1434         180 :   gcoeff(R,2,1) = FlxX_sub(gcoeff(R,2,1),
    1435         180 :                            FlxqX_mul_pre(q, gcoeff(R,2,2), T, p, pi), p);
    1436         180 :   return !a && b ? gc_all(av, 2, &R, b): gc_all(av, 1+!!a+!!b, &R, a, b);
    1437             : }
    1438             : GEN
    1439           7 : FlxqX_halfgcd_all(GEN x, GEN y, GEN T, ulong p, GEN *a, GEN *b)
    1440           7 : { return FlxqX_halfgcd_all_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), a, b); }
    1441             : 
    1442             : GEN
    1443         253 : FlxqX_halfgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
    1444         253 : { return FlxqX_halfgcd_all_pre(x, y, T, p, pi, NULL, NULL); }
    1445             : 
    1446             : GEN
    1447           0 : FlxqX_halfgcd(GEN x, GEN y, GEN T, ulong p)
    1448           0 : { return FlxqX_halfgcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1449             : 
    1450             : static GEN
    1451      166770 : FlxqX_gcd_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
    1452             : {
    1453      166770 :   pari_sp av = avma, av0=avma;
    1454     1076592 :   while (signe(b))
    1455             :   {
    1456             :     GEN c;
    1457      909822 :     if (gc_needed(av0,2))
    1458             :     {
    1459           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (d = %ld)",degpol(b));
    1460           0 :       gerepileall(av0,2, &a,&b);
    1461             :     }
    1462      909822 :     av = avma; c = FlxqX_rem_pre(a, b, T, p, pi); a=b; b=c;
    1463             :   }
    1464      166770 :   return gc_const(av, a);
    1465             : }
    1466             : 
    1467             : GEN
    1468      175808 : FlxqX_gcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
    1469             : {
    1470      175808 :   pari_sp av = avma;
    1471      175808 :   x = FlxqX_red_pre(x, T, p, pi);
    1472      175808 :   y = FlxqX_red_pre(y, T, p, pi);
    1473      175808 :   if (!signe(x)) return gerepileupto(av, y);
    1474      167146 :   while (lgpol(y)>=FlxqX_GCD_LIMIT)
    1475             :   {
    1476         376 :     if (lgpol(y)<=(lgpol(x)>>1))
    1477             :     {
    1478           0 :       GEN r = FlxqX_rem_pre(x, y, T, p, pi);
    1479           0 :       x = y; y = r;
    1480             :     }
    1481         376 :     (void) FlxqX_halfgcd_all_pre(x,y, T, p, pi, &x, &y);
    1482         376 :     if (gc_needed(av,2))
    1483             :     {
    1484           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (y = %ld)",degpol(y));
    1485           0 :       gerepileall(av,2,&x,&y);
    1486             :     }
    1487             :   }
    1488      166770 :   return gerepileupto(av, FlxqX_gcd_basecase(x, y, T, p, pi));
    1489             : }
    1490             : GEN
    1491       23458 : FlxqX_gcd(GEN x, GEN y, GEN T, ulong p)
    1492       23458 : { return FlxqX_gcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1493             : 
    1494             : static GEN
    1495      133824 : FlxqX_extgcd_basecase(GEN a, GEN b, GEN T, ulong p,ulong pi, GEN *ptu, GEN *ptv)
    1496             : {
    1497      133824 :   pari_sp av=avma;
    1498             :   GEN u,v,d,d1,v1;
    1499      133824 :   long vx = varn(a);
    1500      133824 :   d = a; d1 = b;
    1501      133824 :   v = pol_0(vx); v1 = pol1_FlxX(vx, get_Flx_var(T));
    1502      470908 :   while (signe(d1))
    1503             :   {
    1504      337079 :     GEN r, q = FlxqX_divrem_pre(d, d1, T, p, pi, &r);
    1505      337095 :     v = FlxX_sub(v, FlxqX_mul_pre(q,v1,T, p, pi),p);
    1506      337081 :     u=v; v=v1; v1=u;
    1507      337081 :     u=r; d=d1; d1=u;
    1508      337081 :     if (gc_needed(av,2))
    1509             :     {
    1510           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_extgcd (d = %ld)",degpol(d));
    1511           0 :       gerepileall(av,5, &d,&d1,&u,&v,&v1);
    1512             :     }
    1513             :   }
    1514      133829 :   if (ptu)
    1515      133815 :     *ptu = FlxqX_div_pre(FlxX_sub(d,FlxqX_mul_pre(b,v, T,p,pi), p), a, T,p,pi);
    1516      133829 :   *ptv = v; return d;
    1517             : }
    1518             : 
    1519             : static GEN
    1520         130 : FlxqX_extgcd_halfgcd(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
    1521             : {
    1522             :   GEN u,v;
    1523         130 :   GEN V = cgetg(expu(lgpol(y))+2,t_VEC);
    1524         130 :   long i, n = 0, vs = varn(x), vT = get_Flx_var(T);
    1525         269 :   while (lgpol(y) >= FlxqX_EXTGCD_LIMIT)
    1526             :   {
    1527         139 :     if (lgpol(y)<=(lgpol(x)>>1))
    1528             :     {
    1529           0 :       GEN r, q = FlxqX_divrem_pre(x, y, T, p, pi, &r);
    1530           0 :       x = y; y = r;
    1531           0 :       gel(V,++n) = mkmat22(pol_0(vs),pol1_FlxX(vs,vT),pol1_FlxX(vs,vT),FlxX_neg(q,p));
    1532             :     } else
    1533         139 :       gel(V,++n) = FlxqX_halfgcd_all_pre(x, y, T, p, pi, &x, &y);
    1534             :   }
    1535         130 :   y = FlxqX_extgcd_basecase(x,y, T, p, pi, &u,&v);
    1536         139 :   for (i = n; i>1; i--)
    1537             :   {
    1538           9 :     GEN R = gel(V,i);
    1539           9 :     GEN u1 = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
    1540           9 :     GEN v1 = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
    1541           9 :     u = u1; v = v1;
    1542             :   }
    1543             :   {
    1544         130 :     GEN R = gel(V,1);
    1545         130 :     if (ptu)
    1546         130 :       *ptu = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
    1547         130 :     *ptv   = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
    1548             :   }
    1549         130 :   return y;
    1550             : }
    1551             : 
    1552             : /* x and y in Z[Y][X], return lift(gcd(x mod T,p, y mod T,p)). Set u and v st
    1553             :  * ux + vy = gcd (mod T,p) */
    1554             : GEN
    1555      133826 : FlxqX_extgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
    1556             : {
    1557      133826 :   pari_sp av = avma;
    1558             :   GEN d;
    1559      133826 :   x = FlxqX_red_pre(x, T, p, pi);
    1560      133824 :   y = FlxqX_red_pre(y, T, p, pi);
    1561      133824 :   if (lgpol(y)>=FlxqX_EXTGCD_LIMIT)
    1562         130 :     d = FlxqX_extgcd_halfgcd(x, y, T, p, pi, ptu, ptv);
    1563             :   else
    1564      133694 :     d = FlxqX_extgcd_basecase(x, y, T, p, pi, ptu, ptv);
    1565      133829 :   return gc_all(av, ptu?3:2, &d, ptv, ptu);
    1566             : }
    1567             : GEN
    1568      133811 : FlxqX_extgcd(GEN x, GEN y, GEN T, ulong p, GEN *ptu, GEN *ptv)
    1569             : {
    1570      133811 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1571      133811 :   return FlxqX_extgcd_pre(x, y, T, p, pi, ptu, ptv);
    1572             : }
    1573             : 
    1574             : static GEN
    1575      366700 : FlxqX_saferem(GEN P, GEN Q, GEN T, ulong p, ulong pi)
    1576             : {
