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 - Flx.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.16.1 lcov report (development 28403-bea3a26501) Lines: 2285 2611 87.5 %
Date: 2023-03-30 07:42:39 Functions: 290 335 86.6 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2004  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             : /* Not so fast arithmetic with polynomials with small coefficients. */
      19             : 
      20             : static GEN
      21   886789313 : get_Flx_red(GEN T, GEN *B)
      22             : {
      23   886789313 :   if (typ(T)!=t_VEC) { *B=NULL; return T; }
      24      586202 :   *B = gel(T,1); return gel(T,2);
      25             : }
      26             : 
      27             : /***********************************************************************/
      28             : /**                              Flx                                  **/
      29             : /***********************************************************************/
      30             : /* Flx objects are defined as follows:
      31             :  * Let l an ulong. An Flx is a t_VECSMALL:
      32             :  * x[0] = codeword
      33             :  * x[1] = evalvarn(variable number)  (signe is not stored).
      34             :  * x[2] = a_0 x[3] = a_1, etc. with 0 <= a_i < l
      35             :  *
      36             :  * signe(x) is not valid. Use degpol(x)>0 instead. */
      37             : /***********************************************************************/
      38             : /**                      Conversion from Flx                          **/
      39             : /***********************************************************************/
      40             : 
      41             : GEN
      42    35611914 : Flx_to_ZX(GEN z)
      43             : {
      44    35611914 :   long i, l = lg(z);
      45    35611914 :   GEN x = cgetg(l,t_POL);
      46   236380012 :   for (i=2; i<l; i++) gel(x,i) = utoi(z[i]);
      47    35575944 :   x[1] = evalsigne(l-2!=0)| z[1]; return x;
      48             : }
      49             : 
      50             : GEN
      51       68638 : Flx_to_FlxX(GEN z, long sv)
      52             : {
      53       68638 :   long i, l = lg(z);
      54       68638 :   GEN x = cgetg(l,t_POL);
      55      269873 :   for (i=2; i<l; i++) gel(x,i) = Fl_to_Flx(z[i], sv);
      56       68638 :   x[1] = evalsigne(l-2!=0)| z[1]; return x;
      57             : }
      58             : 
      59             : /* same as Flx_to_ZX, in place */
      60             : GEN
      61    36120660 : Flx_to_ZX_inplace(GEN z)
      62             : {
      63    36120660 :   long i, l = lg(z);
      64   228057490 :   for (i=2; i<l; i++) gel(z,i) = utoi(z[i]);
      65    36071709 :   settyp(z, t_POL); z[1]=evalsigne(l-2!=0)|z[1]; return z;
      66             : }
      67             : 
      68             : /*Flx_to_Flv=zx_to_zv*/
      69             : GEN
      70    61853797 : Flx_to_Flv(GEN x, long N)
      71             : {
      72    61853797 :   GEN z = cgetg(N+1,t_VECSMALL);
      73    61840402 :   long i, l = lg(x)-1;
      74    61840402 :   x++;
      75   698958221 :   for (i=1; i<l ; i++) z[i]=x[i];
      76   324510218 :   for (   ; i<=N; i++) z[i]=0;
      77    61840402 :   return z;
      78             : }
      79             : 
      80             : /*Flv_to_Flx=zv_to_zx*/
      81             : GEN
      82    26166059 : Flv_to_Flx(GEN x, long sv)
      83             : {
      84    26166059 :   long i, l=lg(x)+1;
      85    26166059 :   GEN z = cgetg(l,t_VECSMALL); z[1]=sv;
      86    26154444 :   x--;
      87   291539492 :   for (i=2; i<l ; i++) z[i]=x[i];
      88    26154444 :   return Flx_renormalize(z,l);
      89             : }
      90             : 
      91             : /*Flm_to_FlxV=zm_to_zxV*/
      92             : GEN
      93        2268 : Flm_to_FlxV(GEN x, long sv)
      94        6153 : { pari_APPLY_type(t_VEC, Flv_to_Flx(gel(x,i), sv)) }
      95             : 
      96             : /*FlxC_to_ZXC=zxC_to_ZXC*/
      97             : GEN
      98      106341 : FlxC_to_ZXC(GEN x)
      99      555431 : { pari_APPLY_type(t_COL, Flx_to_ZX(gel(x,i))) }
     100             : 
     101             : /*FlxC_to_ZXC=zxV_to_ZXV*/
     102             : GEN
     103      591763 : FlxV_to_ZXV(GEN x)
     104     2399268 : { pari_APPLY_type(t_VEC, Flx_to_ZX(gel(x,i))) }
     105             : 
     106             : void
     107     2765537 : FlxV_to_ZXV_inplace(GEN v)
     108             : {
     109             :   long i;
     110     7390833 :   for(i=1;i<lg(v);i++) gel(v,i)= Flx_to_ZX(gel(v,i));
     111     2765467 : }
     112             : 
     113             : /*FlxM_to_ZXM=zxM_to_ZXM*/
     114             : GEN
     115        4515 : FlxM_to_ZXM(GEN x)
     116       15734 : { pari_APPLY_same(FlxC_to_ZXC(gel(x,i))) }
     117             : 
     118             : GEN
     119      378439 : FlxV_to_FlxX(GEN x, long v)
     120             : {
     121      378439 :   long i, l = lg(x)+1;
     122      378439 :   GEN z = cgetg(l,t_POL); z[1] = evalvarn(v);
     123      378439 :   x--;
     124     4911174 :   for (i=2; i<l ; i++) gel(z,i) = gel(x,i);
     125      378439 :   return FlxX_renormalize(z,l);
     126             : }
     127             : 
     128             : GEN
     129           0 : FlxM_to_FlxXV(GEN x, long v)
     130           0 : { pari_APPLY_type(t_COL, FlxV_to_FlxX(gel(x,i), v)) }
     131             : 
     132             : GEN
     133           0 : FlxM_Flx_add_shallow(GEN x, GEN y, ulong p)
     134             : {
     135           0 :   long l = lg(x), i, j;
     136           0 :   GEN z = cgetg(l,t_MAT);
     137             : 
     138           0 :   if (l==1) return z;
     139           0 :   if (l != lgcols(x)) pari_err_OP( "+", x, y);
     140           0 :   for (i=1; i<l; i++)
     141             :   {
     142           0 :     GEN zi = cgetg(l,t_COL), xi = gel(x,i);
     143           0 :     gel(z,i) = zi;
     144           0 :     for (j=1; j<l; j++) gel(zi,j) = gel(xi,j);
     145           0 :     gel(zi,i) = Flx_add(gel(zi,i), y, p);
     146             :   }
     147           0 :   return z;
     148             : }
     149             : 
     150             : /***********************************************************************/
     151             : /**                      Conversion to Flx                            **/
     152             : /***********************************************************************/
     153             : /* Take an integer and return a scalar polynomial mod p,  with evalvarn=vs */
     154             : GEN
     155    15941153 : Fl_to_Flx(ulong x, long sv) { return x? mkvecsmall2(sv, x): pol0_Flx(sv); }
     156             : 
     157             : /* a X^d */
     158             : GEN
     159      785808 : monomial_Flx(ulong a, long d, long vs)
     160             : {
     161             :   GEN P;
     162      785808 :   if (a==0) return pol0_Flx(vs);
     163      785808 :   P = const_vecsmall(d+2, 0);
     164      785823 :   P[1] = vs; P[d+2] = a; return P;
     165             : }
     166             : 
     167             : GEN
     168     2576749 : Z_to_Flx(GEN x, ulong p, long sv)
     169             : {
     170     2576749 :   long u = umodiu(x,p);
     171     2576880 :   return u? mkvecsmall2(sv, u): pol0_Flx(sv);
     172             : }
     173             : 
     174             : /* return x[0 .. dx] mod p as t_VECSMALL. Assume x a t_POL*/
     175             : GEN
     176   156500466 : ZX_to_Flx(GEN x, ulong p)
     177             : {
     178   156500466 :   long i, lx = lg(x);
     179   156500466 :   GEN a = cgetg(lx, t_VECSMALL);
     180   156278154 :   a[1]=((ulong)x[1])&VARNBITS;
     181  1061363943 :   for (i=2; i<lx; i++) a[i] = umodiu(gel(x,i), p);
     182   156489476 :   return Flx_renormalize(a,lx);
     183             : }
     184             : 
     185             : /* return x[0 .. dx] mod p as t_VECSMALL. Assume x a t_POL*/
     186             : GEN
     187     5234563 : zx_to_Flx(GEN x, ulong p)
     188             : {
     189     5234563 :   long i, lx = lg(x);
     190     5234563 :   GEN a = cgetg(lx, t_VECSMALL);
     191     5225521 :   a[1] = x[1];
     192    16168029 :   for (i=2; i<lx; i++) uel(a,i) = umodsu(x[i], p);
     193     5223626 :   return Flx_renormalize(a,lx);
     194             : }
     195             : 
     196             : ulong
     197    57436189 : Rg_to_Fl(GEN x, ulong p)
     198             : {
     199    57436189 :   switch(typ(x))
     200             :   {
     201    28830589 :     case t_INT: return umodiu(x, p);
     202      330451 :     case t_FRAC: {
     203      330451 :       ulong z = umodiu(gel(x,1), p);
     204      330453 :       if (!z) return 0;
     205      326152 :       return Fl_div(z, umodiu(gel(x,2), p), p);
     206             :     }
     207      205957 :     case t_PADIC: return padic_to_Fl(x, p);
     208    28069209 :     case t_INTMOD: {
     209    28069209 :       GEN q = gel(x,1), a = gel(x,2);
     210    28069209 :       if (absequaliu(q, p)) return itou(a);
     211           0 :       if (!dvdiu(q,p)) pari_err_MODULUS("Rg_to_Fl", q, utoipos(p));
     212           0 :       return umodiu(a, p);
     213             :     }
     214           0 :     default: pari_err_TYPE("Rg_to_Fl",x);
     215             :       return 0; /* LCOV_EXCL_LINE */
     216             :   }
     217             : }
     218             : 
     219             : ulong
     220     1665346 : Rg_to_F2(GEN x)
     221             : {
     222     1665346 :   switch(typ(x))
     223             :   {
     224      262330 :     case t_INT: return mpodd(x);
     225           0 :     case t_FRAC:
     226           0 :       if (!mpodd(gel(x,2))) (void)Fl_inv(0,2); /* error */
     227           0 :       return mpodd(gel(x,1));
     228           0 :     case t_PADIC:
     229           0 :       if (!absequaliu(gel(x,2),2)) pari_err_OP("",x, mkintmodu(1,2));
     230           0 :       if (valp(x) < 0) (void)Fl_inv(0,2);
     231           0 :       return valp(x) & 1;
     232     1403017 :     case t_INTMOD: {
     233     1403017 :       GEN q = gel(x,1), a = gel(x,2);
     234     1403017 :       if (mpodd(q)) pari_err_MODULUS("Rg_to_F2", q, gen_2);
     235     1403017 :       return mpodd(a);
     236             :     }
     237           0 :     default: pari_err_TYPE("Rg_to_F2",x);
     238             :       return 0; /* LCOV_EXCL_LINE */
     239             :   }
     240             : }
     241             : 
     242             : GEN
     243     2700471 : RgX_to_Flx(GEN x, ulong p)
     244             : {
     245     2700471 :   long i, lx = lg(x);
     246     2700471 :   GEN a = cgetg(lx, t_VECSMALL);
     247     2700471 :   a[1]=((ulong)x[1])&VARNBITS;
     248    23696100 :   for (i=2; i<lx; i++) a[i] = Rg_to_Fl(gel(x,i), p);
     249     2700471 :   return Flx_renormalize(a,lx);
     250             : }
     251             : 
     252             : GEN
     253           7 : RgXV_to_FlxV(GEN x, ulong p)
     254         175 : { pari_APPLY_type(t_VEC, RgX_to_Flx(gel(x,i), p)) }
     255             : 
     256             : /* If x is a POLMOD, assume modulus is a multiple of T. */
     257             : GEN
     258     3328545 : Rg_to_Flxq(GEN x, GEN T, ulong p)
     259             : {
     260     3328545 :   long ta, tx = typ(x), v = get_Flx_var(T);
     261             :   ulong pi;
     262             :   GEN a, b;
     263     3328548 :   if (is_const_t(tx))
     264             :   {
     265     3168827 :     if (tx == t_FFELT) return FF_to_Flxq(x);
     266     2437917 :     return Fl_to_Flx(Rg_to_Fl(x, p), v);
     267             :   }
     268      159717 :   switch(tx)
     269             :   {
     270        8576 :     case t_POLMOD:
     271        8576 :       b = gel(x,1);
     272        8576 :       a = gel(x,2); ta = typ(a);
     273        8576 :       if (is_const_t(ta)) return Fl_to_Flx(Rg_to_Fl(a, p), v);
     274        8422 :       b = RgX_to_Flx(b, p); if (b[1] != v) break;
     275        8422 :       a = RgX_to_Flx(a, p); if (Flx_equal(b,T)) return a;
     276           0 :       pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
     277           0 :       if (lgpol(Flx_rem_pre(b,T,p,pi))==0) return Flx_rem_pre(a, T, p, pi);
     278           0 :       break;
     279      151141 :     case t_POL:
     280      151141 :       x = RgX_to_Flx(x,p);
     281      151141 :       if (x[1] != v) break;
     282      151141 :       return Flx_rem(x, T, p);
     283           0 :     case t_RFRAC:
     284           0 :       a = Rg_to_Flxq(gel(x,1), T,p);
     285           0 :       b = Rg_to_Flxq(gel(x,2), T,p);
     286           0 :       return Flxq_div(a,b, T,p);
     287             :   }
     288           0 :   pari_err_TYPE("Rg_to_Flxq",x);
     289             :   return NULL; /* LCOV_EXCL_LINE */
     290             : }
     291             : 
     292             : /***********************************************************************/
     293             : /**                   Basic operation on Flx                          **/
     294             : /***********************************************************************/
     295             : /* = zx_renormalize. Similar to normalizepol, in place */
     296             : GEN
     297  1971353147 : Flx_renormalize(GEN /*in place*/ x, long lx)
     298             : {
     299             :   long i;
     300  2220776163 :   for (i = lx-1; i>1; i--)
     301  2129333321 :     if (x[i]) break;
     302  1971353147 :   stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
     303  1969137634 :   setlg(x, i+1); return x;
     304             : }
     305             : 
     306             : GEN
     307     1884426 : Flx_red(GEN z, ulong p)
     308             : {
     309     1884426 :   long i, l = lg(z);
     310     1884426 :   GEN x = cgetg(l, t_VECSMALL);
     311     1884324 :   x[1] = z[1];
     312    34749873 :   for (i=2; i<l; i++) x[i] = uel(z,i)%p;
     313     1884324 :   return Flx_renormalize(x,l);
     314             : }
     315             : 
     316             : int
     317    27972407 : Flx_equal(GEN V, GEN W)
     318             : {
     319    27972407 :   long l = lg(V);
     320    27972407 :   if (lg(W) != l) return 0;
     321    28993161 :   while (--l > 1) /* do not compare variables, V[1] */
     322    27736117 :     if (V[l] != W[l]) return 0;
     323     1257044 :   return 1;
     324             : }
     325             : 
     326             : GEN
     327     2447597 : random_Flx(long d1, long vs, ulong p)
     328             : {
     329     2447597 :   long i, d = d1+2;
     330     2447597 :   GEN y = cgetg(d,t_VECSMALL); y[1] = vs;
     331    17303144 :   for (i=2; i<d; i++) y[i] = random_Fl(p);
     332     2447944 :   return Flx_renormalize(y,d);
     333             : }
     334             : 
     335             : static GEN
     336     5986746 : Flx_addspec(GEN x, GEN y, ulong p, long lx, long ly)
     337             : {
     338             :   long i,lz;
     339             :   GEN z;
     340             : 
     341     5986746 :   if (ly>lx) swapspec(x,y, lx,ly);
     342     5986746 :   lz = lx+2; z = cgetg(lz, t_VECSMALL);
     343   101048052 :   for (i=0; i<ly; i++) z[i+2] = Fl_add(x[i], y[i], p);
     344    85389080 :   for (   ; i<lx; i++) z[i+2] = x[i];
     345     5986746 :   z[1] = 0; return Flx_renormalize(z, lz);
     346             : }
     347             : 
     348             : GEN
     349    56227355 : Flx_add(GEN x, GEN y, ulong p)
     350             : {
     351             :   long i,lz;
     352             :   GEN z;
     353    56227355 :   long lx=lg(x);
     354    56227355 :   long ly=lg(y);
     355    56227355 :   if (ly>lx) swapspec(x,y, lx,ly);
     356    56227355 :   lz = lx; z = cgetg(lz, t_VECSMALL); z[1]=x[1];