    1577      366700 :   GEN U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
    1578      366712 :   if (!U) return NULL;
    1579      366712 :   Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
    1580      366719 :   return FlxqX_rem_pre(P,Q,T,p,pi);
    1581             : }
    1582             : 
    1583             : GEN
    1584           0 : FlxqX_eval(GEN x, GEN y, GEN T, ulong p)
    1585             : {
    1586             :   pari_sp av;
    1587             :   GEN p1, r;
    1588           0 :   long j, i=lg(x)-1;
    1589           0 :   if (i<=2)
    1590           0 :     return (i==2)? gcopy(gel(x,2)): pol0_Flx(get_Flx_var(T));
    1591           0 :   av=avma; p1=gel(x,i);
    1592             :   /* specific attention to sparse polynomials (see poleval)*/
    1593             :   /*You've guessed it! It's a copy-paste(tm)*/
    1594           0 :   for (i--; i>=2; i=j-1)
    1595             :   {
    1596           0 :     for (j=i; lg(gel(x,j))==1; j--)
    1597           0 :       if (j==2)
    1598             :       {
    1599           0 :         if (i!=j) y = Flxq_powu(y, i-j+1, T, p);
    1600           0 :         return gerepileupto(av, Flxq_mul(p1,y, T, p));
    1601             :       }
    1602           0 :     r = (i==j)? y: Flxq_powu(y, i-j+1, T, p);
    1603           0 :     p1 = Flx_add(Flxq_mul(p1,r,T,p), gel(x,j), p);
    1604             :   }
    1605           0 :   return gerepileupto(av, p1);
    1606             : }
    1607             : 
    1608             : GEN
    1609       91184 : FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
    1610             : {
    1611       91184 :   pari_sp av = avma;
    1612             :   ulong pi;
    1613             :   GEN U;
    1614       91184 :   if (!signe(P)) return gcopy(Q);
    1615       91184 :   if (!signe(Q)) return gcopy(P);
    1616       91184 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1617       91184 :   T = Flx_get_red_pre(T,p,pi);
    1618             :   for(;;)
    1619             :   {
    1620      313494 :     P = FlxqX_saferem(P,Q,T,p,pi);
    1621      313496 :     if (!P) return gc_NULL(av);
    1622      313496 :     if (!signe(P)) break;
    1623      222310 :     if (gc_needed(av, 1))
    1624             :     {
    1625           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_safegcd");
    1626           0 :       gerepileall(av, 2, &P,&Q);
    1627             :     }
    1628      222310 :     swap(P, Q);
    1629             :   }
    1630       91186 :   U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
    1631       91185 :   if (!U) return gc_NULL(av);
    1632       91185 :   Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
    1633       91186 :   return gerepileupto(av, Q);
    1634             : }
    1635             : 
    1636             : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
    1637             : GEN
    1638       10588 : FlxqX_saferesultant(GEN a, GEN b, GEN T, ulong p)
    1639             : {
    1640       10588 :   long vT = get_Flx_var(T), da,db,dc;
    1641             :   ulong pi;
    1642             :   pari_sp av;
    1643       10588 :   GEN c,lb, res = pol1_Flx(vT);
    1644             : 
    1645       10588 :   if (!signe(a) || !signe(b)) return pol0_Flx(vT);
    1646             : 
    1647       10588 :   da = degpol(a);
    1648       10588 :   db = degpol(b);
    1649       10588 :   if (db > da)
    1650             :   {
    1651           0 :     swapspec(a,b, da,db);
    1652           0 :     if (both_odd(da,db)) res = Flx_neg(res, p);
    1653             :   }
    1654       10588 :   if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
    1655       10588 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p); av = avma;
    1656       63762 :   while (db)
    1657             :   {
    1658       53202 :     lb = gel(b,db+2);
    1659       53202 :     c = FlxqX_saferem(a,b, T,p,pi);
    1660       53264 :     if (!c) return gc_NULL(av);
    1661       53264 :     a = b; b = c; dc = degpol(c);
    1662       53260 :     if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
    1663             : 
    1664       53246 :     if (both_odd(da,db)) res = Flx_neg(res, p);
    1665       53244 :     if (!Flx_equal1(lb))
    1666       53186 :       res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T, p, pi), T, p, pi);
    1667       53174 :     if (gc_needed(av,2))
    1668             :     {
    1669           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
    1670           0 :       gerepileall(av,3, &a,&b,&res);
    1671             :     }
    1672       53174 :     da = db; /* = degpol(a) */
    1673       53174 :     db = dc; /* = degpol(b) */
    1674             :   }
    1675       10560 :   res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T, p, pi), T, p, pi);
    1676       10574 :   return gerepileupto(av, res);
    1677             : }
    1678             : 
    1679             : static GEN
    1680           0 : FlxqX_halfres(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, GEN *r)
    1681             : {
    1682             :   struct FlxqX_res res;
    1683             :   GEN V;
    1684             :   long dB;
    1685             : 
    1686           0 :   res.res  = *r;
    1687           0 :   res.lc   = leading_coeff(y);
    1688           0 :   res.deg0 = degpol(x);
    1689           0 :   res.deg1 = degpol(y);
    1690           0 :   res.off = 0;
    1691           0 :   V = FlxqX_halfres_i(x, y, T, p, pi, a, b, &res);
    1692           0 :   dB = degpol(*b);
    1693           0 :   if (dB < degpol(y))
    1694           0 :     FlxqX_halfres_update(res.deg0, res.deg1, dB, T, p, pi, &res);
    1695           0 :   *r = res.res;
    1696           0 :   return V;
    1697             : }
    1698             : 
    1699             : static GEN
    1700          56 : FlxqX_resultant_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
    1701             : {
    1702          56 :   pari_sp av = avma;
    1703          56 :   long vT = get_Flx_var(T), da,db,dc;
    1704          56 :   GEN c,lb, res = pol1_Flx(vT);
    1705             : 
    1706          56 :   if (!signe(a) || !signe(b)) return pol0_Flx(vT);
    1707             : 
    1708          56 :   da = degpol(a);
    1709          56 :   db = degpol(b);
    1710          56 :   if (db > da)
    1711             :   {
    1712           0 :     swapspec(a,b, da,db);
    1713           0 :     if (both_odd(da,db)) res = Flx_neg(res, p);
    1714             :   }
    1715          56 :   if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
    1716         147 :   while (db)
    1717             :   {
    1718          91 :     lb = gel(b,db+2);
    1719          91 :     c = FlxqX_rem_pre(a,b, T,p,pi);
    1720          91 :     a = b; b = c; dc = degpol(c);
    1721          91 :     if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
    1722             : 
    1723          91 :     if (both_odd(da,db)) res = Flx_neg(res, p);
    1724          91 :     if (!Flx_equal1(lb))
    1725          63 :       res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T,p,pi), T,p,pi);
    1726          91 :     if (gc_needed(av,2))
    1727             :     {
    1728           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
    1729           0 :       gerepileall(av,3, &a,&b,&res);
    1730             :     }
    1731          91 :     da = db; /* = degpol(a) */
    1732          91 :     db = dc; /* = degpol(b) */
    1733             :   }
    1734          56 :   res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T,p,pi), T,p,pi);
    1735          56 :   return gerepileupto(av, res);
    1736             : }
    1737             : 
    1738             : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
    1739             : GEN
    1740          56 : FlxqX_resultant_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
    1741             : {
    1742          56 :   pari_sp av = avma;
    1743          56 :   long dx, dy, vT = get_Flx_var(T);
    1744          56 :   GEN res = pol1_Flx(vT);
    1745          56 :   if (!signe(x) || !signe(y)) return pol0_Flx(vT);
    1746          56 :   dx = degpol(x); dy = degpol(y);
    1747          56 :   if (dx < dy)
    1748             :   {
    1749          21 :     swap(x,y);
    1750          21 :     if (both_odd(dx, dy))
    1751           0 :       res = Flx_neg(res, p);
    1752             :   }
    1753          56 :   while (lgpol(y) >= FlxqX_GCD_LIMIT)
    1754             :   {
    1755           0 :     if (lgpol(y)<=(lgpol(x)>>1))
    1756             :     {
    1757           0 :       GEN r = FlxqX_rem_pre(x, y, T, p, pi);
    1758           0 :       long dx = degpol(x), dy = degpol(y), dr = degpol(r);
    1759           0 :       GEN ly = gel(y,dy+2);
    1760           0 :       if (!Flx_equal1(ly))
    1761           0 :         res = Flxq_mul_pre(res, Flxq_powu_pre(ly, dx - dr, T, p, pi), T, p, pi);
    1762           0 :       if (both_odd(dx, dy))
    1763           0 :         res = Flx_neg(res, p);
    1764           0 :       x = y; y = r;
    1765             :     }
    1766           0 :     (void) FlxqX_halfres(x, y, T, p, pi, &x, &y, &res);
    1767           0 :     if (gc_needed(av,2))
    1768             :     {
    1769           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (y = %ld)",degpol(y));
    1770           0 :       gerepileall(av,3,&x,&y,&res);
    1771             :     }
    1772             :   }
    1773          56 :   res = Flxq_mul_pre(res, FlxqX_resultant_basecase(x, y, T, p, pi), T, p, pi);
    1774          56 :   return gerepileupto(av, res);
    1775             : }
    1776             : GEN
    1777          56 : FlxqX_resultant(GEN x, GEN y, GEN T, ulong p)
    1778          56 : { return FlxqX_resultant_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1779             : 
    1780             : /* disc P = (-1)^(n(n-1)/2) lc(P)^(n - deg P' - 2) Res(P,P'), n = deg P */
    1781             : GEN
    1782          14 : FlxqX_disc(GEN P, GEN T, ulong p)
    1783             : {
    1784          14 :   pari_sp av = avma;
    1785          14 :   GEN L, dP = FlxX_deriv(P, p), D = FlxqX_resultant(P, dP, T, p);
    1786             :   long dd;
    1787          14 :   if (!lgpol(D)) return pol0_Flx(get_Flx_var(T));
    1788          14 :   dd = degpol(P) - 2 - degpol(dP); /* >= -1; > -1 iff p | deg(P) */
    1789          14 :   L = leading_coeff(P);
    1790          14 :   if (dd && !Flx_equal1(L))
    1791             :   {
    1792           0 :     ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1793           0 :     D = (dd == -1)? Flxq_div_pre(D,L,T,p,pi)
    1794           0 :                   : Flxq_mul_pre(D, Flxq_powu_pre(L, dd, T,p,pi), T,p,pi); }
    1795          14 :   if (degpol(P) & 2) D = Flx_neg(D, p);
    1796          14 :   return gerepileupto(av, D);
    1797             : }
    1798             : 
    1799             : INLINE GEN
    1800        6080 : FlxXn_recip(GEN x, long n, long v)
    1801        6080 : { return FlxX_recipspec(x+2, minss(lgpol(x), n), n, v); }
    1802             : 
    1803             : GEN
    1804        2432 : FlxqX_Newton_pre(GEN P, long n, GEN T, ulong p, ulong pi)
    1805             : {
    1806        2432 :   pari_sp av = avma;
    1807        2432 :   long d = degpol(P), vT = get_Flx_var(T);
    1808        2432 :   GEN dP = FlxXn_recip(FlxX_deriv(P, p), d, vT);
    1809        2432 :   GEN Q = FlxqXn_mul_pre(FlxqXn_inv_pre(FlxXn_recip(P, d+1, vT), n, T,p,pi),
    1810             :                          dP, n, T, p, pi);
    1811        2432 :   return gc_GEN(av, Q);
    1812             : }
    1813             : GEN
    1814           0 : FlxqX_Newton(GEN P, long n, GEN T, ulong p)
    1815           0 : { return FlxqX_Newton_pre(P, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1816             : 
    1817             : GEN
    1818        1216 : FlxqX_fromNewton_pre(GEN P, GEN T, ulong p, ulong pi)
    1819             : {
    1820        1216 :   pari_sp av = avma;
    1821        1216 :   long vT = get_Flx_var(T);
    1822        1216 :   long n = Flx_constant(constant_coeff(P))+1;
    1823        1216 :   GEN z = FlxX_neg(FlxX_shift(P, -1, vT), p);
    1824        1216 :   GEN Q = FlxXn_recip(FlxqXn_expint_pre(z, n, T, p, pi), n, vT);
    1825        1216 :   return gc_GEN(av, Q);
    1826             : }
    1827             : GEN
    1828           0 : FlxqX_fromNewton(GEN P, GEN T, ulong p)
    1829           0 : { return FlxqX_fromNewton_pre(P, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1830             : 
    1831             : GEN
    1832        1216 : FlxqX_composedsum(GEN P, GEN Q, GEN T, ulong p)
    1833             : {
    1834        1216 :   pari_sp av = avma;
    1835        1216 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1836        1216 :   long n = 1+ degpol(P)*degpol(Q);
    1837        1216 :   GEN Pl = FlxX_invLaplace(FlxqX_Newton_pre(P,n, T,p,pi), p);
    1838        1216 :   GEN Ql = FlxX_invLaplace(FlxqX_Newton_pre(Q,n, T,p,pi), p);
    1839        1216 :   GEN L = FlxX_Laplace(FlxqXn_mul_pre(Pl, Ql, n, T,p,pi), p);
    1840        1216 :   GEN R = FlxqX_fromNewton_pre(L, T, p, pi);
    1841        1216 :   GEN lead = Flxq_mul_pre(Flxq_powu_pre(leading_coeff(P),degpol(Q), T,p,pi),
    1842        1216 :                           Flxq_powu_pre(leading_coeff(Q),degpol(P), T,p,pi),
    1843             :                           T, p, pi);
    1844        1216 :   return gerepileupto(av, FlxqX_Flxq_mul_pre(R, lead, T, p, pi));
    1845             : }
    1846             : 
    1847             : GEN
    1848      223094 : FlxqXV_prod(GEN V, GEN T, ulong p)
    1849             : {
    1850      223094 :   struct _FlxqXQ d; d.p=p; d.T=T; d.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1851      223094 :   return gen_product(V, (void*)&d, &_FlxqX_mul);
    1852             : }
    1853             : 
    1854             : static GEN
    1855       32152 : FlxqV_roots_to_deg1(GEN x, GEN T, ulong p, long v)
    1856             : {
    1857       32152 :   long sv = get_Flx_var(T);
    1858      124251 :   pari_APPLY_same(deg1pol_shallow(pol1_Flx(sv),Flx_neg(gel(x,i),p),v))
    1859             : }
    1860             : 
    1861             : GEN
    1862       32152 : FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
    1863             : {
    1864       32152 :   pari_sp ltop = avma;
    1865       32152 :   GEN W = FlxqV_roots_to_deg1(V, T, p, v);
    1866       32152 :   return gerepileupto(ltop, FlxqXV_prod(W, T, p));