     357   530873383 :   for (i=2; i<ly; i++) z[i] = Fl_add(x[i], y[i], p);
     358   116250428 :   for (   ; i<lx; i++) z[i] = x[i];
     359    56175971 :   return Flx_renormalize(z, lz);
     360             : }
     361             : 
     362             : GEN
     363     9259468 : Flx_Fl_add(GEN y, ulong x, ulong p)
     364             : {
     365             :   GEN z;
     366             :   long lz, i;
     367     9259468 :   if (!lgpol(y))
     368      225951 :     return Fl_to_Flx(x,y[1]);
     369     9034424 :   lz=lg(y);
     370     9034424 :   z=cgetg(lz,t_VECSMALL);
     371     9032911 :   z[1]=y[1];
     372     9032911 :   z[2] = Fl_add(y[2],x,p);
     373    45057838 :   for(i=3;i<lz;i++)
     374    36024996 :     z[i] = y[i];
     375     9032842 :   if (lz==3) z = Flx_renormalize(z,lz);
     376     9032881 :   return z;
     377             : }
     378             : 
     379             : static GEN
     380      897414 : Flx_subspec(GEN x, GEN y, ulong p, long lx, long ly)
     381             : {
     382             :   long i,lz;
     383             :   GEN z;
     384             : 
     385      897414 :   if (ly <= lx)
     386             :   {
     387      897459 :     lz = lx+2; z = cgetg(lz, t_VECSMALL);
     388    54194716 :     for (i=0; i<ly; i++) z[i+2] = Fl_sub(x[i],y[i],p);
     389     1442850 :     for (   ; i<lx; i++) z[i+2] = x[i];
     390             :   }
     391             :   else
     392             :   {
     393           0 :     lz = ly+2; z = cgetg(lz, t_VECSMALL);
     394           0 :     for (i=0; i<lx; i++) z[i+2] = Fl_sub(x[i],y[i],p);
     395           0 :     for (   ; i<ly; i++) z[i+2] = Fl_neg(y[i],p);
     396             :   }
     397      896613 :   z[1] = 0; return Flx_renormalize(z, lz);
     398             : }
     399             : 
     400             : GEN
     401   135083766 : Flx_sub(GEN x, GEN y, ulong p)
     402             : {
     403   135083766 :   long i,lz,lx = lg(x), ly = lg(y);
     404             :   GEN z;
     405             : 
     406   135083766 :   if (ly <= lx)
     407             :   {
     408    87108240 :     lz = lx; z = cgetg(lz, t_VECSMALL);
     409   466934465 :     for (i=2; i<ly; i++) z[i] = Fl_sub(x[i],y[i],p);
     410   174577712 :     for (   ; i<lx; i++) z[i] = x[i];
     411             :   }
     412             :   else
     413             :   {
     414    47975526 :     lz = ly; z = cgetg(lz, t_VECSMALL);
     415   328012067 :     for (i=2; i<lx; i++) z[i] = Fl_sub(x[i],y[i],p);
     416   236062286 :     for (   ; i<ly; i++) z[i] = y[i]? (long)(p - y[i]): y[i];
     417             :   }
     418   135012468 :   z[1]=x[1]; return Flx_renormalize(z, lz);
     419             : }
     420             : 
     421             : GEN
     422       32918 : Flx_Fl_sub(GEN y, ulong x, ulong p)
     423             : {
     424             :   GEN z;
     425       32918 :   long lz = lg(y), i;
     426       32918 :   if (lz==2)
     427         506 :     return Fl_to_Flx(Fl_neg(x, p),y[1]);
     428       32412 :   z = cgetg(lz, t_VECSMALL);
     429       32412 :   z[1] = y[1];
     430       32412 :   z[2] = Fl_sub(uel(y,2), x, p);
     431      208798 :   for(i=3; i<lz; i++)
     432      176386 :     z[i] = y[i];
     433       32412 :   if (lz==3) z = Flx_renormalize(z,lz);
     434       32412 :   return z;
     435             : }
     436             : 
     437             : static GEN
     438     3331002 : Flx_negspec(GEN x, ulong p, long l)
     439             : {
     440             :   long i;
     441     3331002 :   GEN z = cgetg(l+2, t_VECSMALL) + 2;
     442    20901101 :   for (i=0; i<l; i++) z[i] = Fl_neg(x[i], p);
     443     3331025 :   return z-2;
     444             : }
     445             : 
     446             : GEN
     447     3331030 : Flx_neg(GEN x, ulong p)
     448             : {
     449     3331030 :   GEN z = Flx_negspec(x+2, p, lgpol(x));
     450     3331332 :   z[1] = x[1];
     451     3331332 :   return z;
     452             : }
     453             : 
     454             : GEN
     455     1463215 : Flx_neg_inplace(GEN x, ulong p)
     456             : {
     457     1463215 :   long i, l = lg(x);
     458    49859636 :   for (i=2; i<l; i++)
     459    48396421 :     if (x[i]) x[i] = p - x[i];
     460     1463215 :   return x;
     461             : }
     462             : 
     463             : GEN
     464     2163730 : Flx_double(GEN y, ulong p)
     465             : {
     466             :   long i, l;
     467     2163730 :   GEN z = cgetg_copy(y, &l); z[1] = y[1];
     468    20016322 :   for(i=2; i<l; i++) z[i] = Fl_double(y[i], p);
     469     2163730 :   return Flx_renormalize(z, l);
     470             : }
     471             : GEN
     472      901988 : Flx_triple(GEN y, ulong p)
     473             : {
     474             :   long i, l;
     475      901988 :   GEN z = cgetg_copy(y, &l); z[1] = y[1];
     476     7972336 :   for(i=2; i<l; i++) z[i] = Fl_triple(y[i], p);
     477      901988 :   return Flx_renormalize(z, l);
     478             : }
     479             : GEN
     480    17424015 : Flx_Fl_mul(GEN y, ulong x, ulong p)
     481             : {
     482             :   GEN z;
     483             :   long i, l;
     484    17424015 :   if (!x) return pol0_Flx(y[1]);
     485    16737504 :   z = cgetg_copy(y, &l); z[1] = y[1];
     486    16736515 :   if (HIGHWORD(x | p))
     487    14346508 :     for(i=2; i<l; i++) z[i] = Fl_mul(y[i], x, p);
     488             :   else
     489    89294583 :     for(i=2; i<l; i++) z[i] = (y[i] * x) % p;
     490    16736838 :   return Flx_renormalize(z, l);
     491             : }
     492             : GEN
     493    11492990 : Flx_Fl_mul_to_monic(GEN y, ulong x, ulong p)
     494             : {
     495             :   GEN z;
     496             :   long i, l;
     497    11492990 :   z = cgetg_copy(y, &l); z[1] = y[1];
     498    11487933 :   if (HIGHWORD(x | p))
     499     5308324 :     for(i=2; i<l-1; i++) z[i] = Fl_mul(y[i], x, p);
     500             :   else
     501    25551584 :     for(i=2; i<l-1; i++) z[i] = (y[i] * x) % p;
     502    11487918 :   z[l-1] = 1; return z;
     503             : }
     504             : 
     505             : /* Return a*x^n if n>=0 and a\x^(-n) if n<0 */
     506             : GEN
     507    24388681 : Flx_shift(GEN a, long n)
     508             : {
     509    24388681 :   long i, l = lg(a);
     510             :   GEN  b;
     511    24388681 :   if (l==2 || !n) return Flx_copy(a);
     512    24047531 :   if (l+n<=2) return pol0_Flx(a[1]);
     513    23834336 :   b = cgetg(l+n, t_VECSMALL);
     514    23830749 :   b[1] = a[1];
     515    23830749 :   if (n < 0)
     516    65695219 :     for (i=2-n; i<l; i++) b[i+n] = a[i];
     517             :   else
     518             :   {
     519    43063311 :     for (i=0; i<n; i++) b[2+i] = 0;
     520   140350290 :     for (i=2; i<l; i++) b[i+n] = a[i];
     521             :   }
     522    23830749 :   return b;
     523             : }
     524             : 
     525             : GEN
     526    59254171 : Flx_normalize(GEN z, ulong p)
     527             : {
     528    59254171 :   long l = lg(z)-1;
     529    59254171 :   ulong p1 = z[l]; /* leading term */
     530    59254171 :   if (p1 == 1) return z;
     531    11471017 :   return Flx_Fl_mul_to_monic(z, Fl_inv(p1,p), p);
     532             : }
     533             : 
     534             : /* return (x * X^d) + y. Assume d > 0, shallow if x == 0*/
     535             : static GEN
     536     3090830 : Flx_addshift(GEN x, GEN y, ulong p, long d)
     537             : {
     538     3090830 :   GEN xd,yd,zd = (GEN)avma;
     539     3090830 :   long a,lz,ny = lgpol(y), nx = lgpol(x);
     540     3090830 :   long vs = x[1];
     541     3090830 :   if (nx == 0) return y;
     542     3088978 :   x += 2; y += 2; a = ny-d;
     543     3088978 :   if (a <= 0)
     544             :   {
     545       85040 :     lz = (a>nx)? ny+2: nx+d+2;
     546       85040 :     (void)new_chunk(lz); xd = x+nx; yd = y+ny;
     547     1729752 :     while (xd > x) *--zd = *--xd;
     548       85040 :     x = zd + a;
     549      166127 :     while (zd > x) *--zd = 0;
     550             :   }
     551             :   else
     552             :   {
     553     3003938 :     xd = new_chunk(d); yd = y+d;
     554     3003938 :     x = Flx_addspec(x,yd,p, nx,a);
     555     3003938 :     lz = (a>nx)? ny+2: lg(x)+d;
     556   126606614 :     x += 2; while (xd > x) *--zd = *--xd;
     557             :   }
     558    57245727 :   while (yd > y) *--zd = *--yd;
     559     3088978 :   *--zd = vs;
     560     3088978 :   *--zd = evaltyp(t_VECSMALL) | evallg(lz); return zd;
     561             : }
     562             : 
     563             : /* shift polynomial + gerepile */
     564             : /* Do not set evalvarn*/
     565             : static GEN
     566   601363555 : Flx_shiftip(pari_sp av, GEN x, long v)
     567             : {
     568   601363555 :   long i, lx = lg(x), ly;
     569             :   GEN y;
     570   601363555 :   if (!v || lx==2) return gerepileuptoleaf(av, x);
     571   169926031 :   ly = lx + v; /* result length */
     572   169926031 :   (void)new_chunk(ly); /* check that result fits */
     573   169772153 :   x += lx; y = (GEN)av;
     574  1240717159 :   for (i = 2; i<lx; i++) *--y = *--x;
     575   693453562 :   for (i = 0; i< v; i++) *--y = 0;
     576   169772153 :   y -= 2; y[0] = evaltyp(t_VECSMALL) | evallg(ly);
     577   170154654 :   return gc_const((pari_sp)y, y);
     578             : }
     579             : 
     580             : static long
     581  2145269889 : get_Fl_threshold(ulong p, long mul, long mul2)
     582             : {
     583  2145269889 :   return SMALL_ULONG(p) ? mul: mul2;
     584             : }
     585             : 
     586             : #define BITS_IN_QUARTULONG (BITS_IN_HALFULONG >> 1)
     587             : #define QUARTMASK ((1UL<<BITS_IN_QUARTULONG)-1UL)
     588             : #define LLQUARTWORD(x) ((x) & QUARTMASK)
     589             : #define HLQUARTWORD(x) (((x) >> BITS_IN_QUARTULONG) & QUARTMASK)
     590             : #define LHQUARTWORD(x) (((x) >> (2*BITS_IN_QUARTULONG)) & QUARTMASK)
     591             : #define HHQUARTWORD(x) (((x) >> (3*BITS_IN_QUARTULONG)) & QUARTMASK)
     592             : INLINE long
     593     7563037 : maxbitcoeffpol(ulong p, long n)
     594             : {
     595     7563037 :   GEN z = muliu(sqru(p - 1), n);
     596     7557992 :   long b = expi(z) + 1;
     597             :   /* only do expensive bit-packing if it saves at least 1 limb */
     598     7560789 :   if (b <= BITS_IN_QUARTULONG)
     599             :   {
     600      887044 :     if (nbits2nlong(n*b) == (n + 3)>>2)
     601      106928 :       b = BITS_IN_QUARTULONG;
     602             :   }
     603     6673745 :   else if (b <= BITS_IN_HALFULONG)
     604             :   {
     605     1566245 :     if (nbits2nlong(n*b) == (n + 1)>>1)
     606        5584 :       b = BITS_IN_HALFULONG;
     607             :   }
     608             :   else
     609             :   {
     610     5107500 :     long l = lgefint(z) - 2;
     611     5107500 :     if (nbits2nlong(n*b) == n*l)
     612      306027 :       b = l*BITS_IN_LONG;
     613             :   }
     614     7560796 :   return b;
     615             : }
     616             : 
     617             : INLINE ulong
     618  3465328292 : Flx_mullimb_ok(GEN x, GEN y, ulong p, long a, long b)
     619             : { /* Assume OK_ULONG*/
     620  3465328292 :   ulong p1 = 0;
     621             :   long i;
     622 16428188279 :   for (i=a; i<b; i++)
     623 12962859987 :     if (y[i])
     624             :     {
     625 10882074586 :       p1 += y[i] * x[-i];
     626 10882074586 :       if (p1 & HIGHBIT) p1 %= p;
     627             :     }
     628  3465328292 :   return p1 % p;
     629             : }
     630             : 
     631             : INLINE ulong
     632  1063714445 : Flx_mullimb(GEN x, GEN y, ulong p, ulong pi, long a, long b)
     633             : {
     634  1063714445 :   ulong p1 = 0;
     635             :   long i;
     636  3322670461 :   for (i=a; i<b; i++)
     637  2257317100 :     if (y[i])
     638  2215896772 :       p1 = Fl_addmul_pre(p1, y[i], x[-i], p, pi);
     639  1065353361 :   return p1;
     640             : }
     641             : 
     642             : /* assume nx >= ny > 0 */
     643             : static GEN
     644   322243247 : Flx_mulspec_basecase(GEN x, GEN y, ulong p, ulong pi, long nx, long ny)
     645             : {
     646             :   long i,lz,nz;
     647             :   GEN z;
     648             : 
     649   322243247 :   lz = nx+ny+1; nz = lz-2;
     650   322243247 :   z = cgetg(lz, t_VECSMALL) + 2; /* x:y:z [i] = term of degree i */
     651   321745151 :   if (!pi)
     652             :   {
     653  1150402166 :     for (i=0; i<ny; i++)z[i] = Flx_mullimb_ok(x+i,y,p,0,i+1);
     654   772723656 :     for (  ; i<nx; i++) z[i] = Flx_mullimb_ok(x+i,y,p,0,ny);
     655   903498133 :     for (  ; i<nz; i++) z[i] = Flx_mullimb_ok(x+i,y,p,i-nx+1,ny);
     656             :   }
     657             :   else
     658             :   {
     659   263792675 :     for (i=0; i<ny; i++)z[i] = Flx_mullimb(x+i,y,p,pi,0,i+1);
     660   197340356 :     for (  ; i<nx; i++) z[i] = Flx_mullimb(x+i,y,p,pi,0,ny);
     661   191257131 :     for (  ; i<nz; i++) z[i] = Flx_mullimb(x+i,y,p,pi,i-nx+1,ny);
     662             :   }
     663   322121431 :   z -= 2; return Flx_renormalize(z, lz);
     664             : }
     665             : 
     666             : static GEN
     667       12567 : int_to_Flx(GEN z, ulong p)
     668             : {
     669       12567 :   long i, l = lgefint(z);
     670       12567 :   GEN x = cgetg(l, t_VECSMALL);
     671     1083877 :   for (i=2; i<l; i++) x[i] = uel(z,i)%p;
     672       12562 :   return Flx_renormalize(x, l);
     673             : }
     674             : 
     675             : INLINE GEN
     676       10298 : Flx_mulspec_mulii(GEN a, GEN b, ulong p, long na, long nb)
     677             : {
     678       10298 :   GEN z=muliispec(a,b,na,nb);
     679       10302 :   return int_to_Flx(z,p);
     680             : }
     681             : 
     682             : static GEN
     683      491319 : Flx_to_int_halfspec(GEN a, long na)
     684             : {
     685             :   long j;
     686      491319 :   long n = (na+1)>>1UL;
     687      491319 :   GEN V = cgetipos(2+n);
     688             :   GEN w;
     689     1402700 :   for (w = int_LSW(V), j=0; j+1<na; j+=2, w=int_nextW(w))
     690      911381 :     *w = a[j]|(a[j+1]<<BITS_IN_HALFULONG);
     691      491319 :   if (j<na)
     692      337962 :     *w = a[j];
     693      491319 :   return V;
     694             : }
     695             : 
     696             : static GEN
     697      589294 : int_to_Flx_half(GEN z, ulong p)
     698             : {
     699             :   long i;
     700      589294 :   long lx = (lgefint(z)-2)*2+2;
     701      589294 :   GEN w, x = cgetg(lx, t_VECSMALL);
     702     2004691 :   for (w = int_LSW(z), i=2; i<lx; i+=2, w=int_nextW(w))
     703             :   {
     704     1415397 :     x[i]   = LOWWORD((ulong)*w)%p;
     705     1415397 :     x[i+1] = HIGHWORD((ulong)*w)%p;
     706             :   }
     707      589294 :   return Flx_renormalize(x, lx);
     708             : }
     709             : 
     710             : static GEN
     711        5448 : Flx_mulspec_halfmulii(GEN a, GEN b, ulong p, long na, long nb)
     712             : {
     713        5448 :   GEN A = Flx_to_int_halfspec(a,na);
     714        5448 :   GEN B = Flx_to_int_halfspec(b,nb);
     715        5448 :   GEN z = mulii(A,B);
     716        5448 :   return int_to_Flx_half(z,p);
     717             : }
     718             : 
     719             : static GEN
     720      203661 : Flx_to_int_quartspec(GEN a, long na)
     721             : {