    1867             : }
    1868             : 
    1869             : /*******************************************************************/
    1870             : /*                                                                 */
    1871             : /*                       (Fl[X]/T(X))[Y] / S(Y)                    */
    1872             : /*                                                                 */
    1873             : /*******************************************************************/
    1874             : 
    1875             : GEN
    1876      470985 : FlxqXQ_mul_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
    1877      470985 : { return FlxqX_rem_pre(FlxqX_mul_pre(x,y,T,p,pi),S,T,p,pi); }
    1878             : GEN
    1879        1947 : FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
    1880        1947 : { return FlxqXQ_mul_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1881             : 
    1882             : GEN
    1883      261973 : FlxqXQ_sqr_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
    1884      261973 : { return FlxqX_rem_pre(FlxqX_sqr_pre(x,T,p,pi),S,T,p,pi); }
    1885             : GEN
    1886           0 : FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
    1887           0 : { return FlxqXQ_sqr_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1888             : 
    1889             : GEN
    1890          14 : FlxqXQ_invsafe_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
    1891             : {
    1892          14 :   GEN V, z = FlxqX_extgcd_pre(get_FlxqX_mod(S), x, T, p, pi, NULL, &V);
    1893          14 :   if (degpol(z)) return NULL;
    1894          14 :   z = Flxq_invsafe_pre(gel(z,2),T,p,pi);
    1895          14 :   if (!z) return NULL;
    1896          14 :   return FlxqX_Flxq_mul_pre(V, z, T, p, pi);
    1897             : }
    1898             : GEN
    1899           0 : FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
    1900           0 : { return FlxqXQ_invsafe_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1901             : 
    1902             : GEN
    1903          14 : FlxqXQ_inv_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
    1904             : {
    1905          14 :   pari_sp av = avma;
    1906          14 :   GEN U = FlxqXQ_invsafe_pre(x, S, T, p, pi);
    1907          14 :   if (!U) pari_err_INV("FlxqXQ_inv",x);
    1908          14 :   return gerepileupto(av, U);
    1909             : }
    1910             : GEN
    1911          14 : FlxqXQ_inv(GEN x, GEN S, GEN T,ulong p)
    1912          14 : { return FlxqXQ_inv_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1913             : 
    1914             : GEN
    1915           0 : FlxqXQ_div_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
    1916           0 : { return FlxqXQ_mul_pre(x, FlxqXQ_inv_pre(y,S,T,p,pi),S,T,p,pi); }
    1917             : GEN
    1918           0 : FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
    1919           0 : { return FlxqXQ_div_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1920             : 
    1921             : static GEN
    1922           0 : _FlxqX_add(void *data, GEN x, GEN y) {
    1923           0 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1924           0 :   return FlxX_add(x,y, d->p);
    1925             : }
    1926             : static GEN
    1927        5526 : _FlxqX_sub(void *data, GEN x, GEN y) {
    1928        5526 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1929        5526 :   return FlxX_sub(x,y, d->p);
    1930             : }
    1931             : #if 0
    1932             : static GEN
    1933             : _FlxqXQ_cmul(void *data, GEN P, long a, GEN x) {
    1934             :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1935             :   return FlxX_Flx_mul(x,gel(P,a+2), d->p);
    1936             : }
    1937             : #endif
    1938             : static GEN
    1939        6044 : _FlxqXQ_red(void *data, GEN x) {
    1940        6044 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1941        6044 :   return FlxqX_red_pre(x, d->T, d->p, d->pi);
    1942             : }
    1943             : static GEN
    1944      179118 : _FlxqXQ_mul(void *data, GEN x, GEN y) {
    1945      179118 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1946      179118 :   return FlxqXQ_mul_pre(x,y, d->S,d->T, d->p, d->pi);
    1947             : }
    1948             : static GEN
    1949      261525 : _FlxqXQ_sqr(void *data, GEN x) {
    1950      261525 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1951      261525 :   return FlxqXQ_sqr_pre(x, d->S,d->T, d->p, d->pi);
    1952             : }
    1953             : 
    1954             : static GEN
    1955      111276 : _FlxqXQ_one(void *data) {
    1956      111276 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1957      111276 :   return pol1_FlxX(get_FlxqX_var(d->S),get_Flx_var(d->T));
    1958             : }
    1959             : 
    1960             : static GEN
    1961         316 : _FlxqXQ_zero(void *data) {
    1962         316 :   struct _FlxqXQ *d = (struct _FlxqXQ*) data;
    1963         316 :   return pol_0(get_FlxqX_var(d->S));
    1964             : }
    1965             : 
    1966             : static struct bb_algebra FlxqXQ_algebra = { _FlxqXQ_red, _FlxqX_add,
    1967             :        _FlxqX_sub, _FlxqXQ_mul, _FlxqXQ_sqr, _FlxqXQ_one, _FlxqXQ_zero };
    1968             : 
    1969             : const struct bb_algebra *
    1970         761 : get_FlxqXQ_algebra(void **E, GEN S, GEN T, ulong p)
    1971             : {
    1972         761 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1973         761 :   GEN z = new_chunk(sizeof(struct _FlxqXQ));
    1974         761 :   struct _FlxqXQ *e = (struct _FlxqXQ *) z;
    1975         761 :   e->T = Flx_get_red_pre(T, p, pi);
    1976         761 :   e->S = FlxqX_get_red_pre(S, e->T, p, pi);
    1977         761 :   e->p = p;
    1978         761 :   e->pi= pi; *E = (void*)e;
    1979         761 :   return &FlxqXQ_algebra;
    1980             : }
    1981             : 
    1982             : static struct bb_algebra FlxqX_algebra = { _FlxqXQ_red, _FlxqX_add,
    1983             :        _FlxqX_sub, _FlxqX_mul, _FlxqX_sqr, _FlxqXQ_one, _FlxqXQ_zero };
    1984             : 
    1985             : const struct bb_algebra *
    1986           0 : get_FlxqX_algebra(void **E, GEN T, ulong p, long v)
    1987             : {
    1988           0 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1989           0 :   GEN z = new_chunk(sizeof(struct _FlxqXQ));
    1990           0 :   struct _FlxqXQ *e = (struct _FlxqXQ *) z;
    1991           0 :   e->T = Flx_get_red(T, p);
    1992           0 :   e->S = pol_x(v);
    1993           0 :   e->p = p;
    1994           0 :   e->pi= pi; *E = (void*)e;
    1995           0 :   return &FlxqX_algebra;
    1996             : }
    1997             : 
    1998             : /* x over Fq, return lift(x^n) mod S */
    1999             : GEN
    2000          91 : FlxqXQ_pow_pre(GEN x, GEN n, GEN S, GEN T, ulong p, ulong pi)
    2001             : {
    2002          91 :   pari_sp av = avma;
    2003             :   struct _FlxqXQ D;
    2004          91 :   long s = signe(n);