     722             :   long j;
     723      203661 :   long n = (na+3)>>2UL;
     724      203661 :   GEN V = cgetipos(2+n);
     725             :   GEN w;
     726     4348964 :   for (w = int_LSW(V), j=0; j+3<na; j+=4, w=int_nextW(w))
     727     4145303 :     *w = a[j]|(a[j+1]<<BITS_IN_QUARTULONG)|(a[j+2]<<(2*BITS_IN_QUARTULONG))|(a[j+3]<<(3*BITS_IN_QUARTULONG));
     728      203661 :   switch (na-j)
     729             :   {
     730      116094 :   case 3:
     731      116094 :     *w = a[j]|(a[j+1]<<BITS_IN_QUARTULONG)|(a[j+2]<<(2*BITS_IN_QUARTULONG));
     732      116094 :     break;
     733       34240 :   case 2:
     734       34240 :     *w = a[j]|(a[j+1]<<BITS_IN_QUARTULONG);
     735       34240 :     break;
     736       26973 :   case 1:
     737       26973 :     *w = a[j];
     738       26973 :     break;
     739       26354 :   case 0:
     740       26354 :     break;
     741             :   }
     742      203661 :   return V;
     743             : }
     744             : 
     745             : static GEN
     746      106930 : int_to_Flx_quart(GEN z, ulong p)
     747             : {
     748             :   long i;
     749      106930 :   long lx = (lgefint(z)-2)*4+2;
     750      106930 :   GEN w, x = cgetg(lx, t_VECSMALL);
     751     4844610 :   for (w = int_LSW(z), i=2; i<lx; i+=4, w=int_nextW(w))
     752             :   {
     753     4737680 :     x[i]   = LLQUARTWORD((ulong)*w)%p;
     754     4737680 :     x[i+1] = HLQUARTWORD((ulong)*w)%p;
     755     4737680 :     x[i+2] = LHQUARTWORD((ulong)*w)%p;
     756     4737680 :     x[i+3] = HHQUARTWORD((ulong)*w)%p;
     757             :   }
     758      106930 :   return Flx_renormalize(x, lx);
     759             : }
     760             : 
     761             : static GEN
     762       96731 : Flx_mulspec_quartmulii(GEN a, GEN b, ulong p, long na, long nb)
     763             : {
     764       96731 :   GEN A = Flx_to_int_quartspec(a,na);
     765       96732 :   GEN B = Flx_to_int_quartspec(b,nb);
     766       96732 :   GEN z = mulii(A,B);
     767       96733 :   return int_to_Flx_quart(z,p);
     768             : }
     769             : 
     770             : /*Eval x in 2^(k*BIL) in linear time, k==2 or 3*/
     771             : static GEN
     772      578822 : Flx_eval2BILspec(GEN x, long k, long l)
     773             : {
     774      578822 :   long i, lz = k*l, ki;
     775      578822 :   GEN pz = cgetipos(2+lz);
     776    16299316 :   for (i=0; i < lz; i++)
     777    15720494 :     *int_W(pz,i) = 0UL;
     778     8439069 :   for (i=0, ki=0; i<l; i++, ki+=k)
     779     7860247 :     *int_W(pz,ki) = x[i];
     780      578822 :   return int_normalize(pz,0);
     781             : }
     782             : 
     783             : static GEN
     784      296393 : Z_mod2BIL_Flx_2(GEN x, long d, ulong p)
     785             : {
     786      296393 :   long i, offset, lm = lgefint(x)-2, l = d+3;
     787      296393 :   ulong pi = get_Fl_red(p);
     788      296393 :   GEN pol = cgetg(l, t_VECSMALL);
     789      296393 :   pol[1] = 0;
     790     7976864 :   for (i=0, offset=0; offset+1 < lm; i++, offset += 2)
     791     7680471 :     pol[i+2] = remll_pre(*int_W(x,offset+1), *int_W(x,offset), p, pi);
     792      296393 :   if (offset < lm)
     793      224805 :     pol[i+2] = (*int_W(x,offset)) % p;
     794      296393 :   return Flx_renormalize(pol,l);
     795             : }
     796             : 
     797             : static GEN
     798           0 : Z_mod2BIL_Flx_3(GEN x, long d, ulong p)
     799             : {
     800           0 :   long i, offset, lm = lgefint(x)-2, l = d+3;
     801           0 :   ulong pi = get_Fl_red(p);
     802           0 :   GEN pol = cgetg(l, t_VECSMALL);
     803           0 :   pol[1] = 0;
     804           0 :   for (i=0, offset=0; offset+2 < lm; i++, offset += 3)
     805           0 :     pol[i+2] = remlll_pre(*int_W(x,offset+2), *int_W(x,offset+1),
     806           0 :                           *int_W(x,offset), p, pi);
     807           0 :   if (offset+1 < lm)
     808           0 :     pol[i+2] = remll_pre(*int_W(x,offset+1), *int_W(x,offset), p, pi);
     809           0 :   else if (offset < lm)
     810           0 :     pol[i+2] = (*int_W(x,offset)) % p;
     811           0 :   return Flx_renormalize(pol,l);
     812             : }
     813             : 
     814             : static GEN
     815      293463 : Z_mod2BIL_Flx(GEN x, long bs, long d, ulong p)
     816             : {
     817      293463 :   return bs==2 ? Z_mod2BIL_Flx_2(x, d, p): Z_mod2BIL_Flx_3(x, d, p);
     818             : }
     819             : 
     820             : static GEN
     821      281970 : Flx_mulspec_mulii_inflate(GEN x, GEN y, long N, ulong p, long nx, long ny)
     822             : {
     823      281970 :   pari_sp av = avma;
     824      281970 :   GEN z = mulii(Flx_eval2BILspec(x,N,nx), Flx_eval2BILspec(y,N,ny));
     825      281970 :   return gerepileupto(av, Z_mod2BIL_Flx(z, N, nx+ny-2, p));
     826             : }
     827             : 
     828             : static GEN
     829    19183411 : kron_pack_Flx_spec_bits(GEN x, long b, long l) {
     830             :   GEN y;
     831             :   long i;
     832    19183411 :   if (l == 0)
     833     3418657 :     return gen_0;
     834    15764754 :   y = cgetg(l + 1, t_VECSMALL);
     835   789199241 :   for(i = 1; i <= l; i++)
     836   773448700 :     y[i] = x[l - i];
     837    15750541 :   return nv_fromdigits_2k(y, b);
     838             : }
     839             : 
     840             : /* assume b < BITS_IN_LONG */
     841             : static GEN
     842     5679989 : kron_unpack_Flx_bits_narrow(GEN z, long b, ulong p) {
     843     5679989 :   GEN v = binary_2k_nv(z, b), x;
     844     5679964 :   long i, l = lg(v) + 1;
     845     5679964 :   x = cgetg(l, t_VECSMALL);
     846   614350215 :   for (i = 2; i < l; i++)
     847   608669935 :     x[i] = v[l - i] % p;
     848     5680280 :   return Flx_renormalize(x, l);
     849             : }
     850             : 
     851             : static GEN
     852     4739273 : kron_unpack_Flx_bits_wide(GEN z, long b, ulong p, ulong pi) {
     853     4739273 :   GEN v = binary_2k(z, b), x, y;
     854     4741339 :   long i, l = lg(v) + 1, ly;
     855     4741339 :   x = cgetg(l, t_VECSMALL);
     856   219181675 :   for (i = 2; i < l; i++) {
     857   214439916 :     y = gel(v, l - i);
     858   214439916 :     ly = lgefint(y);
     859   214439916 :     switch (ly) {
     860     8851513 :     case 2: x[i] = 0; break;
     861    29093460 :     case 3: x[i] = *int_W_lg(y, 0, ly) % p; break;
     862   161193556 :     case 4: x[i] = remll_pre(*int_W_lg(y, 1, ly), *int_W_lg(y, 0, ly), p, pi); break;
     863    30602904 :     case 5: x[i] = remlll_pre(*int_W_lg(y, 2, ly), *int_W_lg(y, 1, ly),
     864    15301387 :                               *int_W_lg(y, 0, ly), p, pi); break;
     865           0 :     default: x[i] = umodiu(gel(v, l - i), p);
     866             :     }
     867             :   }
     868     4741759 :   return Flx_renormalize(x, l);
     869             : }
     870             : 
     871             : static GEN
     872     6439560 : Flx_mulspec_Kronecker(GEN A, GEN B, long b, ulong p, long lA, long lB)
     873             : {
     874             :   GEN C, D;
     875     6439560 :   pari_sp av = avma;
     876     6439560 :   A =  kron_pack_Flx_spec_bits(A, b, lA);
     877     6443957 :   B =  kron_pack_Flx_spec_bits(B, b, lB);
     878     6444150 :   C = gerepileuptoint(av, mulii(A, B));
     879     6441392 :   if (b < BITS_IN_LONG)
     880     2074007 :     D =  kron_unpack_Flx_bits_narrow(C, b, p);
     881             :   else
     882             :   {
     883     4367385 :     ulong pi = get_Fl_red(p);
     884     4365456 :     D = kron_unpack_Flx_bits_wide(C, b, p, pi);
     885             :   }
     886     6440096 :   return D;
     887             : }
     888             : 
     889             : static GEN
     890      702538 : Flx_sqrspec_Kronecker(GEN A, long b, ulong p, long lA)
     891             : {
     892             :   GEN C, D;
     893      702538 :   A =  kron_pack_Flx_spec_bits(A, b, lA);
     894      702608 :   C = sqri(A);
     895      702625 :   if (b < BITS_IN_LONG)
     896      496084 :     D =  kron_unpack_Flx_bits_narrow(C, b, p);
     897             :   else
     898             :   {
     899      206541 :     ulong pi = get_Fl_red(p);
     900      206533 :     D = kron_unpack_Flx_bits_wide(C, b, p, pi);
     901             :   }
     902      702594 :   return D;
     903             : }
     904             : 
     905             : /* fast product (Karatsuba) of polynomials a,b. These are not real GENs, a+2,
     906             :  * b+2 were sent instead. na, nb = number of terms of a, b.
     907             :  * Only c, c0, c1, c2 are genuine GEN.
     908             :  */
     909             : static GEN
     910   359175045 : Flx_mulspec(GEN a, GEN b, ulong p, ulong pi, long na, long nb)
     911             : {
     912             :   GEN a0,c,c0;
     913   359175045 :   long n0, n0a, i, v = 0;
     914             :   pari_sp av;
     915             : 
     916   464398636 :   while (na && !a[0]) { a++; na--; v++; }
     917   545003221 :   while (nb && !b[0]) { b++; nb--; v++; }
     918   359175045 :   if (na < nb) swapspec(a,b, na,nb);
     919   359175045 :   if (!nb) return pol0_Flx(0);
     920             : 
     921   330299245 :   av = avma;
     922   330299245 :   if (nb >= get_Fl_threshold(p, Flx_MUL_MULII_LIMIT, Flx_MUL2_MULII_LIMIT))
     923             :   {
     924     6836597 :     long m = maxbitcoeffpol(p,nb);
     925     6833623 :     switch (m)
     926             :     {
     927       96731 :     case BITS_IN_QUARTULONG:
     928       96731 :       return Flx_shiftip(av,Flx_mulspec_quartmulii(a,b,p,na,nb), v);
     929        5448 :     case BITS_IN_HALFULONG:
     930        5448 :       return Flx_shiftip(av,Flx_mulspec_halfmulii(a,b,p,na,nb), v);
     931       10299 :     case BITS_IN_LONG:
     932       10299 :       return Flx_shiftip(av,Flx_mulspec_mulii(a,b,p,na,nb), v);
     933      281970 :     case 2*BITS_IN_LONG:
     934      281970 :       return Flx_shiftip(av,Flx_mulspec_mulii_inflate(a,b,2,p,na,nb), v);
     935           0 :     case 3*BITS_IN_LONG:
     936           0 :       return Flx_shiftip(av,Flx_mulspec_mulii_inflate(a,b,3,p,na,nb), v);
     937     6439175 :     default:
     938     6439175 :       return Flx_shiftip(av,Flx_mulspec_Kronecker(a,b,m,p,na,nb), v);
     939             :     }
     940             :   }
     941   323719343 :   if (nb < get_Fl_threshold(p, Flx_MUL_KARATSUBA_LIMIT, Flx_MUL2_KARATSUBA_LIMIT))
     942   322221386 :     return Flx_shiftip(av,Flx_mulspec_basecase(a,b,p,pi,na,nb), v);
     943     1514840 :   i=(na>>1); n0=na-i; na=i;
     944     1514840 :   a0=a+n0; n0a=n0;
     945     2292713 :   while (n0a && !a[n0a-1]) n0a--;
     946             : 
     947     1514840 :   if (nb > n0)
     948             :   {
     949             :     GEN b0,c1,c2;
     950             :     long n0b;
     951             : 
     952     1463215 :     nb -= n0; b0 = b+n0; n0b = n0;
     953     2549660 :     while (n0b && !b[n0b-1]) n0b--;
     954     1463215 :     c =  Flx_mulspec(a,b,p,pi,n0a,n0b);
     955     1463215 :     c0 = Flx_mulspec(a0,b0,p,pi,na,nb);
     956             : 
     957     1463215 :     c2 = Flx_addspec(a0,a,p,na,n0a);
     958     1463215 :     c1 = Flx_addspec(b0,b,p,nb,n0b);
     959             : 
     960     1463215 :     c1 = Flx_mul_pre(c1,c2,p,pi);
     961     1463215 :     c2 = Flx_add(c0,c,p);
     962             : 
     963     1463215 :     c2 = Flx_neg_inplace(c2,p);
     964     1463215 :     c2 = Flx_add(c1,c2,p);
     965     1463215 :     c0 = Flx_addshift(c0,c2 ,p, n0);
     966             :   }
     967             :   else
     968             :   {
     969       51625 :     c  = Flx_mulspec(a,b,p,pi,n0a,nb);
     970       51625 :     c0 = Flx_mulspec(a0,b,p,pi,na,nb);
     971             :   }
     972     1514840 :   c0 = Flx_addshift(c0,c,p,n0);
     973     1514840 :   return Flx_shiftip(av,c0, v);
     974             : }
     975             : 
     976             : GEN
     977   354008031 : Flx_mul_pre(GEN x, GEN y, ulong p, ulong pi)
     978             : {
     979   354008031 :   GEN z = Flx_mulspec(x+2,y+2,p, pi, lgpol(x),lgpol(y));
     980   354202051 :   z[1] = x[1]; return z;
     981             : }
     982             : GEN
     983    20045605 : Flx_mul(GEN x, GEN y, ulong p)
     984    20045605 : { return Flx_mul_pre(x, y, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
     985             : 
     986             : static GEN
     987   272242196 : Flx_sqrspec_basecase(GEN x, ulong p, ulong pi, long nx)
     988             : {
     989             :   long i, lz, nz;
     990             :   ulong p1;
     991             :   GEN z;
     992             : 
     993   272242196 :   if (!nx) return pol0_Flx(0);
     994   272242196 :   lz = (nx << 1) + 1, nz = lz-2;
     995   272242196 :   z = cgetg(lz, t_VECSMALL) + 2;
     996   271346649 :   if (!pi)
     997             :   {
     998   210020607 :     z[0] = x[0]*x[0]%p;
     999   915895748 :     for (i=1; i<nx; i++)
    1000             :     {
    1001   705546196 :       p1 = Flx_mullimb_ok(x+i,x,p,0, (i+1)>>1);
    1002   705875141 :       p1 <<= 1;
    1003   705875141 :       if ((i&1) == 0) p1 += x[i>>1] * x[i>>1];
    1004   705875141 :       z[i] = p1 % p;
    1005             :     }
    1006   921323222 :     for (  ; i<nz; i++)
    1007             :     {
    1008   710434003 :       p1 = Flx_mullimb_ok(x+i,x,p,i-nx+1, (i+1)>>1);
    1009   710973670 :       p1 <<= 1;
    1010   710973670 :       if ((i&1) == 0) p1 += x[i>>1] * x[i>>1];
    1011   710973670 :       z[i] = p1 % p;
    1012             :     }
    1013             :   }
    1014             :   else
    1015             :   {
    1016    61326042 :     z[0] = Fl_sqr_pre(x[0], p, pi);
    1017   382813975 :     for (i=1; i<nx; i++)
    1018             :     {
    1019   321472087 :       p1 = Flx_mullimb(x+i,x,p,pi,0, (i+1)>>1);
    1020   322099918 :       p1 = Fl_add(p1, p1, p);
    1021   321662540 :       if ((i&1) == 0) p1 = Fl_add(p1, Fl_sqr_pre(x[i>>1], p, pi), p);
    1022   321347656 :       z[i] = p1;
    1023             :     }
    1024   383062026 :     for (  ; i<nz; i++)
    1025             :     {
    1026   321580473 :       p1 = Flx_mullimb(x+i,x,p,pi,i-nx+1, (i+1)>>1);
    1027   322499584 :       p1 = Fl_add(p1, p1, p);
    1028   322106838 :       if ((i&1) == 0) p1 = Fl_add(p1, Fl_sqr_pre(x[i>>1], p, pi), p);
    1029   321720138 :       z[i] = p1;
    1030             :     }
    1031             :   }
    1032   272370772 :   z -= 2; return Flx_renormalize(z, lz);
    1033             : }
    1034             : 
    1035             : static GEN
    1036        2265 : Flx_sqrspec_sqri(GEN a, ulong p, long na)
    1037             : {
    1038        2265 :   GEN z=sqrispec(a,na);
    1039        2265 :   return int_to_Flx(z,p);
    1040             : }
    1041             : 
    1042             : static GEN
    1043         136 : Flx_sqrspec_halfsqri(GEN a, ulong p, long na)
    1044             : {
    1045         136 :   GEN z = sqri(Flx_to_int_halfspec(a,na));
    1046         136 :   return int_to_Flx_half(z,p);
    1047             : }
    1048             : 
    1049             : static GEN
    1050       10197 : Flx_sqrspec_quartsqri(GEN a, ulong p, long na)
    1051             : {
    1052       10197 :   GEN z = sqri(Flx_to_int_quartspec(a,na));
    1053       10197 :   return int_to_Flx_quart(z,p);
    1054             : }
    1055             : 
    1056             : static GEN
    1057       11493 : Flx_sqrspec_sqri_inflate(GEN x, long N, ulong p, long nx)
    1058             : {
    1059       11493 :   pari_sp av = avma;
    1060       11493 :   GEN  z = sqri(Flx_eval2BILspec(x,N,nx));
    1061       11493 :   return gerepileupto(av, Z_mod2BIL_Flx(z, N, (nx-1)*2, p));
    1062             : }
    1063             : 
    1064             : static GEN
    1065   272615334 : Flx_sqrspec(GEN a, ulong p, ulong pi, long na)
    1066             : {
    1067             :   GEN a0, c, c0;
    1068   272615334 :   long n0, n0a, i, v = 0, m;
    1069             :   pari_sp av;
    1070             : 
    1071   390789324 :   while (na && !a[0]) { a++; na--; v += 2; }
    1072   272615334 :   if (!na) return pol0_Flx(0);
    1073             : 
    1074   272379310 :   av = avma;
    1075   272379310 :   if (na >= get_Fl_threshold(p, Flx_SQR_SQRI_LIMIT, Flx_SQR2_SQRI_LIMIT))
    1076             :   {
    1077      726628 :     m = maxbitcoeffpol(p,na);
    1078      726626 :     switch(m)
    1079             :     {
    1080       10197 :     case BITS_IN_QUARTULONG:
    1081       10197 :       return Flx_shiftip(av, Flx_sqrspec_quartsqri(a,p,na), v);
    1082         136 :     case BITS_IN_HALFULONG:
    1083         136 :       return Flx_shiftip(av, Flx_sqrspec_halfsqri(a,p,na), v);
    1084        2265 :     case BITS_IN_LONG:
    1085        2265 :       return Flx_shiftip(av, Flx_sqrspec_sqri(a,p,na), v);
    1086       11493 :     case 2*BITS_IN_LONG:
    1087       11493 :       return Flx_shiftip(av, Flx_sqrspec_sqri_inflate(a,2,p,na), v);
    1088           0 :     case 3*BITS_IN_LONG:
    1089           0 :       return Flx_shiftip(av, Flx_sqrspec_sqri_inflate(a,3,p,na), v);
    1090      702535 :     default:
    1091      702535 :       return Flx_shiftip(av, Flx_sqrspec_Kronecker(a,m,p,na), v);
    1092             :     }
    1093             :   }
    1094   272001792 :   if (na < get_Fl_threshold(p, Flx_SQR_KARATSUBA_LIMIT, Flx_SQR2_KARATSUBA_LIMIT))
    1095   271941299 :     return Flx_shiftip(av, Flx_sqrspec_basecase(a,p,pi,na), v);
    1096       56397 :   i=(na>>1); n0=na-i; na=i;
    1097       56397 :   a0=a+n0; n0a=n0;
    1098       71162 :   while (n0a && !a[n0a-1]) n0a--;
    1099             : 
    1100       56397 :   c = Flx_sqrspec(a,p,pi,n0a);
    1101       56397 :   c0= Flx_sqrspec(a0,p,pi,na);
    1102       56397 :   if (p == 2) n0 *= 2;
    1103             :   else
    1104             :   {
    1105       56378 :     GEN c1, t = Flx_addspec(a0,a,p,na,n0a);
    1106       56378 :     t = Flx_sqr_pre(t,p,pi);
    1107       56378 :     c1= Flx_add(c0,c, p);
    1108       56378 :     c1= Flx_sub(t, c1, p);
    1109       56378 :     c0 = Flx_addshift(c0,c1,p,n0);
    1110             :   }
    1111       56397 :   c0 = Flx_addshift(c0,c,p,n0);
    1112       56397 :   return Flx_shiftip(av,c0,v);
    1113             : }
    1114             : 
    1115             : GEN
    1116   272330763 : Flx_sqr_pre(GEN x, ulong p, ulong pi)
    1117             : {
    1118   272330763 :   GEN z = Flx_sqrspec(x+2,p, pi, lgpol(x));
    1119   273460660 :   z[1] = x[1]; return z;
    1120             : }
    1121             : GEN
    1122      282064 : Flx_sqr(GEN x, ulong p)
    1123      282064 : { return Flx_sqr_pre(x, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1124             : 
    1125             : GEN
    1126        8316 : Flx_powu_pre(GEN x, ulong n, ulong p, ulong pi)
    1127             : {
    1128        8316 :   GEN y = pol1_Flx(x[1]), z;
    1129             :   ulong m;
    1130        8307 :   if (n == 0) return y;
    1131        8307 :   m = n; z = x;
    1132             :   for (;;)
    1133             :   {
    1134       32042 :     if (m&1UL) y = Flx_mul_pre(y,z, p, pi);
    1135       32019 :     m >>= 1; if (!m) return y;
    1136       23717 :     z = Flx_sqr_pre(z, p, pi);
    1137             :   }
    1138             : }
    1139             : GEN
    1140           0 : Flx_powu(GEN x, ulong n, ulong p)
    1141             : {
    1142           0 :   if (n == 0) return pol1_Flx(x[1]);
    1143           0 :   return Flx_powu_pre(x, n, p, SMALL_ULONG(p)? 0: get_Fl_red(p));
    1144             : }
    1145             : 
    1146             : GEN
    1147       13633 : Flx_halve(GEN y, ulong p)
    1148             : {
    1149             :   GEN z;
    1150             :   long i, l;
    1151       13633 :   z = cgetg_copy(y, &l); z[1] = y[1];
    1152       58446 :   for(i=2; i<l; i++) uel(z,i) = Fl_halve(uel(y,i), p);
    1153       13633 :   return z;
    1154             : }
    1155             : 
    1156             : static GEN
    1157     6375097 : Flx_recipspec(GEN x, long l, long n)
    1158             : {
    1159             :   long i;
    1160     6375097 :   GEN z=cgetg(n+2,t_VECSMALL)+2;
    1161   113487622 :   for(i=0; i<l; i++)
    1162   107114122 :     z[n-i-1] = x[i];
    1163    14039552 :   for(   ; i<n; i++)
    1164     7666052 :     z[n-i-1] = 0;
    1165     6373500 :   return Flx_renormalize(z-2,n+2);
    1166             : }
    1167             : 
    1168             : GEN
    1169           0 : Flx_recip(GEN x)
    1170             : {
    1171           0 :   GEN z=Flx_recipspec(x+2,lgpol(x),lgpol(x));
    1172           0 :   z[1]=x[1];
    1173           0 :   return z;
    1174             : }
    1175             : 
    1176             : /* Return h^degpol(P) P(x / h) */
    1177             : GEN
    1178        1117 : Flx_rescale(GEN P, ulong h, ulong p)
    1179             : {
    1180        1117 :   long i, l = lg(P);
    1181        1117 :   GEN Q = cgetg(l,t_VECSMALL);
    1182        1117 :   ulong hi = h;
    1183        1117 :   Q[l-1] = P[l-1];
    1184       12538 :   for (i=l-2; i>=2; i--)
    1185             :   {
    1186       12538 :     Q[i] = Fl_mul(P[i], hi, p);
    1187       12538 :     if (i == 2) break;
    1188       11421 :     hi = Fl_mul(hi,h, p);
    1189             :   }
    1190        1117 :   Q[1] = P[1]; return Q;
    1191             : }
    1192             : 
    1193             : /* x/polrecip(P)+O(x^n); allow pi = 0 */
    1194             : static GEN
    1195      134080 : Flx_invBarrett_basecase(GEN T, ulong p, ulong pi)
    1196             : {
    1197      134080 :   long i, l=lg(T)-1, lr=l-1, k;
    1198      134080 :   GEN r=cgetg(lr,t_VECSMALL); r[1] = T[1];
    1199      134080 :   r[2] = 1;
    1200      134080 :   if (!pi)
    1201      761670 :     for (i=3;i<lr;i++)
    1202             :     {
    1203      754724 :       ulong u = uel(T, l-i+2);
    1204    45286854 :       for (k=3; k<i; k++)
    1205    44532130 :         { u += uel(T,l-i+k) * uel(r, k); if (u & HIGHBIT) u %= p; }
    1206      754724 :       r[i] = Fl_neg(u % p, p);
    1207             :     }
    1208             :   else
    1209     2108040 :     for (i=3;i<lr;i++)
    1210             :     {
    1211     1980907 :       ulong u = Fl_neg(uel(T,l-i+2), p);
    1212    59495455 :       for (k=3; k<i; k++)
    1213             :       {
    1214    57514549 :         ulong t = Fl_neg(uel(T,l-i+k), p);
    1215    57514550 :         u = Fl_addmul_pre(u, t, uel(r,k), p, pi);
    1216             :       }
    1217     1980906 :       r[i] = u;
    1218             :     }
    1219      134079 :   return Flx_renormalize(r,lr);
    1220             : }
    1221             : 
    1222             : /* Return new lgpol */
    1223             : static long
    1224     2131064 : Flx_lgrenormalizespec(GEN x, long lx)
    1225             : {
    1226             :   long i;
    1227     7401017 :   for (i = lx-1; i>=0; i--)
    1228     7400200 :     if (x[i]) break;
    1229     2131064 :   return i+1;
    1230             : }
    1231             : /* allow pi = 0 */
    1232             : static GEN
    1233       23054 : Flx_invBarrett_Newton(GEN T, ulong p, ulong pi)
    1234             : {
    1235       23054 :   long nold, lx, lz, lq, l = degpol(T), lQ;
    1236       23054 :   GEN q, y, z, x = zero_zv(l+1) + 2;
    1237       23056 :   ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
    1238             :   pari_sp av;
    1239             : 
    1240       23056 :   y = T+2;
    1241       23056 :   q = Flx_recipspec(y,l+1,l+1); lQ = lgpol(q); q+=2;
    1242       23054 :   av = avma;
    1243             :   /* We work on _spec_ Flx's, all the l[xzq12] below are lgpol's */
    1244             : 
    1245             :   /* initialize */
    1246       23054 :   x[0] = Fl_inv(q[0], p);
    1247       23055 :   if (lQ>1 && q[1])
    1248        5106 :   {
    1249        5106 :     ulong u = q[1];
    1250        5106 :     if (x[0] != 1) u = Fl_mul(u, Fl_sqr(x[0],p), p);
    1251        5106 :     x[1] = p - u; lx = 2;
    1252             :   }
    1253             :   else
    1254       17949 :     lx = 1;
    1255       23055 :   nold = 1;
    1256      158279 :   for (; mask > 1; set_avma(av))
    1257             :   { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
    1258      135228 :     long i, lnew, nnew = nold << 1;
    1259             : 
    1260      135228 :     if (mask & 1) nnew--;
    1261      135228 :     mask >>= 1;
    1262             : 
    1263      135228 :     lnew = nnew + 1;
    1264      135228 :     lq = Flx_lgrenormalizespec(q, minss(lQ, lnew));
    1265      135239 :     z = Flx_mulspec(x, q, p, pi, lx, lq); /* FIXME: high product */
    1266      135226 :     lz = lgpol(z); if (lz > lnew) lz = lnew;
    1267      135225 :     z += 2;
    1268             :     /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
    1269      290427 :     for (i = nold; i < lz; i++) if (z[i]) break;
    1270      135225 :     nold = nnew;
    1271      135225 :     if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
    1272             : 
    1273             :     /* z + i represents (x*q - 1) / t^i */
    1274      100825 :     lz = Flx_lgrenormalizespec (z+i, lz-i);
    1275      100829 :     z = Flx_mulspec(x, z+i, p, pi, lx, lz); /* FIXME: low product */
    1276      100825 :     lz = lgpol(z); z += 2;
    1277      100825 :     if (lz > lnew-i) lz = Flx_lgrenormalizespec(z, lnew-i);
    1278             : 
    1279      100826 :     lx = lz+ i;
    1280      100826 :     y  = x + i; /* x -= z * t^i, in place */
    1281      913408 :     for (i = 0; i < lz; i++) y[i] = Fl_neg(z[i], p);
    1282             :   }
    1283       23056 :   x -= 2; setlg(x, lx + 2); x[1] = T[1];
    1284       23056 :   return x;
    1285             : }
    1286             : 
    1287             : /* allow pi = 0 */
    1288             : static GEN
    1289      158500 : Flx_invBarrett_pre(GEN T, ulong p, ulong pi)
    1290             : {
    1291      158500 :   pari_sp ltop = avma;
    1292      158500 :   long l = lgpol(T);
    1293             :   GEN r;
    1294      158500 :   if (l < 3) return pol0_Flx(T[1]);
    1295      157134 :   if (l < get_Fl_threshold(p, Flx_INVBARRETT_LIMIT, Flx_INVBARRETT2_LIMIT))
    1296             :   {
    1297      134080 :     ulong c = T[l+1];
    1298      134080 :     if (c != 1)
    1299             :     {
    1300       98101 :       ulong ci = Fl_inv(c,p);
    1301       98101 :       T = Flx_Fl_mul(T, ci, p);
    1302       98101 :       r = Flx_invBarrett_basecase(T, p, pi);
    1303       98100 :       r = Flx_Fl_mul(r, ci, p);
    1304             :     }
    1305             :     else
    1306       35979 :       r = Flx_invBarrett_basecase(T, p, pi);
    1307             :   }
    1308             :   else
    1309       23054 :     r = Flx_invBarrett_Newton(T, p, pi);
    1310      157136 :   return gerepileuptoleaf(ltop, r);
    1311             : }
    1312             : GEN
    1313           0 : Flx_invBarrett(GEN T, ulong p)
    1314           0 : { return Flx_invBarrett_pre(T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1315             : 
    1316             : /* allow pi = 0 */
    1317             : GEN
    1318    96618957 : Flx_get_red_pre(GEN T, ulong p, ulong pi)
    1319             : {
    1320    96618957 :   if (typ(T)!=t_VECSMALL
    1321    96588326 :     || lgpol(T) < get_Fl_threshold(p, Flx_BARRETT_LIMIT,
    1322             :                                        Flx_BARRETT2_LIMIT))
    1323    96592730 :     return T;
    1324        7629 :   retmkvec2(Flx_invBarrett_pre(T, p, pi),T);
    1325             : }
    1326             : GEN
    1327    13563433 : Flx_get_red(GEN T, ulong p)
    1328             : {
    1329    13563433 :   if (typ(T)!=t_VECSMALL
    1330    13563460 :     || lgpol(T) < get_Fl_threshold(p, Flx_BARRETT_LIMIT,
    1331             :                                        Flx_BARRETT2_LIMIT))
    1332    13556518 :     return T;
    1333        5220 :   retmkvec2(Flx_invBarrett_pre(T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)),T);
    1334             : }
    1335             : 
    1336             : /* separate from Flx_divrem for maximal speed. */
    1337             : static GEN
    1338   704210591 : Flx_rem_basecase(GEN x, GEN y, ulong p, ulong pi)
    1339             : {
    1340             :   pari_sp av;
    1341             :   GEN z, c;
    1342             :   long dx,dy,dy1,dz,i,j;
    1343             :   ulong p1,inv;
    1344   704210591 :   long vs=x[1];
    1345             : 
    1346   704210591 :   dy = degpol(y); if (!dy) return pol0_Flx(x[1]);
    1347   673526082 :   dx = degpol(x);
    1348   673739140 :   dz = dx-dy; if (dz < 0) return Flx_copy(x);
    1349   673739140 :   x += 2; y += 2;
    1350   673739140 :   inv = y[dy];
    1351   673739140 :   if (inv != 1UL) inv = Fl_inv(inv,p);
    1352   813885202 :   for (dy1=dy-1; dy1>=0 && !y[dy1]; dy1--);
    1353             : 
    1354   675116064 :   c = cgetg(dy+3, t_VECSMALL); c[1]=vs; c += 2; av=avma;
    1355   672953718 :   z = cgetg(dz+3, t_VECSMALL); z[1]=vs; z += 2;
    1356             : 
    1357   671465617 :   if (!pi)
    1358             :   {
    1359   471744183 :     z[dz] = (inv*x[dx]) % p;
    1360  1816678069 :     for (i=dx-1; i>=dy; --i)
    1361             :     {
    1362  1344933886 :       p1 = p - x[i]; /* compute -p1 instead of p1 (pb with ulongs otherwise) */
    1363 10730206315 :       for (j=i-dy1; j<=i && j<=dz; j++)
    1364             :       {
    1365  9385272429 :         p1 += z[j]*y[i-j];
    1366  9385272429 :         if (p1 & HIGHBIT) p1 %= p;
    1367             :       }
    1368  1344933886 :       p1 %= p;
    1369  1344933886 :       z[i-dy] = p1? ((p - p1)*inv) % p: 0;
    1370             :     }
    1371  3299479142 :     for (i=0; i<dy; i++)
    1372             :     {
    1373  2827137742 :       p1 = z[0]*y[i];
    1374 14805807026 :       for (j=maxss(1,i-dy1); j<=i && j<=dz; j++)
    1375             :       {
    1376 11978669284 :         p1 += z[j]*y[i-j];
    1377 11978669284 :         if (p1 & HIGHBIT) p1 %= p;
    1378             :       }
    1379  2827513792 :       c[i] = Fl_sub(x[i], p1%p, p);
    1380             :     }
    1381             :   }
    1382             :   else
    1383             :   {
    1384   199721434 :     z[dz] = Fl_mul_pre(inv, x[dx], p, pi);
    1385   663534219 :     for (i=dx-1; i>=dy; --i)
    1386             :     {
    1387   463803774 :       p1 = p - x[i]; /* compute -p1 instead of p1 (pb with ulongs otherwise) */
    1388  1994558547 :       for (j=i-dy1; j<=i && j<=dz; j++)
    1389  1530883956 :         p1 = Fl_addmul_pre(p1, z[j], y[i - j], p, pi);
    1390   463674591 :       z[i-dy] = p1? Fl_mul_pre(p - p1, inv, p, pi): 0;
    1391             :     }
    1392  1465287400 :     for (i=0; i<dy; i++)
    1393             :     {
    1394  1266028474 :       p1 = Fl_mul_pre(z[0],y[i],p,pi);
    1395  3639711105 :       for (j=maxss(1,i-dy1); j<=i && j<=dz; j++)
    1396  2366682489 :         p1 = Fl_addmul_pre(p1, z[j], y[i - j], p, pi);
    1397  1255172978 :       c[i] = Fl_sub(x[i], p1, p);
    1398             :     }
    1399             :   }
    1400   835896431 :   i = dy-1; while (i>=0 && !c[i]) i--;
    1401   671600326 :   set_avma(av); return Flx_renormalize(c-2, i+3);
    1402             : }
    1403             : 
    1404             : /* as FpX_divrem but working only on ulong types.