    2005          91 :   if (!s) return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
    2006          91 :   if (s < 0) x = FlxqXQ_inv_pre(x,S,T,p,pi);
    2007          91 :   if (is_pm1(n)) return s < 0 ? x : gcopy(x);
    2008          91 :   if (degpol(x) >= get_FlxqX_degree(S)) x = FlxqX_rem_pre(x,S,T,p,pi);
    2009          91 :   T = Flx_get_red_pre(T, p, pi);
    2010          91 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2011          91 :   D.S = S; D.T = T; D.p = p; D.pi = pi;
    2012          91 :   x = gen_pow_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
    2013          91 :   return gc_GEN(av, x);
    2014             : }
    2015             : GEN
    2016          35 : FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
    2017          35 : { return FlxqXQ_pow_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2018             : 
    2019             : /* x over Fq, return lift(x^n) mod S */
    2020             : GEN
    2021       82058 : FlxqXQ_powu_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
    2022             : {
    2023       82058 :   pari_sp av = avma;
    2024             :   struct _FlxqXQ D;
    2025       82058 :   switch(n)
    2026             :   {
    2027           0 :     case 0: return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
    2028        7690 :     case 1: return gcopy(x);
    2029         448 :     case 2: return FlxqXQ_sqr_pre(x, S, T, p, pi);
    2030             :   }
    2031       73920 :   T = Flx_get_red_pre(T, p, pi);
    2032       73920 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2033       73920 :   D.S = S; D.T = T; D.p = p; D.pi = pi;
    2034       73920 :   x = gen_powu_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
    2035       73920 :   return gc_GEN(av, x);
    2036             : }
    2037             : GEN
    2038           0 : FlxqXQ_powu(GEN x, ulong n, GEN S, GEN T, ulong p)
    2039           0 : { return FlxqXQ_powu_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2040             : 
    2041             : GEN
    2042      108241 : FlxqXQ_powers_pre(GEN x, long l, GEN S, GEN T, ulong p, ulong pi)
    2043             : {
    2044             :   struct _FlxqXQ D;
    2045      108241 :   int use_sqr = 2*degpol(x) >= get_FlxqX_degree(S);
    2046      108241 :   T = Flx_get_red_pre(T, p, pi);
    2047      108241 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2048      108241 :   D.S = S; D.T = T; D.p = p; D.pi = pi;
    2049      108241 :   return gen_powers(x, l, use_sqr, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul,&_FlxqXQ_one);
    2050             : }
    2051             : GEN
    2052           0 : FlxqXQ_powers(GEN x, long l, GEN S, GEN T, ulong p)
    2053           0 : { return FlxqXQ_powers_pre(x, l, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2054             : 
    2055             : /* Let v a linear form, return the linear form z->v(tau*z)
    2056             :    that is, v*(M_tau) */
    2057             : static GEN
    2058         506 : FlxqXQ_transmul_init(GEN tau, GEN S, GEN T, ulong p, ulong pi)
    2059             : {
    2060             :   GEN bht;
    2061         506 :   GEN h, Sp = get_FlxqX_red(S, &h);
    2062         506 :   long n = degpol(Sp), vS = varn(Sp), vT = get_Flx_var(T);
    2063         506 :   GEN ft = FlxX_recipspec(Sp+2, n+1, n+1, vT);
    2064         506 :   GEN bt = FlxX_recipspec(tau+2, lgpol(tau), n, vT);
    2065         506 :   setvarn(ft, vS); setvarn(bt, vS);
    2066         506 :   if (h)
    2067           0 :     bht = FlxqXn_mul_pre(bt, h, n-1, T, p, pi);
    2068             :   else
    2069             :   {
    2070         506 :     GEN bh = FlxqX_div_pre(FlxX_shift(tau, n-1, vT), S, T, p, pi);
    2071         506 :     bht = FlxX_recipspec(bh+2, lgpol(bh), n-1, vT);
    2072         506 :     setvarn(bht, vS);
    2073             :   }
    2074         506 :   return mkvec3(bt, bht, ft);
    2075             : }
    2076             : 
    2077             : static GEN
    2078        1071 : FlxqXQ_transmul(GEN tau, GEN a, long n, GEN T, ulong p, ulong pi)
    2079             : {
    2080        1071 :   pari_sp ltop = avma;
    2081             :   GEN t1, t2, t3, vec;
    2082        1071 :   GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
    2083        1071 :   long vT = get_Flx_var(T);
    2084        1071 :   if (signe(a)==0) return pol_0(varn(a));
    2085        1061 :   t2 = FlxX_shift(FlxqX_mul_pre(bt, a, T, p, pi),1-n,vT);
    2086        1061 :   if (signe(bht)==0) return gc_GEN(ltop, t2);
    2087         767 :   t1 = FlxX_shift(FlxqX_mul_pre(ft, a, T, p, pi),-n,vT);
    2088         767 :   t3 = FlxqXn_mul_pre(t1, bht, n-1, T, p, pi);
    2089         767 :   vec = FlxX_sub(t2, FlxX_shift(t3, 1, vT), p);
    2090         767 :   return gerepileupto(ltop, vec);
    2091             : }
    2092             : 
    2093             : static GEN
    2094         253 : polxn_FlxX(long n, long v, long vT)
    2095             : {
    2096         253 :   long i, a = n+2;
    2097         253 :   GEN p = cgetg(a+1, t_POL);
    2098         253 :   p[1] = evalsigne(1)|evalvarn(v);
    2099        2171 :   for (i = 2; i < a; i++) gel(p,i) = pol0_Flx(vT);
    2100         253 :   gel(p,a) = pol1_Flx(vT); return p;
    2101             : }
    2102             : 
    2103             : GEN
    2104         224 : FlxqXQ_minpoly_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
    2105             : {
    2106         224 :   pari_sp ltop = avma;
    2107             :   long vS, vT, n;
    2108             :   GEN v_x, g, tau;
    2109         224 :   vS = get_FlxqX_var(S);
    2110         224 :   vT = get_Flx_var(T);
    2111         224 :   n = get_FlxqX_degree(S);
    2112         224 :   g = pol1_FlxX(vS,vT);
    2113         224 :   tau = pol1_FlxX(vS,vT);
    2114         224 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2115         224 :   v_x = FlxqXQ_powers_pre(x, usqrt(2*n), S, T, p, pi);
    2116         477 :   while(signe(tau) != 0)
    2117             :   {
    2118             :     long i, j, m, k1;
    2119             :     GEN M, v, tr;
    2120             :     GEN g_prime, c;
    2121         253 :     if (degpol(g) == n) { tau = pol1_FlxX(vS, vT); g = pol1_FlxX(vS, vT); }
    2122         253 :     v = random_FlxqX(n, vS, T, p);
    2123         253 :     tr = FlxqXQ_transmul_init(tau, S, T, p, pi);
    2124         253 :     v = FlxqXQ_transmul(tr, v, n, T, p, pi);
    2125         253 :     m = 2*(n-degpol(g));
    2126         253 :     k1 = usqrt(m);
    2127         253 :     tr = FlxqXQ_transmul_init(gel(v_x,k1+1), S, T, p, pi);
    2128         253 :     c = cgetg(m+2,t_POL);
    2129         253 :     c[1] = evalsigne(1)|evalvarn(vS);
    2130        1071 :     for (i=0; i<m; i+=k1)
    2131             :     {
    2132         818 :       long mj = minss(m-i, k1);
    2133        2736 :       for (j=0; j<mj; j++)
    2134        1918 :         gel(c,m+1-(i+j)) = FlxqX_dotproduct(v, gel(v_x,j+1), T, p);
    2135         818 :       v = FlxqXQ_transmul(tr, v, n, T, p, pi);
    2136             :     }
    2137         253 :     c = FlxX_renormalize(c, m+2);
    2138             :     /* now c contains <v,x^i> , i = 0..m-1  */
    2139         253 :     M = FlxqX_halfgcd_pre(polxn_FlxX(m, vS, vT), c, T, p, pi);
    2140         253 :     g_prime = gmael(M, 2, 2);
    2141         253 :     if (degpol(g_prime) < 1) continue;
    2142         252 :     g = FlxqX_mul_pre(g, g_prime, T, p, pi);
    2143         252 :     tau = FlxqXQ_mul_pre(tau, FlxqX_FlxqXQV_eval_pre(g_prime, v_x, S, T,p,pi),
    2144             :                          S, T, p,pi);
    2145             :   }
    2146         224 :   g = FlxqX_normalize_pre(g,T,p,pi);
    2147         224 :   return gc_GEN(ltop,g);
    2148             : }
    2149             : GEN
    2150          62 : FlxqXQ_minpoly(GEN x, GEN S, GEN T, ulong p)
    2151          62 : { return FlxqXQ_minpoly_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2152             : 
    2153             : GEN
    2154           0 : FlxqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, ulong p)
    2155           0 : { return FlxXV_to_FlxM(FlxqXQ_powers(y,m-1,S,T,p), n, get_Flx_var(T)); }
    2156             : 
    2157             : static GEN
    2158      138362 : FlxX_blocks_FlxM(GEN P, long n, long m, long v)
    2159             : {
    2160      138362 :   GEN z = cgetg(m+1,t_MAT);
    2161      138362 :   long i,j, k=2, l = lg(P);
    2162      536339 :   for(i=1; i<=m; i++)
    2163             :   {
    2164      397977 :     GEN zi = cgetg(n+1,t_COL);
    2165      397977 :     gel(z,i) = zi;
    2166     1274305 :     for(j=1; j<=n; j++)
    2167      876328 :       gel(zi, j) = k==l ? pol0_Flx(v) : gel(P,k++);
    2168             :   }
    2169      138362 :   return z;
    2170             : }
    2171             : 
    2172             : GEN
    2173      138362 : FlxqX_FlxqXQV_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
    2174             : {
    2175      138362 :   pari_sp btop, av = avma;
    2176      138362 :   long v = get_FlxqX_var(S), m = get_FlxqX_degree(S);
    2177      138362 :   long vT = get_Flx_var(T);
    2178      138362 :   long i, l = lg(x)-1, lQ = lgpol(Q), n,  d;
    2179             :   GEN A, B, C, R, g;
    2180      138362 :   if (lQ == 0) return pol_0(v);
    2181      138362 :   if (lQ <= l)
    2182             :   {
    2183       43859 :     n = l;
    2184       43859 :     d = 1;
    2185             :   }
    2186             :   else
    2187             :   {
    2188       94503 :     n = l-1;
    2189       94503 :     d = (lQ+n-1)/n;
    2190             :   }
    2191      138362 :   A = FlxXV_to_FlxM_lg(x, m, n, vT);
    2192      138362 :   B = FlxX_blocks_FlxM(Q, n, d, vT);
    2193      138362 :   C = gerepileupto(av, FlxqM_mul(A, B, T, p));
    2194      138362 :   g = gel(x, l);
    2195      138362 :   T = Flx_get_red_pre(T, p, pi);
    2196      138362 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2197      138362 :   btop = avma;
    2198      138362 :   R = FlxV_to_FlxX(gel(C, d), v);
    2199      397977 :   for (i = d-1; i>0; i--)
    2200             :   {
    2201      259615 :     R = FlxX_add(FlxqXQ_mul_pre(R, g, S, T,p,pi), FlxV_to_FlxX(gel(C,i), v), p);
    2202      259615 :     if (gc_needed(btop,1))
    2203           6 :       R = gerepileupto(btop, R);
    2204             :   }
    2205      138362 :   return gc_GEN(av, R);
    2206             : }
    2207             : GEN
    2208           0 : FlxqX_FlxqXQV_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
    2209           0 : { return FlxqX_FlxqXQV_eval_pre(Q,x,S,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2210             : 
    2211             : GEN
    2212       76758 : FlxqX_FlxqXQ_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
    2213             : {
    2214       76758 :   pari_sp av = avma;
    2215             :   GEN z, V;
    2216       76758 :   long d = degpol(Q), rtd;
    2217       76758 :   if (d < 0) return pol_0(get_FlxqX_var(S));
    2218       76758 :   rtd = (long) sqrt((double)d);
    2219       76758 :   T = Flx_get_red_pre(T, p, pi);
    2220       76758 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2221       76758 :   V = FlxqXQ_powers_pre(x, rtd, S, T, p, pi);
    2222       76758 :   z = FlxqX_FlxqXQV_eval_pre(Q, V, S, T, p, pi);
    2223       76758 :   return gerepileupto(av, z);
    2224             : }
    2225             : GEN
    2226           0 : FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
    2227           0 : { return FlxqX_FlxqXQ_eval_pre(Q, x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2228             : 
    2229             : GEN
    2230           0 : FlxqXC_FlxqXQV_eval_pre(GEN x, GEN v, GEN S, GEN T, ulong p, ulong pi)
    2231           0 : { pari_APPLY_type(t_COL, FlxqX_FlxqXQV_eval_pre(gel(x,i), v, S, T, p, pi)) }
    2232             : GEN
    2233           0 : FlxqXC_FlxqXQV_eval(GEN x, GEN v, GEN S, GEN T, ulong p)
    2234           0 : { return FlxqXC_FlxqXQV_eval_pre(x, v, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2235             : 
    2236             : GEN
    2237           0 : FlxqXC_FlxqXQ_eval(GEN x, GEN F, GEN S, GEN T, ulong p)
    2238             : {
    2239           0 :   long d = brent_kung_optpow(get_FlxqX_degree(S)-1,lg(x)-1,1);
    2240           0 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2241           0 :   GEN Fp = FlxqXQ_powers_pre(F, d, S, T, p, pi);
    2242           0 :   return FlxqXC_FlxqXQV_eval_pre(x, Fp, S, T, p, pi);
    2243             : }
    2244             : 
    2245             : static GEN
    2246       72682 : FlxqXQ_autpow_sqr(void * E, GEN x)
    2247             : {
    2248       72682 :   struct _FlxqXQ *D = (struct _FlxqXQ *)E;
    2249       72682 :   GEN S = D->S, T = D->T;
    2250       72682 :   ulong p = D->p, pi = D->pi;
    2251       72682 :   GEN phi = gel(x,1), S1 = gel(x,2);
    2252       72682 :   long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
    2253       72682 :   GEN V = Flxq_powers_pre(phi, n, T, p, pi);
    2254       72682 :   GEN phi2 = Flx_FlxqV_eval_pre(phi, V, T, p, pi);
    2255       72682 :   GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
    2256       72682 :   GEN S2 = FlxqX_FlxqXQ_eval_pre(Sphi, S1, S, T, p, pi);
    2257       72682 :   return mkvec2(phi2, S2);
    2258             : }
    2259             : 
    2260             : static GEN
    2261        3714 : FlxqXQ_autpow_mul(void * E, GEN x, GEN y)
    2262             : {
    2263        3714 :   struct _FlxqXQ *D = (struct _FlxqXQ *)E;
    2264        3714 :   GEN S = D->S, T = D->T;
    2265        3714 :   ulong p = D->p, pi = D->pi;
    2266        3714 :   GEN phi1 = gel(x,1), S1 = gel(x,2);
    2267        3714 :   GEN phi2 = gel(y,1), S2 = gel(y,2);
    2268        3714 :   long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
    2269        3714 :   GEN V = Flxq_powers_pre(phi2, n, T, p, pi);
    2270        3714 :   GEN phi3 = Flx_FlxqV_eval_pre(phi1, V, T, p, pi);
    2271        3714 :   GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
    2272        3714 :   GEN S3 = FlxqX_FlxqXQ_eval_pre(Sphi, S2, S, T, p, pi);
    2273        3714 :   return mkvec2(phi3, S3);
    2274             : }
    2275             : 
    2276             : GEN
    2277       69275 : FlxqXQ_autpow_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
    2278             : {
    2279       69275 :   pari_sp av = avma;
    2280             :   struct _FlxqXQ D;