    1405             :  * if relevant, *pr is the last object on stack */
    1406             : static GEN
    1407    60530125 : Flx_divrem_basecase(GEN x, GEN y, ulong p, ulong pi, GEN *pr)
    1408             : {
    1409             :   GEN z,q,c;
    1410             :   long dx,dy,dy1,dz,i,j;
    1411             :   ulong p1,inv;
    1412    60530125 :   long sv=x[1];
    1413             : 
    1414    60530125 :   dy = degpol(y);
    1415    60528458 :   if (dy<0) pari_err_INV("Flx_divrem",y);
    1416    60528894 :   if (pr == ONLY_REM) return Flx_rem_basecase(x, y, p, pi);
    1417    60528448 :   if (!dy)
    1418             :   {
    1419     7166693 :     if (pr && pr != ONLY_DIVIDES) *pr = pol0_Flx(sv);
    1420     7166561 :     if (y[2] == 1UL) return Flx_copy(x);
    1421     4979630 :     return Flx_Fl_mul(x, Fl_inv(y[2], p), p);
    1422             :   }
    1423    53361755 :   dx = degpol(x);
    1424    53367576 :   dz = dx-dy;
    1425    53367576 :   if (dz < 0)
    1426             :   {
    1427      928838 :     q = pol0_Flx(sv);
    1428      928824 :     if (pr && pr != ONLY_DIVIDES) *pr = Flx_copy(x);
    1429      928824 :     return q;
    1430             :   }
    1431    52438738 :   x += 2;
    1432    52438738 :   y += 2;
    1433    52438738 :   z = cgetg(dz + 3, t_VECSMALL); z[1] = sv; z += 2;
    1434    52424732 :   inv = uel(y, dy);
    1435    52424732 :   if (inv != 1UL) inv = Fl_inv(inv,p);
    1436    77392965 :   for (dy1=dy-1; dy1>=0 && !y[dy1]; dy1--);
    1437             : 
    1438    52430882 :   if (SMALL_ULONG(p))
    1439             :   {
    1440    50570611 :     z[dz] = (inv*x[dx]) % p;
    1441   129893024 :     for (i=dx-1; i>=dy; --i)
    1442             :     {
    1443    79322413 :       p1 = p - x[i]; /* compute -p1 instead of p1 (pb with ulongs otherwise) */
    1444   259964268 :       for (j=i-dy1; j<=i && j<=dz; j++)
    1445             :       {
    1446   180641855 :         p1 += z[j]*y[i-j];
    1447   180641855 :         if (p1 & HIGHBIT) p1 %= p;
    1448             :       }
    1449    79322413 :       p1 %= p;
    1450    79322413 :       z[i-dy] = p1? (long) ((p - p1)*inv) % p: 0;
    1451             :     }
    1452             :   }
    1453             :   else
    1454             :   {
    1455     1860271 :     z[dz] = Fl_mul(inv, x[dx], p);
    1456     9191718 :     for (i=dx-1; i>=dy; --i)
    1457             :     { /* compute -p1 instead of p1 (pb with ulongs otherwise) */
    1458     7333721 :       p1 = p - uel(x,i);
    1459    26278588 :       for (j=i-dy1; j<=i && j<=dz; j++)
    1460    18944870 :         p1 = Fl_add(p1, Fl_mul(z[j],y[i-j],p), p);
    1461     7333718 :       z[i-dy] = p1? Fl_mul(p - p1, inv, p): 0;
    1462             :     }
    1463             :   }
    1464    52428608 :   q = Flx_renormalize(z-2, dz+3);
    1465    52435448 :   if (!pr) return q;
    1466             : 
    1467    26352230 :   c = cgetg(dy + 3, t_VECSMALL); c[1] = sv; c += 2;
    1468    26355857 :   if (SMALL_ULONG(p))
    1469             :   {
    1470   233205488 :     for (i=0; i<dy; i++)
    1471             :     {
    1472   208473359 :       p1 = (ulong)z[0]*y[i];
    1473   488860740 :       for (j=maxss(1,i-dy1); j<=i && j<=dz; j++)
    1474             :       {
    1475   280387381 :         p1 += (ulong)z[j]*y[i-j];
    1476   280387381 :         if (p1 & HIGHBIT) p1 %= p;
    1477             :       }
    1478   208473200 :       c[i] = Fl_sub(x[i], p1%p, p);
    1479             :     }
    1480             :   }
    1481             :   else
    1482             :   {
    1483    17168531 :     for (i=0; i<dy; i++)
    1484             :     {
    1485    15544301 :       p1 = Fl_mul(z[0],y[i],p);
    1486    52509007 :       for (j=maxss(1,i-dy1); j<=i && j<=dz; j++)
    1487    36964704 :         p1 = Fl_add(p1, Fl_mul(z[j],y[i-j],p), p);
    1488    15544303 :       c[i] = Fl_sub(x[i], p1, p);
    1489             :     }
    1490             :   }
    1491    35452429 :   i=dy-1; while (i>=0 && !c[i]) i--;
    1492    26356359 :   c = Flx_renormalize(c-2, i+3);
    1493    26356112 :   if (pr == ONLY_DIVIDES)
    1494         420 :   { if (lg(c) != 2) return NULL; }
    1495             :   else
    1496    26355692 :     *pr = c;
    1497    26355972 :   return q;
    1498             : }
    1499             : 
    1500             : /* Compute x mod T where 2 <= degpol(T) <= l+1 <= 2*(degpol(T)-1)
    1501             :  * and mg is the Barrett inverse of T. */
    1502             : static GEN
    1503      905077 : Flx_divrem_Barrettspec(GEN x, long l, GEN mg, GEN T, ulong p, ulong pi, GEN *pr)
    1504             : {
    1505             :   GEN q, r;
    1506      905077 :   long lt = degpol(T); /*We discard the leading term*/
    1507             :   long ld, lm, lT, lmg;
    1508      905016 :   ld = l-lt;
    1509      905016 :   lm = minss(ld, lgpol(mg));
    1510      905173 :   lT  = Flx_lgrenormalizespec(T+2,lt);
    1511      905275 :   lmg = Flx_lgrenormalizespec(mg+2,lm);
    1512      905206 :   q = Flx_recipspec(x+lt,ld,ld);               /* q = rec(x)      lz<=ld*/
    1513      904640 :   q = Flx_mulspec(q+2,mg+2,p,pi,lgpol(q),lmg); /* q = rec(x) * mg lz<=ld+lm*/
    1514      905165 :   q = Flx_recipspec(q+2,minss(ld,lgpol(q)),ld);/* q = rec (rec(x) * mg) lz<=ld*/
    1515      904553 :   if (!pr) return q;
    1516      896899 :   r = Flx_mulspec(q+2,T+2,p,pi,lgpol(q),lT);   /* r = q*pol      lz<=ld+lt*/
    1517      897558 :   r = Flx_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* r = x - q*pol lz<=lt */
    1518      897346 :   if (pr == ONLY_REM) return r;
    1519      424116 :   *pr = r; return q;
    1520             : }
    1521             : 
    1522             : static GEN
    1523      608341 : Flx_divrem_Barrett(GEN x, GEN mg, GEN T, ulong p, ulong pi, GEN *pr)
    1524             : {
    1525      608341 :   GEN q = NULL, r = Flx_copy(x);
    1526      608373 :   long l = lgpol(x), lt = degpol(T), lm = 2*lt-1, v = T[1];
    1527             :   long i;
    1528      608367 :   if (l <= lt)
    1529             :   {
    1530           0 :     if (pr == ONLY_REM) return Flx_copy(x);
    1531           0 :     if (pr == ONLY_DIVIDES) return lgpol(x)? NULL: pol0_Flx(v);
    1532           0 :     if (pr) *pr = Flx_copy(x);
    1533           0 :     return pol0_Flx(v);
    1534             :   }
    1535      608367 :   if (lt <= 1)
    1536        1366 :     return Flx_divrem_basecase(x,T,p,pi,pr);
    1537      607001 :   if (pr != ONLY_REM && l>lm)
    1538       28877 :   { q = zero_zv(l-lt+1); q[1] = T[1]; }
    1539      906578 :   while (l>lm)
    1540             :   {
    1541      299727 :     GEN zr, zq = Flx_divrem_Barrettspec(r+2+l-lm,lm,mg,T,p,pi,&zr);
    1542      299623 :     long lz = lgpol(zr);
    1543      299577 :     if (pr != ONLY_REM)
    1544             :     {
    1545       57046 :       long lq = lgpol(zq);
    1546      851892 :       for(i=0; i<lq; i++) q[2+l-lm+i] = zq[2+i];
    1547             :     }
    1548     4348608 :     for(i=0; i<lz; i++)   r[2+l-lm+i] = zr[2+i];
    1549      299577 :     l = l-lm+lz;
    1550             :   }
    1551      606851 :   if (pr == ONLY_REM)
    1552             :   {
    1553      473300 :     if (l > lt)
    1554      473258 :       r = Flx_divrem_Barrettspec(r+2,l,mg,T,p,pi,ONLY_REM);
    1555             :     else
    1556          42 :       r = Flx_renormalize(r, l+2);
    1557      473272 :     r[1] = v; return r;
    1558             :   }
    1559      133551 :   if (l > lt)
    1560             :   {
    1561      132123 :     GEN zq = Flx_divrem_Barrettspec(r+2,l,mg,T,p,pi, pr ? &r: NULL);
    1562      132123 :     if (!q) q = zq;
    1563             :     else
    1564             :     {
    1565       27300 :       long lq = lgpol(zq);
    1566      158521 :       for(i=0; i<lq; i++) q[2+i] = zq[2+i];
    1567             :     }
    1568             :   }
    1569        1428 :   else if (pr)
    1570        1535 :     r = Flx_renormalize(r, l+2);
    1571      133551 :   q[1] = v; q = Flx_renormalize(q, lg(q));
    1572      133700 :   if (pr == ONLY_DIVIDES) return lgpol(r)? NULL: q;
    1573      133700 :   if (pr) { r[1] = v; *pr = r; }
    1574      133700 :   return q;
    1575             : }
    1576             : 
    1577             : /* allow pi = 0 (SMALL_ULONG) */
    1578             : GEN
    1579    77678001 : Flx_divrem_pre(GEN x, GEN T, ulong p, ulong pi, GEN *pr)
    1580             : {
    1581             :   GEN B, y;
    1582             :   long dy, dx, d;
    1583    77678001 :   if (pr==ONLY_REM) return Flx_rem_pre(x, T, p, pi);
    1584    60654648 :   y = get_Flx_red(T, &B);
    1585    60674652 :   dy = degpol(y); dx = degpol(x); d = dx-dy;
    1586    60663241 :   if (!B && d+3 < get_Fl_threshold(p, Flx_DIVREM_BARRETT_LIMIT,Flx_DIVREM2_BARRETT_LIMIT))
    1587    60526993 :     return Flx_divrem_basecase(x,y,p,pi,pr);
    1588             :   else
    1589             :   {
    1590      134620 :     pari_sp av = avma;
    1591      134620 :     GEN mg = B? B: Flx_invBarrett_pre(y, p, pi);
    1592      134620 :     GEN q1 = Flx_divrem_Barrett(x,mg,y,p,pi,pr);
    1593      134620 :     if (!q1) return gc_NULL(av);
    1594      134620 :     if (!pr || pr==ONLY_DIVIDES) return gerepileuptoleaf(av, q1);
    1595      126369 :     return gc_all(av, 2, &q1, pr);
    1596             :   }
    1597             : }
    1598             : GEN
    1599    29669924 : Flx_divrem(GEN x, GEN T, ulong p, GEN *pr)
    1600    29669924 : { return Flx_divrem_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), pr); }
    1601             : 
    1602             : GEN
    1603   825158653 : Flx_rem_pre(GEN x, GEN T, ulong p, ulong pi)
    1604             : {
    1605   825158653 :   GEN B, y = get_Flx_red(T, &B);
    1606   824879197 :   long d = degpol(x) - degpol(y);
    1607   824671730 :   if (d < 0) return Flx_copy(x);
    1608   704864591 :   if (!B && d+3 < get_Fl_threshold(p, Flx_REM_BARRETT_LIMIT,Flx_REM2_BARRETT_LIMIT))
    1609   704104073 :     return Flx_rem_basecase(x,y,p, pi);
    1610             :   else
    1611             :   {
    1612      473720 :     pari_sp av=avma;
    1613      473720 :     GEN mg = B ? B: Flx_invBarrett_pre(y, p, pi);
    1614      473722 :     GEN r  = Flx_divrem_Barrett(x, mg, y, p, pi, ONLY_REM);
    1615      473716 :     return gerepileuptoleaf(av, r);
    1616             :   }
    1617             : }
    1618             : GEN
    1619    40812235 : Flx_rem(GEN x, GEN T, ulong p)
    1620    40812235 : { return Flx_rem_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1621             : 
    1622             : /* reduce T mod (X^n - 1, p). Shallow function */
    1623             : GEN
    1624     5023973 : Flx_mod_Xnm1(GEN T, ulong n, ulong p)
    1625             : {
    1626     5023973 :   long i, j, L = lg(T), l = n+2;
    1627             :   GEN S;
    1628     5023973 :   if (L <= l || n & ~LGBITS) return T;
    1629        3470 :   S = cgetg(l, t_VECSMALL);
    1630        3470 :   S[1] = T[1];
    1631       13838 :   for (i = 2; i < l; i++) S[i] = T[i];
    1632        9594 :   for (j = 2; i < L; i++) {
    1633        6124 :     S[j] = Fl_add(S[j], T[i], p);
    1634        6124 :     if (++j == l) j = 2;
    1635             :   }
    1636        3470 :   return Flx_renormalize(S, l);
    1637             : }
    1638             : /* reduce T mod (X^n + 1, p). Shallow function */
    1639             : GEN
    1640       27539 : Flx_mod_Xn1(GEN T, ulong n, ulong p)
    1641             : {
    1642       27539 :   long i, j, L = lg(T), l = n+2;
    1643             :   GEN S;
    1644       27539 :   if (L <= l || n & ~LGBITS) return T;
    1645        2721 :   S = cgetg(l, t_VECSMALL);
    1646        2721 :   S[1] = T[1];
    1647       11227 :   for (i = 2; i < l; i++) S[i] = T[i];
    1648        7214 :   for (j = 2; i < L; i++) {
    1649        4493 :     S[j] = Fl_sub(S[j], T[i], p);
    1650        4493 :     if (++j == l) j = 2;
    1651             :   }
    1652        2721 :   return Flx_renormalize(S, l);
    1653             : }
    1654             : 
    1655             : struct _Flxq {
    1656             :   GEN aut, T;
    1657             :   ulong p, pi;
    1658             : };
    1659             : /* allow pi = 0 */
    1660             : static void
    1661    70366224 : set_Flxq_pre(struct _Flxq *D, GEN T, ulong p, ulong pi)
    1662             : {
    1663    70366224 :   D->p = p;
    1664    70366224 :   D->pi = pi;
    1665    70366224 :   D->T = Flx_get_red_pre(T, p, pi);
    1666    70375884 : }
    1667             : static void
    1668       67942 : set_Flxq(struct _Flxq *D, GEN T, ulong p)
    1669       67942 : { set_Flxq_pre(D, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    1670             : 
    1671             : static GEN
    1672           0 : _Flx_divrem(void * E, GEN x, GEN y, GEN *r)
    1673             : {
    1674           0 :   struct _Flxq *D = (struct _Flxq*) E;
    1675           0 :   return Flx_divrem_pre(x, y, D->p, D->pi, r);
    1676             : }
    1677             : static GEN
    1678      582784 : _Flx_add(void * E, GEN x, GEN y) {
    1679      582784 :   struct _Flxq *D = (struct _Flxq*) E;
    1680      582784 :   return Flx_add(x, y, D->p);
    1681             : }
    1682             : static GEN
    1683    10175980 : _Flx_mul(void *E, GEN x, GEN y) {
    1684    10175980 :   struct _Flxq *D = (struct _Flxq*) E;
    1685    10175980 :   return Flx_mul_pre(x, y, D->p, D->pi);
    1686             : }
    1687             : static GEN
    1688           0 : _Flx_sqr(void *E, GEN x) {
    1689           0 :   struct _Flxq *D = (struct _Flxq*) E;
    1690           0 :   return Flx_sqr_pre(x, D->p, D->pi);
    1691             : }
    1692             : 
    1693             : static struct bb_ring Flx_ring = { _Flx_add,_Flx_mul,_Flx_sqr };
    1694             : 
    1695             : GEN
    1696           0 : Flx_digits(GEN x, GEN T, ulong p)
    1697             : {
    1698             :   struct _Flxq D;
    1699           0 :   long d = degpol(T), n = (lgpol(x)+d-1)/d;
    1700           0 :   D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1701           0 :   return gen_digits(x,T,n,(void *)&D, &Flx_ring, _Flx_divrem);
    1702             : }
    1703             : 
    1704             : GEN
    1705           0 : FlxV_Flx_fromdigits(GEN x, GEN T, ulong p)
    1706             : {
    1707             :   struct _Flxq D;
    1708           0 :   D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1709           0 :   return gen_fromdigits(x,T,(void *)&D, &Flx_ring);
    1710             : }
    1711             : 
    1712             : long
    1713     3657626 : Flx_val(GEN x)
    1714             : {
    1715     3657626 :   long i, l=lg(x);
    1716     3657626 :   if (l==2)  return LONG_MAX;
    1717     3666025 :   for (i=2; i<l && x[i]==0; i++) /*empty*/;
    1718     3657626 :   return i-2;
    1719             : }
    1720             : long
    1721    25504004 : Flx_valrem(GEN x, GEN *Z)
    1722             : {
    1723    25504004 :   long v, i, l=lg(x);
    1724             :   GEN y;
    1725    25504004 :   if (l==2) { *Z = Flx_copy(x); return LONG_MAX; }
    1726    27673064 :   for (i=2; i<l && x[i]==0; i++) /*empty*/;
    1727    25504004 :   v = i-2;
    1728    25504004 :   if (v == 0) { *Z = x; return 0; }
    1729     1022115 :   l -= v;
    1730     1022115 :   y = cgetg(l, t_VECSMALL); y[1] = x[1];
    1731     2612663 :   for (i=2; i<l; i++) y[i] = x[i+v];
    1732     1017952 :   *Z = y; return v;
    1733             : }
    1734             : 
    1735             : GEN
    1736    18268873 : Flx_deriv(GEN z, ulong p)
    1737             : {
    1738    18268873 :   long i,l = lg(z)-1;
    1739             :   GEN x;
    1740    18268873 :   if (l < 2) l = 2;
    1741    18268873 :   x = cgetg(l, t_VECSMALL); x[1] = z[1]; z++;
    1742    18260294 :   if (HIGHWORD(l | p))
    1743    52616903 :     for (i=2; i<l; i++) x[i] = Fl_mul((ulong)i-1, z[i], p);
    1744             :   else
    1745    74656874 :     for (i=2; i<l; i++) x[i] = ((i-1) * z[i]) % p;
    1746    18261216 :   return Flx_renormalize(x,l);
    1747             : }
    1748             : 
    1749             : static GEN
    1750      422556 : Flx_integXn(GEN x, long n, ulong p)
    1751             : {
    1752      422556 :   long i, lx = lg(x);
    1753             :   GEN y;
    1754      422556 :   if (lx == 2) return Flx_copy(x);
    1755      412742 :   y = cgetg(lx, t_VECSMALL); y[1] = x[1];
    1756     2087976 :   for (i=2; i<lx; i++)
    1757             :   {
    1758     1674662 :     ulong xi = uel(x,i);
    1759     1674662 :     if (xi == 0)
    1760       12505 :       uel(y,i) = 0;
    1761             :     else
    1762             :     {
    1763     1662157 :       ulong j = n+i-1;
    1764     1662157 :       ulong d = ugcd(j, xi);
    1765     1662084 :       if (d==1)
    1766     1014521 :         uel(y,i) = Fl_div(xi, j, p);
    1767             :       else
    1768      647563 :         uel(y,i) = Fl_div(xi/d, j/d, p);
    1769             :     }
    1770             :   }
    1771      413314 :   return Flx_renormalize(y, lx);;
    1772             : }
    1773             : 
    1774             : GEN
    1775           0 : Flx_integ(GEN x, ulong p)
    1776             : {
    1777           0 :   long i, lx = lg(x);
    1778             :   GEN y;
    1779           0 :   if (lx == 2) return Flx_copy(x);
    1780           0 :   y = cgetg(lx+1, t_VECSMALL); y[1] = x[1];
    1781           0 :   uel(y,2) = 0;
    1782           0 :   for (i=3; i<=lx; i++)
    1783           0 :     uel(y,i) = uel(x,i-1) ? Fl_div(uel(x,i-1), (i-2)%p, p): 0UL;
    1784           0 :   return Flx_renormalize(y, lx+1);;
    1785             : }
    1786             : 
    1787             : /* assume p prime */
    1788             : GEN
    1789       13447 : Flx_diff1(GEN P, ulong p)
    1790             : {
    1791       13447 :   return Flx_sub(Flx_translate1(P, p), P, p);
    1792             : }
    1793             : 
    1794             : GEN
    1795      344365 : Flx_deflate(GEN x0, long d)
    1796             : {
    1797             :   GEN z, y, x;
    1798      344365 :   long i,id, dy, dx = degpol(x0);
    1799      344365 :   if (d == 1 || dx <= 0) return Flx_copy(x0);
    1800      281155 :   dy = dx/d;
    1801      281155 :   y = cgetg(dy+3, t_VECSMALL); y[1] = x0[1];
    1802      281147 :   z = y + 2;
    1803      281147 :   x = x0+ 2;
    1804      929564 :   for (i=id=0; i<=dy; i++,id+=d) z[i] = x[id];
    1805      281147 :   return y;
    1806             : }
    1807             : 
    1808             : GEN
    1809      163784 : Flx_inflate(GEN x0, long d)
    1810             : {
    1811      163784 :   long i, id, dy, dx = degpol(x0);
    1812      163776 :   GEN x = x0 + 2, z, y;
    1813      163776 :   if (dx <= 0) return Flx_copy(x0);
    1814      162651 :   dy = dx*d;
    1815      162651 :   y = cgetg(dy+3, t_VECSMALL); y[1] = x0[1];
    1816      162624 :   z = y + 2;
    1817     9256178 :   for (i=0; i<=dy; i++) z[i] = 0;
    1818     4510545 :   for (i=id=0; i<=dx; i++,id+=d) z[id] = x[i];
    1819      162624 :   return y;
    1820             : }
    1821             : 
    1822             : /* write p(X) = a_0(X^k) + X*a_1(X^k) + ... + X^(k-1)*a_{k-1}(X^k) */
    1823             : GEN
    1824      149030 : Flx_splitting(GEN p, long k)
    1825             : {
    1826      149030 :   long n = degpol(p), v = p[1], m, i, j, l;
    1827             :   GEN r;
    1828             : 
    1829      149024 :   m = n/k;
    1830      149024 :   r = cgetg(k+1,t_VEC);
    1831      684329 :   for(i=1; i<=k; i++)
    1832             :   {
    1833      535313 :     gel(r,i) = cgetg(m+3, t_VECSMALL);
    1834      535315 :     mael(r,i,1) = v;
    1835             :   }
    1836     4673565 :   for (j=1, i=0, l=2; i<=n; i++)
    1837             :   {
    1838     4524549 :     mael(r,j,l) = p[2+i];
    1839     4524549 :     if (j==k) { j=1; l++; } else j++;
    1840             :   }
    1841      684370 :   for(i=1; i<=k; i++)
    1842      535375 :     gel(r,i) = Flx_renormalize(gel(r,i),i<j?l+1:l);
    1843      148995 :   return r;
    1844             : }
    1845             : 
    1846             : /* ux + vy */
    1847             : static GEN
    1848       23076 : Flx_addmulmul(GEN u, GEN v, GEN x, GEN y, ulong p, ulong pi)
    1849       23076 : { return Flx_add(Flx_mul_pre(u,x, p,pi), Flx_mul_pre(v,y, p,pi), p); }
    1850             : 
    1851             : static GEN
    1852       11532 : FlxM_Flx_mul2(GEN M, GEN x, GEN y, ulong p, ulong pi)
    1853             : {
    1854       11532 :   GEN res = cgetg(3, t_COL);
    1855       11532 :   gel(res, 1) = Flx_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, p, pi);
    1856       11532 :   gel(res, 2) = Flx_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, p, pi);
    1857       11532 :   return res;
    1858             : }
    1859             : 
    1860             : #if 0
    1861             : static GEN
    1862             : FlxM_mul2_old(GEN M, GEN N, ulong p)
    1863             : {
    1864             :   GEN res = cgetg(3, t_MAT);
    1865             :   gel(res, 1) = FlxM_Flx_mul2(M,gcoeff(N,1,1),gcoeff(N,2,1),p);
    1866             :   gel(res, 2) = FlxM_Flx_mul2(M,gcoeff(N,1,2),gcoeff(N,2,2),p);
    1867             :   return res;
    1868             : }
    1869             : #endif
    1870             : /* A,B are 2x2 matrices, Flx entries. Return A x B using Strassen 7M formula */
    1871             : static GEN
    1872        2109 : FlxM_mul2(GEN A, GEN B, ulong p, ulong pi)
    1873             : {
    1874        2109 :   GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
    1875        2109 :   GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
    1876        2109 :   GEN M1 = Flx_mul_pre(Flx_add(A11,A22, p), Flx_add(B11,B22, p), p, pi);
    1877        2109 :   GEN M2 = Flx_mul_pre(Flx_add(A21,A22, p), B11, p, pi);
    1878        2109 :   GEN M3 = Flx_mul_pre(A11, Flx_sub(B12,B22, p), p, pi);
    1879        2109 :   GEN M4 = Flx_mul_pre(A22, Flx_sub(B21,B11, p), p, pi);
    1880        2109 :   GEN M5 = Flx_mul_pre(Flx_add(A11,A12, p), B22, p, pi);
    1881        2109 :   GEN M6 = Flx_mul_pre(Flx_sub(A21,A11, p), Flx_add(B11,B12, p), p, pi);
    1882        2109 :   GEN M7 = Flx_mul_pre(Flx_sub(A12,A22, p), Flx_add(B21,B22, p), p, pi);
    1883        2109 :   GEN T1 = Flx_add(M1,M4, p), T2 = Flx_sub(M7,M5, p);
    1884        2109 :   GEN T3 = Flx_sub(M1,M2, p), T4 = Flx_add(M3,M6, p);
    1885        2109 :   retmkmat2(mkcol2(Flx_add(T1,T2, p), Flx_add(M2,M4, p)),
    1886             :             mkcol2(Flx_add(M3,M5, p), Flx_add(T3,T4, p)));
    1887             : }
    1888             : 
    1889             : /* Return [0,1;1,-q]*M */
    1890             : static GEN
    1891        2103 : Flx_FlxM_qmul(GEN q, GEN M, ulong p, ulong pi)
    1892             : {
    1893        2103 :   GEN u, v, res = cgetg(3, t_MAT);
    1894        2103 :   u = Flx_sub(gcoeff(M,1,1), Flx_mul_pre(gcoeff(M,2,1), q, p, pi), p);
    1895        2103 :   gel(res,1) = mkcol2(gcoeff(M,2,1), u);
    1896        2103 :   v = Flx_sub(gcoeff(M,1,2), Flx_mul_pre(gcoeff(M,2,2), q, p, pi), p);
    1897        2103 :   gel(res,2) = mkcol2(gcoeff(M,2,2), v);
    1898        2103 :   return res;
    1899             : }
    1900             : 
    1901             : static GEN
    1902         851 : matid2_FlxM(long v)
    1903             : {
    1904         851 :   return mkmat2(mkcol2(pol1_Flx(v),pol0_Flx(v)),
    1905             :                 mkcol2(pol0_Flx(v),pol1_Flx(v)));
    1906             : }
    1907             : 
    1908             : struct Flx_res
    1909             : {
    1910             :    ulong res, lc;
    1911             :    long deg0, deg1, off;
    1912             : };
    1913             : 
    1914             : INLINE void
    1915        1696 : Flx_halfres_update_pre(long da, long db, long dr, ulong p, ulong pi, struct Flx_res *res)
    1916             : {
    1917        1696 :   if (dr >= 0)
    1918             :   {
    1919        1696 :     if (res->lc != 1)
    1920             :     {
    1921           3 :       if (pi)
    1922             :       {
    1923           0 :         res->lc  = Fl_powu_pre(res->lc, da - dr, p, pi);
    1924           0 :         res->res = Fl_mul_pre(res->res, res->lc, p, pi);
    1925             :       } else
    1926             :       {
    1927           3 :         res->lc  = Fl_powu(res->lc, da - dr, p);
    1928           3 :         res->res = Fl_mul(res->res, res->lc, p);
    1929             :       }
    1930             :     }
    1931        1696 :     if (both_odd(da + res->off, db + res->off))
    1932           0 :       res->res = Fl_neg(res->res, p);
    1933             :   } else
    1934             :   {
    1935           0 :     if (db == 0)
    1936             :     {
    1937           0 :       if (res->lc != 1)
    1938             :       {
    1939           0 :         if (pi)
    1940             :         {
    1941           0 :           res->lc  = Fl_powu_pre(res->lc, da, p, pi);
    1942           0 :           res->res = Fl_mul_pre(res->res, res->lc, p, pi);
    1943             :         } else
    1944             :         {
    1945           0 :           res->lc  = Fl_powu(res->lc, da, p);
    1946           0 :           res->res = Fl_mul(res->res, res->lc, p);
    1947             :         }
    1948             :       }
    1949             :     } else
    1950           0 :       res->res = 0;
    1951             :   }
    1952        1696 : }
    1953             : 
    1954             : static GEN
    1955      728067 : Flx_halfres_basecase(GEN a, GEN b, ulong p, ulong pi, struct Flx_res *res)
    1956             : {
    1957      728067 :   pari_sp av=avma;
    1958             :   GEN u,u1,v,v1;
    1959      728067 :   long vx = a[1];
    1960      728067 :   long n = lgpol(a)>>1;
    1961      728061 :   u1 = v = pol0_Flx(vx);
    1962      728054 :   u = v1 = pol1_Flx(vx);
    1963     2792716 :   while (lgpol(b)>n)
    1964             :   {
    1965             :     GEN r, q;
    1966     2064634 :     q = Flx_divrem_pre(a,b,p,pi, &r);
    1967     2064675 :     if (res)
    1968             :     {
    1969         851 :       long da = degpol(a), db=degpol(b), dr = degpol(r);
    1970         851 :       res->lc = Flx_lead(b);
    1971         851 :       if (dr >= n)
    1972           3 :         Flx_halfres_update_pre(da, db, dr, p, pi, res);
    1973             :       else
    1974             :       {
    1975         848 :         res->deg0 = da;
    1976         848 :         res->deg1 = db;
    1977             :       }
    1978             :     }
    1979     2064675 :     a = b; b = r; swap(u,u1); swap(v,v1);
    1980     2064675 :     u1 = Flx_sub(u1, Flx_mul(u, q, p), p);
    1981     2064633 :     v1 = Flx_sub(v1, Flx_mul(v, q, p), p);
    1982     2064673 :     if (gc_needed(av,2))
    1983             :     {
    1984           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_halfgcd (d = %ld)",degpol(b));
    1985           0 :       gerepileall(av,6, &a,&b,&u1,&v1,&u,&v);
    1986             :     }
    1987             :   }
    1988      727898 :   return gerepilecopy(av, mkmat2(mkcol2(u,u1), mkcol2(v,v1)));
    1989             : }
    1990             : 
    1991             : static GEN Flx_halfres_i(GEN x, GEN y, ulong p, ulong pi, struct Flx_res *res);
    1992             : 
    1993             : static GEN
    1994       11514 : Flx_halfres_split(GEN x, GEN y, ulong p, ulong pi, struct Flx_res *res)
    1995             : {
    1996       11514 :   pari_sp av = avma;
    1997             :   GEN R, S, V;
    1998             :   GEN x1, y1, r, q;
    1999       11514 :   long l = lgpol(x), n = l>>1, k;
    2000       11514 :   if (lgpol(y) <= n) return matid2_FlxM(x[1]);
    2001       10669 :   if (res)
    2002             :   {
    2003        3054 :      res->lc = Flx_lead(y);
    2004        3054 :      res->deg0 -= n;
    2005        3054 :      res->deg1 -= n;
    2006        3054 :      res->off += n;
    2007             :   }
    2008       10669 :   R = Flx_halfres_i(Flx_shift(x,-n),Flx_shift(y,-n),p,pi,res);
    2009       10669 :   if (res)
    2010             :   {
    2011        3054 :     res->off -= n;
    2012        3054 :     res->deg0 += n;
    2013        3054 :     res->deg1 += n;
    2014             :   }
    2015       10669 :   V = FlxM_Flx_mul2(R,x,y,p,pi); x1 = gel(V,1); y1 = gel(V,2);
    2016       10669 :   if (lgpol(y1) <= n) return gerepilecopy(av, R);
    2017        2103 :   k = 2*n-degpol(y1);
    2018        2103 :   q = Flx_divrem_pre(x1, y1, p, pi, &r);
    2019        2103 :   if (res)
    2020             :   {
    2021         845 :     long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
    2022         845 :     if (dy1 < degpol(y))
    2023           0 :       Flx_halfres_update_pre(res->deg0, res->deg1, dy1, p, pi, res);
    2024         845 :     res->lc = Flx_lead(y1);
    2025         845 :     res->deg0 = dx1;
    2026         845 :     res->deg1 = dy1;
    2027         845 :     if (dr >= n)
    2028             :     {
    2029         845 :       Flx_halfres_update_pre(dx1, dy1, dr, p, pi, res);
    2030         845 :       res->deg0 = dy1;
    2031         845 :       res->deg1 = dr;
    2032             :     }
    2033         845 :     res->deg0 -= k;
    2034         845 :     res->deg1 -= k;
    2035         845 :     res->off += k;
    2036             :   }
    2037        2103 :   S = Flx_halfres_i(Flx_shift(y1,-k), Flx_shift(r,-k),p,pi,res);
    2038        2103 :   if (res)
    2039             :   {
    2040         845 :     res->deg0 += k;
    2041         845 :     res->deg1 += k;
    2042         845 :     res->off -= k;
    2043             :   }
    2044        2103 :   return gerepileupto(av, FlxM_mul2(S,Flx_FlxM_qmul(q,R,p,pi),p,pi));
    2045             : }
    2046             : 
    2047             : static GEN
    2048      739586 : Flx_halfres_i(GEN x, GEN y, ulong p, ulong pi,struct Flx_res *res)
    2049             : {
    2050      739586 :   if (lgpol(x) < get_Fl_threshold(p, Flx_HALFGCD_LIMIT, Flx_HALFGCD2_LIMIT))
    2051      728067 :     return Flx_halfres_basecase(x, y, p, pi, res);
    2052       11514 :   return Flx_halfres_split(x, y, p, pi, res);
    2053             : }
    2054             : 
    2055             : static GEN
    2056      725966 : Flx_halfgcd_i(GEN x, GEN y, ulong p, ulong pi)
    2057      725966 : { return Flx_halfres_i(x, y, p, pi, NULL); }
    2058             : 
    2059             : /* Return M in GL_2(Fl[X]) such that:
    2060             : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
    2061             : */
    2062             : 
    2063             : GEN
    2064      725970 : Flx_halfgcd_pre(GEN x, GEN y, ulong p, ulong pi)
    2065             : {
    2066             :   pari_sp av;
    2067             :   GEN M,q,r;
    2068      725970 :   long lx=lgpol(x), ly=lgpol(y);
    2069      725966 :   if (!lx)
    2070             :   {
    2071           0 :     long v = x[1];
    2072           0 :     retmkmat2(mkcol2(pol0_Flx(v),pol1_Flx(v)),
    2073             :               mkcol2(pol1_Flx(v),pol0_Flx(v)));
    2074             :   }
    2075      725966 :   if (ly < lx) return Flx_halfgcd_i(x,y,p,pi);
    2076        4477 :   av = avma;
    2077        4477 :   q = Flx_divrem(y,x,p,&r);
    2078        4477 :   M = Flx_halfgcd_i(x,r,p,pi);
    2079        4477 :   gcoeff(M,1,1) = Flx_sub(gcoeff(M,1,1), Flx_mul_pre(q,gcoeff(M,1,2), p,pi), p);
    2080        4477 :   gcoeff(M,2,1) = Flx_sub(gcoeff(M,2,1), Flx_mul_pre(q,gcoeff(M,2,2), p,pi), p);
    2081        4477 :   return gerepilecopy(av, M);
    2082             : }
    2083             : 
    2084             : GEN
    2085         112 : Flx_halfgcd(GEN x, GEN y, ulong p)
    2086         112 : { return Flx_halfgcd_pre(x, y, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2087             : 
    2088             : /*Do not garbage collect*/
    2089             : static GEN
    2090    75375533 : Flx_gcd_basecase(GEN a, GEN b, ulong p, ulong pi)
    2091             : {
    2092    75375533 :   pari_sp av = avma;
    2093    75375533 :   ulong iter = 0;
    2094    75375533 :   if (lg(b) > lg(a)) swap(a, b);
    2095   263441229 :   while (lgpol(b))
    2096             :   {
    2097   187448839 :     GEN c = Flx_rem_pre(a,b,p,pi);
    2098   188065696 :     iter++; a = b; b = c;
    2099   188065696 :     if (gc_needed(av,2))
    2100             :     {
    2101           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_gcd (d = %ld)",degpol(c));
    2102           0 :       gerepileall(av,2, &a,&b);
    2103             :     }
    2104             :   }
    2105    75291072 :   return iter < 2 ? Flx_copy(a) : a;
    2106             : }
    2107             : 
    2108             : GEN
    2109    76919595 : Flx_gcd_pre(GEN x, GEN y, ulong p, ulong pi)
    2110             : {
    2111    76919595 :   pari_sp av = avma;
    2112             :   long lim;
    2113    76919595 :   if (!lgpol(x)) return Flx_copy(y);
    2114    75370364 :   lim = get_Fl_threshold(p, Flx_GCD_LIMIT, Flx_GCD2_LIMIT);
    2115    75387951 :   while (lgpol(y) >= lim)
    2116             :   {
    2117             :     GEN c;
    2118           9 :     if (lgpol(y)<=(lgpol(x)>>1))
    2119             :     {
    2120           0 :       GEN r = Flx_rem_pre(x, y, p, pi);
    2121           0 :       x = y; y = r;
    2122             :     }
    2123           9 :     c = FlxM_Flx_mul2(Flx_halfgcd_pre(x, y, p, pi), x, y, p, pi);
    2124           9 :     x = gel(c,1); y = gel(c,2);
    2125           9 :     if (gc_needed(av,2))
    2126             :     {
    2127           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_gcd (y = %ld)",degpol(y));
    2128           0 :       gerepileall(av,2,&x,&y);
    2129             :     }
    2130             :   }
    2131    75376353 :   return gerepileuptoleaf(av, Flx_gcd_basecase(x,y,p,pi));
    2132             : }
    2133             : GEN
    2134    27319961 : Flx_gcd(GEN x, GEN y, ulong p)
    2135    27319961 : { return Flx_gcd_pre(x, y, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2136             : 
    2137             : int
    2138     6231368 : Flx_is_squarefree(GEN z, ulong p)
    2139             : {
    2140     6231368 :   pari_sp av = avma;
    2141     6231368 :   GEN d = Flx_gcd(z, Flx_deriv(z,p) , p);
    2142     6231347 :   return gc_bool(av, degpol(d) == 0);
    2143             : }
    2144             : 
    2145             : static long
    2146      139421 : Flx_is_smooth_squarefree(GEN f, long r, ulong p, ulong pi)
    2147             : {
    2148      139421 :   pari_sp av = avma;
    2149             :   long i;
    2150      139421 :   GEN sx = polx_Flx(f[1]), a = sx;
    2151      593027 :   for(i=1;;i++)
    2152             :   {
    2153      593027 :     if (degpol(f)<=r) return gc_long(av,1);
    2154      567226 :     a = Flxq_powu_pre(Flx_rem_pre(a,f,p,pi), p, f, p, pi);
    2155      571528 :     if (Flx_equal(a, sx)) return gc_long(av,1);
    2156      567335 :     if (i==r) return gc_long(av,0);
    2157      455691 :     f = Flx_div_pre(f, Flx_gcd_pre(Flx_sub(a,sx,p),f,p,pi),p,pi);
    2158             :   }
    2159             : }
    2160             : 
    2161             : static long
    2162        9090 : Flx_is_l_pow(GEN x, ulong p)
    2163             : {
    2164        9090 :   ulong i, lx = lgpol(x);
    2165       18284 :   for (i=1; i<lx; i++)
    2166       16337 :     if (x[i+2] && i%p) return 0;
    2167        1947 :   return 1;
    2168             : }
    2169             : 
    2170             : int
    2171      139393 : Flx_is_smooth_pre(GEN g, long r, ulong p, ulong pi)
    2172             : {
    2173             :   while (1)
    2174        9091 :   {
    2175      139393 :     GEN f = Flx_gcd_pre(g, Flx_deriv(g, p), p, pi);
    2176      139347 :     if (!Flx_is_smooth_squarefree(Flx_div_pre(g, f, p, pi), r, p, pi))
    2177      111613 :       return 0;
    2178       27918 :     if (degpol(f)==0) return 1;
    2179        9078 :     g = Flx_is_l_pow(f,p) ? Flx_deflate(f, p): f;
    2180             :   }
    2181             : }
    2182             : int
    2183       74256 : Flx_is_smooth(GEN g, long r, ulong p)
    2184       74256 : { return Flx_is_smooth_pre(g, r, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2185             : 
    2186             : static GEN
    2187     6281148 : Flx_extgcd_basecase(GEN a, GEN b, ulong p, ulong pi, GEN *ptu, GEN *ptv)
    2188             : {
    2189     6281148 :   pari_sp av=avma;
    2190             :   GEN u,v,d,d1,v1;
    2191     6281148 :   long vx = a[1];
    2192     6281148 :   d = a; d1 = b;
    2193     6281148 :   v = pol0_Flx(vx); v1 = pol1_Flx(vx);
    2194    31636638 :   while (lgpol(d1))
    2195             :   {
    2196    25355242 :     GEN r, q = Flx_divrem_pre(d,d1,p,pi, &r);
    2197    25355504 :     v = Flx_sub(v,Flx_mul_pre(q,v1,p,pi),p);
    2198    25355815 :     u=v; v=v1; v1=u;
    2199    25355815 :     u=r; d=d1; d1=u;
    2200    25355815 :     if (gc_needed(av,2))
    2201             :     {
    2202           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_extgcd (d = %ld)",degpol(d));
    2203           0 :       gerepileall(av,5, &d,&d1,&u,&v,&v1);
    2204             :     }
    2205             :   }
    2206     6279445 :   if (ptu) *ptu = Flx_div_pre(Flx_sub(d, Flx_mul_pre(b,v,p,pi), p), a, p, pi);
    2207     6281003 :   *ptv = v; return d;
    2208             : }
    2209             : 
    2210             : static GEN
    2211           6 : Flx_extgcd_halfgcd(GEN x, GEN y, ulong p, ulong pi, GEN *ptu, GEN *ptv)
    2212             : {
    2213           6 :   pari_sp av=avma;
    2214           6 :   GEN u,v,R = matid2_FlxM(x[1]);
    2215           6 :   long lim = get_Fl_threshold(p, Flx_EXTGCD_LIMIT, Flx_EXTGCD2_LIMIT);
    2216          12 :   while (lgpol(y) >= lim)
    2217             :   {
    2218             :     GEN M, c;