    2281       69275 :   T = Flx_get_red_pre(T, p, pi);
    2282       69275 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2283       69275 :   D.S = S; D.T = T; D.p = p; D.pi = pi;
    2284       69275 :   aut = gen_powu_i(aut,n,&D,FlxqXQ_autpow_sqr,FlxqXQ_autpow_mul);
    2285       69275 :   return gc_GEN(av, aut);
    2286             : }
    2287             : GEN
    2288           0 : FlxqXQ_autpow(GEN aut, long n, GEN S, GEN T, ulong p)
    2289           0 : { return FlxqXQ_autpow_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2290             : 
    2291             : static GEN
    2292       29983 : FlxqXQ_autsum_mul(void *E, GEN x, GEN y)
    2293             : {
    2294       29983 :   struct _FlxqXQ *D = (struct _FlxqXQ *)E;
    2295       29983 :   GEN S = D->S, T = D->T;
    2296       29983 :   ulong p = D->p, pi = D->pi;
    2297       29983 :   GEN phi1 = gel(x,1), S1 = gel(x,2), a1 = gel(x,3);
    2298       29983 :   GEN phi2 = gel(y,1), S2 = gel(y,2), a2 = gel(y,3);
    2299       29983 :   long n2 = brent_kung_optpow(get_Flx_degree(T)-1, lgpol(S1)+lgpol(a1)+1,1);
    2300       29983 :   GEN V2 = Flxq_powers_pre(phi2, n2, T, p, pi);
    2301       29983 :   GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
    2302       29983 :   GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V2, T, p, pi);
    2303       29983 :   GEN aphi = FlxY_FlxqV_evalx_pre(a1, V2, T, p, pi);
    2304       29983 :   long n = brent_kung_optpow(maxss(degpol(Sphi),degpol(aphi)),2,1);
    2305       29983 :   GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
    2306       29983 :   GEN S3 = FlxqX_FlxqXQV_eval_pre(Sphi, V, S, T, p, pi);
    2307       29983 :   GEN aS = FlxqX_FlxqXQV_eval_pre(aphi, V, S, T, p, pi);
    2308       29983 :   GEN a3 = FlxqXQ_mul_pre(aS, a2, S, T, p, pi);
    2309       29983 :   return mkvec3(phi3, S3, a3);
    2310             : }
    2311             : 
    2312             : static GEN
    2313       18582 : FlxqXQ_autsum_sqr(void * T, GEN x)
    2314       18582 : { return FlxqXQ_autsum_mul(T, x, x); }
    2315             : 
    2316             : GEN
    2317       12125 : FlxqXQ_autsum_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
    2318             : {
    2319       12125 :   pari_sp av = avma;
    2320             :   struct _FlxqXQ D;
    2321       12125 :   T = Flx_get_red_pre(T, p, pi);
    2322       12125 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2323       12125 :   D.S=S; D.T=T; D.p=p; D.pi=pi;
    2324       12125 :   aut = gen_powu_i(aut,n,&D,FlxqXQ_autsum_sqr,FlxqXQ_autsum_mul);
    2325       12125 :   return gc_GEN(av, aut);
    2326             : }
    2327             : GEN
    2328           0 : FlxqXQ_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
    2329           0 : { return FlxqXQ_autsum_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2330             : 
    2331             : static GEN
    2332          27 : FlxqXQ_auttrace_mul(void *E, GEN x, GEN y)
    2333             : {
    2334          27 :   struct _FlxqXQ *D = (struct _FlxqXQ *)E;
    2335          27 :   GEN S = D->S, T = D->T;
    2336          27 :   ulong p = D->p, pi = D->pi;
    2337          27 :   GEN S1 = gel(x,1), a1 = gel(x,2);
    2338          27 :   GEN S2 = gel(y,1), a2 = gel(y,2);
    2339          27 :   long n = brent_kung_optpow(maxss(degpol(S1),degpol(a1)),2,1);
    2340          27 :   GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
    2341          27 :   GEN S3 = FlxqX_FlxqXQV_eval_pre(S1, V, S, T, p, pi);
    2342          27 :   GEN aS = FlxqX_FlxqXQV_eval_pre(a1, V, S, T, p, pi);
    2343          27 :   GEN a3 = FlxX_add(aS, a2, p);
    2344          27 :   return mkvec2(S3, a3);
    2345             : }
    2346             : 
    2347             : static GEN
    2348          20 : FlxqXQ_auttrace_sqr(void *E, GEN x)
    2349          20 : { return FlxqXQ_auttrace_mul(E, x, x); }
    2350             : 
    2351             : GEN
    2352         337 : FlxqXQ_auttrace_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
    2353             : {
    2354         337 :   pari_sp av = avma;
    2355             :   struct _FlxqXQ D;
    2356         337 :   T = Flx_get_red_pre(T, p, pi);
    2357         337 :   S = FlxqX_get_red_pre(S, T, p, pi);
    2358         337 :   D.S=S; D.T=T; D.p=p; D.pi = pi;
    2359         337 :   x = gen_powu_i(x,n,(void*)&D,FlxqXQ_auttrace_sqr,FlxqXQ_auttrace_mul);
    2360         337 :   return gc_GEN(av, x);
    2361             : }
    2362             : GEN
    2363           0 : FlxqXQ_auttrace(GEN x, ulong n, GEN S, GEN T, ulong p)
    2364           0 : { return FlxqXQ_auttrace_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2365             : 
    2366             : /*******************************************************************/
    2367             : /*                                                                 */
    2368             : /*                      FlxYqQ                                     */
    2369             : /*                                                                 */
    2370             : /*******************************************************************/
    2371             : 
    2372             : /*Preliminary implementation to speed up FpX_ffisom*/
    2373             : typedef struct {
    2374             :   GEN S, T;
    2375             :   ulong p, pi;
    2376             : } FlxYqq_muldata;
    2377             : 
    2378             : /* reduce x in Fl[X, Y] in the algebra Fl[X, Y]/ (P(X),Q(Y)) */
    2379             : static GEN
    2380       90880 : FlxYqq_redswap(GEN x, GEN S, GEN T, ulong p, ulong pi)
    2381             : {
    2382       90880 :   pari_sp ltop=avma;
    2383       90880 :   long n = get_Flx_degree(S);
    2384       90881 :   long m = get_Flx_degree(T);
    2385       90880 :   long w = get_Flx_var(T);
    2386       90879 :   GEN V = FlxX_swap(x,m,w);
    2387       90878 :   V = FlxqX_red_pre(V,S,p,pi);
    2388       90876 :   V = FlxX_swap(V,n,w);
    2389       90881 :   return gc_GEN(ltop,V);
    2390             : }
    2391             : static GEN
    2392       80515 : FlxYqq_sqr(void *data, GEN x)
    2393             : {
    2394       80515 :   FlxYqq_muldata *D = (FlxYqq_muldata*)data;
    2395       80515 :   return FlxYqq_redswap(FlxqX_sqr_pre(x,D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
    2396             : }
    2397             : 
    2398             : static GEN
    2399       10368 : FlxYqq_mul(void *data, GEN x, GEN y)
    2400             : {
    2401       10368 :   FlxYqq_muldata *D = (FlxYqq_muldata*)data;
    2402       10368 :   return FlxYqq_redswap(FlxqX_mul_pre(x,y, D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
    2403             : }
    2404             : 
    2405             : /* x in Z[X,Y], S in Z[X] over Fq = Z[Y]/(p,T); compute lift(x^n mod (S,T,p)) */
    2406             : GEN
    2407       39226 : FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
    2408             : {
    2409             :   FlxYqq_muldata D;
    2410       39226 :   D.S = S; D.T = T; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2411       39226 :   return gen_pow(x, n, (void*)&D, &FlxYqq_sqr, &FlxYqq_mul);
    2412             : }
    2413             : 
    2414             : /*******************************************************************/
    2415             : /*                                                                 */
    2416             : /*                      FlxqXn                                     */
    2417             : /*                                                                 */
    2418             : /*******************************************************************/
    2419             : 
    2420             : GEN
    2421       66180 : FlxXn_red(GEN a, long n)
    2422             : {
    2423       66180 :   long i, L = n+2, l = lg(a);
    2424             :   GEN  b;
    2425       66180 :   if (L >= l) return a; /* deg(x) < n */
    2426       36741 :   b = cgetg(L, t_POL); b[1] = a[1];
    2427      391987 :   for (i=2; i<L; i++) gel(b,i) = gel(a,i);
    2428       36743 :   return FlxX_renormalize(b,L);
    2429             : }
    2430             : 
    2431             : GEN
    2432       40412 : FlxqXn_mul_pre(GEN a, GEN b, long n, GEN T, ulong p, ulong pi)
    2433       40412 : { return FlxXn_red(FlxqX_mul_pre(a, b, T, p, pi), n); }
    2434             : GEN
    2435           0 : FlxqXn_mul(GEN a, GEN b, long n, GEN T, ulong p)
    2436           0 : { return FlxqXn_mul_pre(a, b, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2437             : 
    2438             : GEN
    2439           0 : FlxqXn_sqr_pre(GEN a, long n, GEN T, ulong p, ulong pi)
    2440           0 : { return FlxXn_red(FlxqX_sqr_pre(a, T, p, pi), n); }
    2441             : GEN
    2442           0 : FlxqXn_sqr(GEN a, long n, GEN T, ulong p)
    2443           0 : { return FlxqXn_sqr_pre(a, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2444             : 
    2445             : /* (f*g) \/ x^n */
    2446             : static GEN
    2447       18000 : FlxqX_mulhigh_i(GEN f, GEN g, long n, GEN T, ulong p, ulong pi)
    2448       18000 : { return FlxX_shift(FlxqX_mul_pre(f, g, T, p, pi), -n , get_Flx_var(T)); }
    2449             : 
    2450             : static GEN
    2451       13194 : FlxqXn_mulhigh(GEN f, GEN g, long n2, long n, GEN T, ulong p, ulong pi)
    2452             : {
    2453       13194 :   long vT = get_Flx_var(T);
    2454       13194 :   GEN F = FlxX_blocks(f, n2, 2, vT), fl = gel(F,1), fh = gel(F,2);
    2455       13196 :   return FlxX_add(FlxqX_mulhigh_i(fl, g, n2, T, p, pi),
    2456             :                   FlxqXn_mul_pre(fh, g, n - n2, T, p, pi), p);
    2457             : }
    2458             : 
    2459             : GEN
    2460        2432 : FlxqXn_inv_pre(GEN f, long e, GEN T, ulong p, ulong pi)
    2461             : {
    2462        2432 :   pari_sp av = avma, av2;
    2463             :   ulong mask;
    2464             :   GEN W, a;
    2465        2432 :   long v = varn(f), n = 1, vT = get_Flx_var(T);
    2466             : 
    2467        2432 :   if (!signe(f)) pari_err_INV("FlxqXn_inv",f);
    2468        2432 :   a = Flxq_inv_pre(gel(f,2), T, p, pi);
    2469        2432 :   if (e == 1) return scalarpol(a, v);
    2470        2432 :   else if (e == 2)
    2471             :   {
    2472             :     GEN b;
    2473           0 :     if (degpol(f) <= 0) return scalarpol(a, v);
    2474           0 :     b = Flx_neg(gel(f,3), p);
    2475           0 :     if (lgpol(b)==0) return scalarpol(a, v);
    2476           0 :     b = Flxq_mul_pre(b, Flxq_sqr_pre(a, T, p, pi), T, p, pi);
    2477           0 :     W = deg1pol_shallow(b, a, v);
    2478           0 :     return gc_GEN(av, W);
    2479             :   }
    2480        2432 :   W = scalarpol_shallow(Flxq_inv_pre(gel(f,2), T, p, pi), v);
    2481        2432 :   mask = quadratic_prec_mask(e);
    2482        2432 :   av2 = avma;
    2483       12039 :   for (;mask>1;)
    2484             :   {
    2485             :     GEN u, fr;
    2486        9607 :     long n2 = n;
    2487        9607 :     n<<=1; if (mask & 1) n--;
    2488        9607 :     mask >>= 1;
    2489        9607 :     fr = FlxXn_red(f, n);
    2490        9607 :     u = FlxqXn_mul_pre(W, FlxqXn_mulhigh(fr, W, n2, n, T,p,pi), n-n2, T,p,pi);
    2491        9608 :     W = FlxX_sub(W, FlxX_shift(u, n2, vT), p);
    2492        9608 :     if (gc_needed(av2,2))
    2493             :     {
    2494           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_inv, e = %ld", n);
    2495           0 :       W = gerepileupto(av2, W);
    2496             :     }
    2497             :   }
    2498        2432 :   return gerepileupto(av, W);
    2499             : }
    2500             : GEN
    2501           0 : FlxqXn_inv(GEN f, long e, GEN T, ulong p)
    2502           0 : { return FlxqXn_inv_pre(f, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2503             : 
    2504             : /* Compute intformal(x^n*S)/x^(n+1) */
    2505             : static GEN
    2506        4804 : FlxX_integXn(GEN x, long n, ulong p)
    2507             : {
    2508        4804 :   long i, lx = lg(x);
    2509             :   GEN y;
    2510        4804 :   if (lx == 2) return gcopy(x);
    2511        3998 :   y = cgetg(lx, t_POL); y[1] = x[1];
    2512       26742 :   for (i=2; i<lx; i++)
    2513             :   {
    2514       22744 :     GEN xi = gel(x,i);
    2515       22744 :     gel(y,i) = Flx_Fl_mul(xi, Fl_inv((n+i-1)%p, p), p);
    2516             :   }
    2517        3998 :   return FlxX_renormalize(y, lx);;
    2518             : }
    2519             : 
    2520             : GEN
    2521        1216 : FlxqXn_expint_pre(GEN h, long e, GEN T, ulong p, ulong pi)
    2522             : {
    2523        1216 :   pari_sp av = avma, av2;
    2524        1216 :   long v = varn(h), n = 1, vT = get_Flx_var(T);
    2525        1216 :   GEN f = pol1_FlxX(v, vT), g = pol1_FlxX(v, vT);
    2526        1216 :   ulong mask = quadratic_prec_mask(e);
    2527        1216 :   av2 = avma;
    2528        4804 :   for (;mask>1;)
    2529             :   {
    2530             :     GEN u, w;
    2531        4804 :     long n2 = n;
    2532        4804 :     n<<=1; if (mask & 1) n--;
    2533        4804 :     mask >>= 1;
    2534        4804 :     u = FlxqXn_mul_pre(g, FlxqX_mulhigh_i(f, FlxXn_red(h, n2-1), n2-1, T,p,pi), n-n2, T,p,pi);
    2535        4804 :     u = FlxX_add(u, FlxX_shift(FlxXn_red(h, n-1), 1-n2, vT), p);
    2536        4804 :     w = FlxqXn_mul_pre(f, FlxX_integXn(u, n2-1, p), n-n2, T, p, pi);
    2537        4804 :     f = FlxX_add(f, FlxX_shift(w, n2, vT), p);
    2538        4804 :     if (mask<=1) break;
    2539        3588 :     u = FlxqXn_mul_pre(g, FlxqXn_mulhigh(f, g, n2, n, T,p,pi), n-n2, T,p,pi);
    2540        3588 :     g = FlxX_sub(g, FlxX_shift(u, n2, vT), p);
    2541        3588 :     if (gc_needed(av2,2))
    2542             :     {
    2543           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_exp, e = %ld", n);
    2544           0 :       gerepileall(av2, 2, &f, &g);
    2545             :     }
    2546             :   }
    2547        1216 :   return gerepileupto(av, f);
    2548             : }
    2549             : GEN
    2550           0 : FlxqXn_expint(GEN h, long e, GEN T, ulong p)
    2551           0 : { return FlxqXn_expint_pre(h, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }

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