    2219           6 :     if (lgpol(y)<=(lgpol(x)>>1))
    2220             :     {
    2221           0 :       GEN r, q = Flx_divrem_pre(x, y, p, pi, &r);
    2222           0 :       x = y; y = r;
    2223           0 :       R = Flx_FlxM_qmul(q, R, p, pi);
    2224             :     }
    2225           6 :     M = Flx_halfgcd_pre(x,y, p, pi);
    2226           6 :     c = FlxM_Flx_mul2(M, x,y, p, pi);
    2227           6 :     R = FlxM_mul2(M, R, p, pi);
    2228           6 :     x = gel(c,1); y = gel(c,2);
    2229           6 :     gerepileall(av,3,&x,&y,&R);
    2230             :   }
    2231           6 :   y = Flx_extgcd_basecase(x,y,p,pi,&u,&v);
    2232           6 :   if (ptu) *ptu = Flx_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), p, pi);
    2233           6 :   *ptv = Flx_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), p, pi);
    2234           6 :   return y;
    2235             : }
    2236             : 
    2237             : /* x and y in Z[X], return lift(gcd(x mod p, y mod p)). Set u and v st
    2238             :  * ux + vy = gcd (mod p) */
    2239             : GEN
    2240     6281140 : Flx_extgcd_pre(GEN x, GEN y, ulong p, ulong pi, GEN *ptu, GEN *ptv)
    2241             : {
    2242     6281140 :   pari_sp av = avma;
    2243             :   GEN d;
    2244     6281140 :   long lim = get_Fl_threshold(p, Flx_EXTGCD_LIMIT, Flx_EXTGCD2_LIMIT);
    2245     6281168 :   if (lgpol(y) >= lim)
    2246           6 :     d = Flx_extgcd_halfgcd(x, y, p, pi, ptu, ptv);
    2247             :   else
    2248     6281144 :     d = Flx_extgcd_basecase(x, y, p, pi, ptu, ptv);
    2249     6281001 :   return gc_all(av, ptu?3:2, &d, ptv, ptu);
    2250             : }
    2251             : GEN
    2252      836840 : Flx_extgcd(GEN x, GEN y, ulong p, GEN *ptu, GEN *ptv)
    2253      836840 : { return Flx_extgcd_pre(x, y, p, SMALL_ULONG(p)? 0: get_Fl_red(p), ptu, ptv); }
    2254             : 
    2255             : static GEN
    2256         848 : Flx_halfres_pre(GEN a, GEN b, ulong p, ulong pi, ulong *r)
    2257             : {
    2258             :   struct Flx_res res;
    2259             :   GEN M, V, A, B;
    2260             :   long dB;
    2261             : 
    2262         848 :   res.res  = *r;
    2263         848 :   res.lc   = Flx_lead(b);
    2264         848 :   res.deg0 = degpol(a);
    2265         848 :   res.deg1 = degpol(b);
    2266         848 :   res.off = 0;
    2267         848 :   M = Flx_halfres_i(a, b, p, pi, &res);
    2268         848 :   V = FlxM_Flx_mul2(M, a, b, p, pi);
    2269         848 :   A = gel(V,1); B = gel(V,2); dB = degpol(B);
    2270             : 
    2271         848 :   if (dB < degpol(b))
    2272         848 :     Flx_halfres_update_pre(res.deg0, res.deg1, dB, p, pi, &res);
    2273         848 :   *r = res.res;
    2274         848 :   return mkvec3(M,A,B);
    2275             : }
    2276             : 
    2277             : static ulong
    2278     5940648 : Flx_resultant_basecase_pre(GEN a, GEN b, ulong p, ulong pi)
    2279             : {
    2280             :   long da,db,dc,cnt;
    2281     5940648 :   ulong lb, res = 1UL;
    2282             :   pari_sp av;
    2283             :   GEN c;
    2284             : 
    2285     5940648 :   if (lgpol(a)==0 || lgpol(b)==0) return 0;
    2286     5940628 :   da = degpol(a);
    2287     5940654 :   db = degpol(b);
    2288     5940652 :   if (db > da)
    2289             :   {
    2290           0 :     swapspec(a,b, da,db);
    2291           0 :     if (both_odd(da,db)) res = p-res;
    2292             :   }
    2293     5940652 :   else if (!da) return 1; /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
    2294     5940652 :   cnt = 0; av = avma;
    2295    50124072 :   while (db)
    2296             :   {
    2297    44195455 :     lb = b[db+2];
    2298    44195455 :     c = Flx_rem_pre(a,b, p,pi);
    2299    44012927 :     a = b; b = c; dc = degpol(c);
    2300    44006699 :     if (dc < 0) return gc_long(av,0);
    2301             : 
    2302    43999194 :     if (both_odd(da,db)) res = p - res;
    2303    44005487 :     if (lb != 1) res = Fl_mul(res, Fl_powu_pre(lb, da - dc, p, pi), p);
    2304    44183115 :     if (++cnt == 100) { cnt = 0; gerepileall(av, 2, &a, &b); }
    2305    44183420 :     da = db; /* = degpol(a) */
    2306    44183420 :     db = dc; /* = degpol(b) */
    2307             :   }
    2308     5928617 :   return gc_ulong(av, Fl_mul(res, Fl_powu_pre(b[2], da, p, pi), p));
    2309             : }
    2310             : 
    2311             : ulong
    2312     5942158 : Flx_resultant_pre(GEN x, GEN y, ulong p, ulong pi)
    2313             : {
    2314     5942158 :   pari_sp av = avma;
    2315             :   long lim;
    2316     5942158 :   ulong res = 1;
    2317     5942158 :   long dx = degpol(x), dy = degpol(y);
    2318     5942138 :   if (dx < 0 || dy < 0) return 0;
    2319     5940696 :   if (dx < dy)
    2320             :   {
    2321      448537 :     swap(x,y);
    2322      448537 :     if (both_odd(dx, dy))
    2323        1906 :       res = Fl_neg(res, p);
    2324             :   }
    2325     5940697 :   lim = get_Fl_threshold(p, Flx_GCD_LIMIT, Flx_GCD2_LIMIT);
    2326     5941536 :   while (lgpol(y) >= lim)
    2327             :   {
    2328             :     GEN c;
    2329         848 :     if (lgpol(y)<=(lgpol(x)>>1))
    2330             :     {
    2331           0 :       GEN r = Flx_rem_pre(x, y, p, pi);
    2332           0 :       long dx = degpol(x), dy = degpol(y), dr = degpol(r);
    2333           0 :       ulong ly = y[dy+2];
    2334           0 :       if (ly != 1) res = Fl_mul(res, Fl_powu_pre(ly, dx - dr, p, pi), p);
    2335           0 :       if (both_odd(dx, dy))
    2336           0 :         res = Fl_neg(res, p);
    2337           0 :       x = y; y = r;
    2338             :     }
    2339         848 :     c = Flx_halfres_pre(x, y, p, pi, &res);
    2340         848 :     x = gel(c,2); y = gel(c,3);
    2341         848 :     if (gc_needed(av,2))
    2342             :     {
    2343           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_res (y = %ld)",degpol(y));
    2344           0 :       gerepileall(av,2,&x,&y);
    2345             :     }
    2346             :   }
    2347     5940657 :   return gc_ulong(av, Fl_mul(res, Flx_resultant_basecase_pre(x, y, p, pi), p));
    2348             : }
    2349             : 
    2350             : ulong
    2351     4731912 : Flx_resultant(GEN a, GEN b, ulong p)
    2352     4731912 : { return Flx_resultant_pre(a, b, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2353             : 
    2354             : /* If resultant is 0, *ptU and *ptV are not set */
    2355             : ulong
    2356           0 : Flx_extresultant_pre(GEN a, GEN b, ulong p, ulong pi, GEN *ptU, GEN *ptV)
    2357             : {
    2358           0 :   GEN z,q,u,v, x = a, y = b;
    2359           0 :   ulong lb, res = 1UL;
    2360           0 :   pari_sp av = avma;
    2361             :   long dx, dy, dz;
    2362           0 :   long vs=a[1];
    2363             : 
    2364           0 :   dx = degpol(x);
    2365           0 :   dy = degpol(y);
    2366           0 :   if (dy > dx)
    2367             :   {
    2368           0 :     swap(x,y); lswap(dx,dy); pswap(ptU, ptV);
    2369           0 :     a = x; b = y;
    2370           0 :     if (both_odd(dx,dy)) res = p-res;
    2371             :   }
    2372             :   /* dy <= dx */
    2373           0 :   if (dy < 0) return 0;
    2374             : 
    2375           0 :   u = pol0_Flx(vs);
    2376           0 :   v = pol1_Flx(vs); /* v = 1 */
    2377           0 :   while (dy)
    2378             :   { /* b u = x (a), b v = y (a) */
    2379           0 :     lb = y[dy+2];
    2380           0 :     q = Flx_divrem_pre(x,y, p, pi, &z);
    2381           0 :     x = y; y = z; /* (x,y) = (y, x - q y) */
    2382           0 :     dz = degpol(z); if (dz < 0) return gc_ulong(av,0);
    2383           0 :     z = Flx_sub(u, Flx_mul_pre(q,v, p, pi), p);
    2384           0 :     u = v; v = z; /* (u,v) = (v, u - q v) */
    2385             : 
    2386           0 :     if (both_odd(dx,dy)) res = p - res;
    2387           0 :     if (lb != 1) res = Fl_mul(res, Fl_powu_pre(lb, dx-dz, p, pi), p);
    2388           0 :     dx = dy; /* = degpol(x) */
    2389           0 :     dy = dz; /* = degpol(y) */
    2390             :   }
    2391           0 :   res = Fl_mul(res, Fl_powu_pre(y[2], dx, p, pi), p);
    2392           0 :   lb = Fl_mul(res, Fl_inv(y[2],p), p);
    2393           0 :   v = gerepileuptoleaf(av, Flx_Fl_mul(v, lb, p));
    2394           0 :   av = avma;
    2395           0 :   u = Flx_sub(Fl_to_Flx(res,vs), Flx_mul_pre(b,v,p,pi), p);
    2396           0 :   u = gerepileuptoleaf(av, Flx_div_pre(u,a,p,pi)); /* = (res - b v) / a */
    2397           0 :   *ptU = u;
    2398           0 :   *ptV = v; return res;
    2399             : }
    2400             : 
    2401             : ulong
    2402           0 : Flx_extresultant(GEN a, GEN b, ulong p, GEN *ptU, GEN *ptV)
    2403           0 : { return Flx_extresultant_pre(a, b, p, SMALL_ULONG(p)? 0: get_Fl_red(p), ptU, ptV); }
    2404             : 
    2405             : /* allow pi = 0 (SMALL_ULONG) */
    2406             : ulong
    2407    41618163 : Flx_eval_powers_pre(GEN x, GEN y, ulong p, ulong pi)
    2408             : {
    2409    41618163 :   ulong l0, l1, h0, h1, v1,  i = 1, lx = lg(x)-1;
    2410             : 
    2411    41618163 :   if (lx == 1) return 0;
    2412    38940504 :   x++;
    2413    38940504 :   if (pi)
    2414             :   {
    2415             :     LOCAL_OVERFLOW;
    2416             :     LOCAL_HIREMAINDER;
    2417    38880274 :     l1 = mulll(uel(x,i), uel(y,i)); h1 = hiremainder; v1 = 0;
    2418    93579534 :     while (++i < lx)
    2419             :     {
    2420    54699260 :       l0 = mulll(uel(x,i), uel(y,i)); h0 = hiremainder;
    2421    54699260 :       l1 = addll(l0, l1); h1 = addllx(h0, h1); v1 += overflow;
    2422             :     }
    2423       80859 :     return v1? remlll_pre(v1, h1, l1, p, pi)
    2424    38961133 :              : remll_pre(h1, l1, p, pi);
    2425             :   }
    2426             :   else
    2427             :   {
    2428       60230 :     l1 = x[i] * y[i];
    2429    30921419 :     while (++i < lx) { l1 += x[i] * y[i]; if (l1 & HIGHBIT) l1 %= p; }
    2430       60230 :     return l1 % p;
    2431             :   }
    2432             : }
    2433             : 
    2434             : /* allow pi = 0 (SMALL_ULONG) */
    2435             : ulong
    2436    34438692 : Flx_eval_pre(GEN x, ulong y, ulong p, ulong pi)
    2437             : {
    2438    34438692 :   long i, n = degpol(x);
    2439             :   ulong t;
    2440    34437564 :   if (n <= 0) return n? 0: x[2];
    2441    27058668 :   if (n > 15)
    2442             :   {
    2443      180418 :     pari_sp av = avma;
    2444      180418 :     GEN v = Fl_powers_pre(y, n, p, pi);
    2445      180464 :     return gc_ulong(av, Flx_eval_powers_pre(x, v, p, pi));
    2446             :   }
    2447    26878250 :   i = n+2; t = x[i];
    2448    26878250 :   if (pi)
    2449             :   {
    2450   103520058 :     for (i--; i>=2; i--) t = Fl_addmul_pre(uel(x, i), t, y, p, pi);
    2451    25776869 :     return t;
    2452             :   }
    2453     2633565 :   for (i--; i>=2; i--) t = (t * y + x[i]) % p;
    2454     1100018 :   return t %= p;
    2455             : }
    2456             : ulong
    2457    20352905 : Flx_eval(GEN x, ulong y, ulong p)
    2458    20352905 : { return Flx_eval_pre(x, y, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2459             : 
    2460             : ulong
    2461        3255 : Flv_prod_pre(GEN x, ulong p, ulong pi)
    2462             : {
    2463        3255 :   pari_sp ltop = avma;
    2464             :   GEN v;
    2465        3255 :   long i,k,lx = lg(x);
    2466        3255 :   if (lx == 1) return 1UL;
    2467        3255 :   if (lx == 2) return uel(x,1);
    2468        3003 :   v = cgetg(1+(lx << 1), t_VECSMALL);
    2469        3003 :   k = 1;
    2470       28593 :   for (i=1; i<lx-1; i+=2)
    2471       25590 :     uel(v,k++) = Fl_mul_pre(uel(x,i), uel(x,i+1), p, pi);
    2472        3003 :   if (i < lx) uel(v,k++) = uel(x,i);
    2473       13529 :   while (k > 2)
    2474             :   {
    2475       10526 :     lx = k; k = 1;
    2476       36116 :     for (i=1; i<lx-1; i+=2)
    2477       25590 :       uel(v,k++) = Fl_mul_pre(uel(v,i), uel(v,i+1), p, pi);
    2478       10526 :     if (i < lx) uel(v,k++) = uel(v,i);
    2479             :   }
    2480        3003 :   return gc_ulong(ltop, uel(v,1));
    2481             : }
    2482             : 
    2483             : ulong
    2484           0 : Flv_prod(GEN v, ulong p)
    2485             : {
    2486           0 :   return Flv_prod_pre(v, p, get_Fl_red(p));
    2487             : }
    2488             : 
    2489             : GEN
    2490           0 : FlxV_prod(GEN V, ulong p)
    2491             : {
    2492             :   struct _Flxq D;
    2493           0 :   D.T = NULL; D.aut = NULL; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2494           0 :   return gen_product(V, (void *)&D, &_Flx_mul);
    2495             : }
    2496             : 
    2497             : /* compute prod (x - a[i]) */
    2498             : GEN
    2499      671756 : Flv_roots_to_pol(GEN a, ulong p, long vs)
    2500             : {
    2501             :   struct _Flxq D;
    2502      671756 :   long i,k,lx = lg(a);
    2503             :   GEN p1;
    2504      671756 :   if (lx == 1) return pol1_Flx(vs);
    2505      671756 :   p1 = cgetg(lx, t_VEC);
    2506    11443796 :   for (k=1,i=1; i<lx-1; i+=2)
    2507    10772269 :     gel(p1,k++) = mkvecsmall4(vs, Fl_mul(a[i], a[i+1], p),
    2508    10772540 :                               Fl_neg(Fl_add(a[i],a[i+1],p),p), 1);
    2509      671256 :   if (i < lx)
    2510       54497 :     gel(p1,k++) = mkvecsmall3(vs, Fl_neg(a[i],p), 1);
    2511      671251 :   D.T = NULL; D.aut = NULL; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2512      671247 :   setlg(p1, k); return gen_product(p1, (void *)&D, _Flx_mul);
    2513             : }
    2514             : 
    2515             : /* set v[i] = w[i]^{-1}; may be called with w = v, suitable for "large" p */
    2516             : INLINE void
    2517    16301371 : Flv_inv_pre_indir(GEN w, GEN v, ulong p, ulong pi)
    2518             : {
    2519    16301371 :   pari_sp av = avma;
    2520    16301371 :   long n = lg(w), i;
    2521             :   ulong u;
    2522             :   GEN c;
    2523             : 
    2524    16301371 :   if (n == 1) return;
    2525    16301371 :   c = cgetg(n, t_VECSMALL); c[1] = w[1];
    2526    72038075 :   for (i = 2; i < n; ++i) c[i] = Fl_mul_pre(w[i], c[i-1], p, pi);
    2527    16459404 :   i = n-1; u = Fl_inv(c[i], p);
    2528    72409707 :   for ( ; i > 1; --i)
    2529             :   {
    2530    55979952 :     ulong t = Fl_mul_pre(u, c[i-1], p, pi);
    2531    55966412 :     u = Fl_mul_pre(u, w[i], p, pi); v[i] = t;
    2532             :   }
    2533    16429755 :   v[1] = u; set_avma(av);
    2534             : }
    2535             : 
    2536             : void
    2537    15955121 : Flv_inv_pre_inplace(GEN v, ulong p, ulong pi) { Flv_inv_pre_indir(v,v, p, pi); }
    2538             : 
    2539             : GEN
    2540       10864 : Flv_inv_pre(GEN w, ulong p, ulong pi)
    2541       10864 : { GEN v = cgetg(lg(w), t_VECSMALL); Flv_inv_pre_indir(w, v, p, pi); return v; }
    2542             : 
    2543             : /* set v[i] = w[i]^{-1}; may be called with w = v, suitable for SMALL_ULONG p */
    2544             : INLINE void
    2545       45739 : Flv_inv_indir(GEN w, GEN v, ulong p)
    2546             : {
    2547       45739 :   pari_sp av = avma;
    2548       45739 :   long n = lg(w), i;
    2549             :   ulong u;
    2550             :   GEN c;
    2551             : 
    2552       45739 :   if (n == 1) return;
    2553       45739 :   c = cgetg(n, t_VECSMALL); c[1] = w[1];
    2554     1673407 :   for (i = 2; i < n; ++i) c[i] = Fl_mul(w[i], c[i-1], p);
    2555       45741 :   i = n-1; u = Fl_inv(c[i], p);
    2556     1673415 :   for ( ; i > 1; --i)
    2557             :   {
    2558     1627675 :     ulong t = Fl_mul(u, c[i-1], p);
    2559     1627667 :     u = Fl_mul(u, w[i], p); v[i] = t;
    2560             :   }
    2561       45740 :   v[1] = u; set_avma(av);
    2562             : }
    2563             : static void
    2564      373201 : Flv_inv_i(GEN v, GEN w, ulong p)
    2565             : {
    2566      373201 :   if (SMALL_ULONG(p)) Flv_inv_indir(w, v, p);
    2567      327463 :   else Flv_inv_pre_indir(w, v, p, get_Fl_red(p));
    2568      373203 : }
    2569             : void
    2570       12017 : Flv_inv_inplace(GEN v, ulong p) { Flv_inv_i(v, v, p); }
    2571             : GEN
    2572      361186 : Flv_inv(GEN w, ulong p)
    2573      361186 : { GEN v = cgetg(lg(w), t_VECSMALL); Flv_inv_i(v, w, p); return v; }
    2574             : 
    2575             : GEN
    2576    31964122 : Flx_div_by_X_x(GEN a, ulong x, ulong p, ulong *rem)
    2577             : {
    2578    31964122 :   long l = lg(a), i;
    2579             :   GEN a0, z0, z;
    2580    31964122 :   if (l <= 3)
    2581             :   {
    2582           0 :     if (rem) *rem = l == 2? 0: a[2];
    2583           0 :     return zero_Flx(a[1]);
    2584             :   }
    2585    31964122 :   z = cgetg(l-1,t_VECSMALL); z[1] = a[1];
    2586    31785621 :   a0 = a + l-1;
    2587    31785621 :   z0 = z + l-2; *z0 = *a0--;
    2588    31785621 :   if (SMALL_ULONG(p))
    2589             :   {
    2590    76814707 :     for (i=l-3; i>1; i--) /* z[i] = (a[i+1] + x*z[i+1]) % p */
    2591             :     {
    2592    57101910 :       ulong t = (*a0-- + x *  *z0--) % p;
    2593    57101910 :       *z0 = (long)t;
    2594             :     }
    2595    19712797 :     if (rem) *rem = (*a0 + x *  *z0) % p;
    2596             :   }
    2597             :   else
    2598             :   {
    2599    47814392 :     for (i=l-3; i>1; i--)
    2600             :     {
    2601    35672956 :       ulong t = Fl_add((ulong)*a0--, Fl_mul(x, *z0--, p), p);
    2602    35741568 :       *z0 = (long)t;
    2603             :     }
    2604    12141436 :     if (rem) *rem = Fl_add((ulong)*a0, Fl_mul(x, *z0, p), p);
    2605             :   }
    2606    31894031 :   return z;
    2607             : }
    2608             : 
    2609             : /* xa, ya = t_VECSMALL */
    2610             : static GEN
    2611      362428 : Flv_producttree(GEN xa, GEN s, ulong p, long vs)
    2612             : {
    2613      362428 :   long n = lg(xa)-1;
    2614      362428 :   long m = n==1 ? 1: expu(n-1)+1;
    2615      362428 :   long i, j, k, ls = lg(s);
    2616             :   ulong pi;
    2617      362428 :   GEN T = cgetg(m+1, t_VEC);
    2618      362422 :   GEN t = cgetg(ls, t_VEC);
    2619     3639532 :   for (j=1, k=1; j<ls; k+=s[j++])
    2620     3276922 :     gel(t, j) = s[j] == 1 ?
    2621     3277105 :              mkvecsmall3(vs, Fl_neg(xa[k], p), 1):
    2622     1064626 :              mkvecsmall4(vs, Fl_mul(xa[k], xa[k+1], p),
    2623     1064630 :                  Fl_neg(Fl_add(xa[k],xa[k+1],p),p), 1);
    2624      362427 :   gel(T,1) = t; pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2625     1098808 :   for (i=2; i<=m; i++)
    2626             :   {
    2627      736460 :     GEN u = gel(T, i-1);
    2628      736460 :     long n = lg(u)-1;
    2629      736460 :     GEN t = cgetg(((n+1)>>1)+1, t_VEC);
    2630     3650610 :     for (j=1, k=1; k<n; j++, k+=2)
    2631     2914229 :       gel(t, j) = Flx_mul_pre(gel(u, k), gel(u, k+1), p, pi);
    2632      736381 :     gel(T, i) = t;
    2633             :   }
    2634      362348 :   return T;
    2635             : }
    2636             : 
    2637             : static GEN
    2638      402732 : Flx_Flv_multieval_tree(GEN P, GEN xa, GEN T, ulong p)
    2639             : {
    2640             :   long i,j,k;
    2641      402732 :   long m = lg(T)-1;
    2642      402732 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2643      402731 :   GEN R = cgetg(lg(xa), t_VECSMALL);
    2644      402725 :   GEN Tp = cgetg(m+1, t_VEC), t;
    2645      402718 :   gel(Tp, m) = mkvec(P);
    2646     1324512 :   for (i=m-1; i>=1; i--)
    2647             :   {
    2648      921789 :     GEN u = gel(T, i), v = gel(Tp, i+1);
    2649      921789 :     long n = lg(u)-1;
    2650      921789 :     t = cgetg(n+1, t_VEC);
    2651     4865838 :     for (j=1, k=1; k<n; j++, k+=2)
    2652             :     {
    2653     3944065 :       gel(t, k)   = Flx_rem_pre(gel(v, j), gel(u, k), p, pi);
    2654     3944057 :       gel(t, k+1) = Flx_rem_pre(gel(v, j), gel(u, k+1), p, pi);
    2655             :     }
    2656      921773 :     gel(Tp, i) = t;
    2657             :   }
    2658             :   {
    2659      402723 :     GEN u = gel(T, i+1), v = gel(Tp, i+1);
    2660      402723 :     long n = lg(u)-1;
    2661     4751927 :     for (j=1, k=1; j<=n; j++)
    2662             :     {
    2663     4349174 :       long c, d = degpol(gel(u,j));
    2664    10012110 :       for (c=1; c<=d; c++, k++) R[k] = Flx_eval_pre(gel(v, j), xa[k], p, pi);
    2665             :     }
    2666      402753 :     return gc_const((pari_sp)R, R);
    2667             :   }
    2668             : }
    2669             : 
    2670             : static GEN
    2671     1077421 : FlvV_polint_tree(GEN T, GEN R, GEN s, GEN xa, GEN ya, ulong p, long vs)
    2672             : {
    2673     1077421 :   pari_sp av = avma;
    2674     1077421 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2675     1077406 :   long m = lg(T)-1;
    2676     1077406 :   long i, j, k, ls = lg(s);
    2677     1077406 :   GEN Tp = cgetg(m+1, t_VEC);
    2678     1076820 :   GEN t = cgetg(ls, t_VEC);
    2679    20240608 :   for (j=1, k=1; j<ls; k+=s[j++])
    2680    19164035 :     if (s[j]==2)
    2681             :     {
    2682     6320037 :       ulong a = Fl_mul(ya[k], R[k], p);
    2683     6322081 :       ulong b = Fl_mul(ya[k+1], R[k+1], p);
    2684     6332082 :       gel(t, j) = mkvecsmall3(vs, Fl_neg(Fl_add(Fl_mul(xa[k], b, p ),
    2685     6327035 :                   Fl_mul(xa[k+1], a, p), p), p), Fl_add(a, b, p));
    2686     6323841 :       gel(t, j) = Flx_renormalize(gel(t, j), 4);
    2687             :     }
    2688             :     else
    2689    12843998 :       gel(t, j) = Fl_to_Flx(Fl_mul(ya[k], R[k], p), vs);
    2690     1076573 :   gel(Tp, 1) = t;
    2691     4933919 :   for (i=2; i<=m; i++)
    2692             :   {
    2693     3857407 :     GEN u = gel(T, i-1);
    2694     3857407 :     GEN t = cgetg(lg(gel(T,i)), t_VEC);
    2695     3854080 :     GEN v = gel(Tp, i-1);
    2696     3854080 :     long n = lg(v)-1;
    2697    21900926 :     for (j=1, k=1; k<n; j++, k+=2)
    2698    18056287 :       gel(t, j) = Flx_add(Flx_mul_pre(gel(u, k), gel(v, k+1), p, pi),
    2699    18043580 :                           Flx_mul_pre(gel(u, k+1), gel(v, k), p, pi), p);
    2700     3857346 :     gel(Tp, i) = t;
    2701             :   }
    2702     1076512 :   return gerepileuptoleaf(av, gmael(Tp,m,1));
    2703             : }
    2704             : 
    2705             : GEN
    2706           0 : Flx_Flv_multieval(GEN P, GEN xa, ulong p)
    2707             : {
    2708           0 :   pari_sp av = avma;
    2709           0 :   GEN s = producttree_scheme(lg(xa)-1);
    2710           0 :   GEN T = Flv_producttree(xa, s, p, P[1]);
    2711           0 :   return gerepileuptoleaf(av, Flx_Flv_multieval_tree(P, xa, T, p));
    2712             : }
    2713             : 
    2714             : static GEN
    2715        2471 : FlxV_Flv_multieval_tree(GEN x, GEN xa, GEN T, ulong p)
    2716       45248 : { pari_APPLY_same(Flx_Flv_multieval_tree(gel(x,i), xa, T, p)) }
    2717             : 
    2718             : GEN
    2719        2471 : FlxV_Flv_multieval(GEN P, GEN xa, ulong p)
    2720             : {
    2721        2471 :   pari_sp av = avma;
    2722        2471 :   GEN s = producttree_scheme(lg(xa)-1);
    2723        2471 :   GEN T = Flv_producttree(xa, s, p, P[1]);
    2724        2471 :   return gerepileupto(av, FlxV_Flv_multieval_tree(P, xa, T, p));
    2725             : }
    2726             : 
    2727             : GEN
    2728      110642 : Flv_polint(GEN xa, GEN ya, ulong p, long vs)
    2729             : {
    2730      110642 :   pari_sp av = avma;
    2731      110642 :   GEN s = producttree_scheme(lg(xa)-1);
    2732      110643 :   GEN T = Flv_producttree(xa, s, p, vs);
    2733      110642 :   long m = lg(T)-1;
    2734      110642 :   GEN P = Flx_deriv(gmael(T, m, 1), p);
    2735      110643 :   GEN R = Flv_inv(Flx_Flv_multieval_tree(P, xa, T, p), p);
    2736      110644 :   return gerepileuptoleaf(av, FlvV_polint_tree(T, R, s, xa, ya, p, vs));
    2737             : }
    2738             : 
    2739             : GEN
    2740       96387 : Flv_Flm_polint(GEN xa, GEN ya, ulong p, long vs)
    2741             : {
    2742       96387 :   pari_sp av = avma;
    2743       96387 :   GEN s = producttree_scheme(lg(xa)-1);
    2744       96386 :   GEN T = Flv_producttree(xa, s, p, vs);
    2745       96384 :   long i, m = lg(T)-1, l = lg(ya)-1;
    2746       96384 :   GEN P = Flx_deriv(gmael(T, m, 1), p);
    2747       96383 :   GEN R = Flv_inv(Flx_Flv_multieval_tree(P, xa, T, p), p);
    2748       96383 :   GEN M = cgetg(l+1, t_VEC);
    2749     1062996 :   for (i=1; i<=l; i++)
    2750      966619 :     gel(M,i) = FlvV_polint_tree(T, R, s, xa, gel(ya,i), p, vs);
    2751       96377 :   return gerepileupto(av, M);
    2752             : }
    2753             : 
    2754             : GEN
    2755      152929 : Flv_invVandermonde(GEN L, ulong den, ulong p)
    2756             : {
    2757      152929 :   pari_sp av = avma;
    2758      152929 :   long i, n = lg(L);
    2759             :   GEN M, R;
    2760      152929 :   GEN s = producttree_scheme(n-1);
    2761      152929 :   GEN tree = Flv_producttree(L, s, p, 0);
    2762      152929 :   long m = lg(tree)-1;
    2763      152929 :   GEN T = gmael(tree, m, 1);
    2764      152929 :   R = Flv_inv(Flx_Flv_multieval_tree(Flx_deriv(T, p), L, tree, p), p);
    2765      152929 :   if (den!=1) R = Flv_Fl_mul(R, den, p);
    2766      152929 :   M = cgetg(n, t_MAT);
    2767      599895 :   for (i = 1; i < n; i++)
    2768             :   {
    2769      446966 :     GEN P = Flx_Fl_mul(Flx_div_by_X_x(T, uel(L,i), p, NULL), uel(R,i), p);
    2770      446966 :     gel(M,i) = Flx_to_Flv(P, n-1);
    2771             :   }
    2772      152929 :   return gerepilecopy(av, M);
    2773             : }
    2774             : 
    2775             : /***********************************************************************/
    2776             : /**                               Flxq                                **/
    2777             : /***********************************************************************/
    2778             : /* Flxq objects are Flx modulo another Flx called q. */
    2779             : 
    2780             : /* Product of y and x in Z/pZ[X]/(T), as t_VECSMALL. */
    2781             : GEN
    2782   187735999 : Flxq_mul_pre(GEN x,GEN y,GEN T,ulong p,ulong pi)
    2783   187735999 : { return Flx_rem_pre(Flx_mul_pre(x,y,p,pi),T,p,pi); }
    2784             : GEN
    2785    13142050 : Flxq_mul(GEN x,GEN y,GEN T,ulong p)
    2786    13142050 : { return Flxq_mul_pre(x,y,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2787             : 
    2788             : GEN
    2789   271380270 : Flxq_sqr_pre(GEN x,GEN T,ulong p,ulong pi)
    2790   271380270 : { return Flx_rem_pre(Flx_sqr_pre(x, p,pi), T, p,pi); }
    2791             : /* Square of y in Z/pZ[X]/(T), as t_VECSMALL. */
    2792             : GEN
    2793     2712612 : Flxq_sqr(GEN x,GEN T,ulong p)
    2794     2712612 : { return Flxq_sqr_pre(x,T,p,SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2795             : 
    2796             : static GEN
    2797     1724600 : _Flxq_red(void *E, GEN x)
    2798     1724600 : { struct _Flxq *s = (struct _Flxq *)E;
    2799     1724600 :   return Flx_rem_pre(x, s->T, s->p, s->pi); }
    2800             : #if 0
    2801             : static GEN
    2802             : _Flx_sub(void *E, GEN x, GEN y)
    2803             : { struct _Flxq *s = (struct _Flxq *)E;
    2804             :   return Flx_sub(x,y,s->p); }
    2805             : #endif
    2806             : static GEN
    2807   264468613 : _Flxq_sqr(void *data, GEN x)
    2808             : {
    2809   264468613 :   struct _Flxq *D = (struct _Flxq*)data;
    2810   264468613 :   return Flxq_sqr_pre(x, D->T, D->p, D->pi);
    2811             : }
    2812             : static GEN
    2813   147140055 : _Flxq_mul(void *data, GEN x, GEN y)
    2814             : {
    2815   147140055 :   struct _Flxq *D = (struct _Flxq*)data;
    2816   147140055 :   return Flxq_mul_pre(x,y, D->T, D->p, D->pi);
    2817             : }
    2818             : static GEN
    2819    21903598 : _Flxq_one(void *data)
    2820             : {
    2821    21903598 :   struct _Flxq *D = (struct _Flxq*)data;
    2822    21903598 :   return pol1_Flx(get_Flx_var(D->T));
    2823             : }
    2824             : 
    2825             : static GEN
    2826    21631286 : _Flxq_powu_i(struct _Flxq *D, GEN x, ulong n)
    2827    21631286 : { return gen_powu_i(x, n, (void*)D, &_Flxq_sqr, &_Flxq_mul); }
    2828             : static GEN
    2829          68 : _Flxq_powu(struct _Flxq *D, GEN x, ulong n)
    2830          68 : { pari_sp av = avma; return gerepileuptoleaf(av, _Flxq_powu_i(D, x, n)); }
    2831             : /* n-Power of x in Z/pZ[X]/(T), as t_VECSMALL. */
    2832             : GEN
    2833    22345790 : Flxq_powu_pre(GEN x, ulong n, GEN T, ulong p, ulong pi)
    2834             : {
    2835             :   pari_sp av;
    2836             :   struct _Flxq D;
    2837    22345790 :   switch(n)
    2838             :   {
    2839           0 :     case 0: return pol1_Flx(get_Flx_var(T));
    2840      135411 :     case 1: return Flx_copy(x);
    2841      587454 :     case 2: return Flxq_sqr_pre(x, T, p, pi);
    2842             :   }
    2843    21622925 :   av = avma; set_Flxq_pre(&D, T, p, pi);
    2844    21631250 :   return gerepileuptoleaf(av, _Flxq_powu_i(&D, x, n));
    2845             : }
    2846             : GEN
    2847      489847 : Flxq_powu(GEN x, ulong n, GEN T, ulong p)
    2848      489847 : { return Flxq_powu_pre(x, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2849             : 
    2850             : /* n-Power of x in Z/pZ[X]/(T), as t_VECSMALL. */
    2851             : GEN
    2852    26859752 : Flxq_pow_pre(GEN x, GEN n, GEN T, ulong p, ulong pi)
    2853             : {
    2854    26859752 :   pari_sp av = avma;
    2855             :   struct _Flxq D;
    2856             :   GEN y;
    2857    26859752 :   long s = signe(n);
    2858    26859752 :   if (!s) return pol1_Flx(get_Flx_var(T));
    2859    26598894 :   if (s < 0) x = Flxq_inv_pre(x,T,p,pi);
    2860    26598888 :   if (is_pm1(n)) return s < 0 ? x : Flx_copy(x);
    2861    25354382 :   set_Flxq_pre(&D, T, p, pi);
    2862    25354434 :   y = gen_pow_i(x, n, (void*)&D, &_Flxq_sqr, &_Flxq_mul);
    2863    25354290 :   return gerepileuptoleaf(av, y);
    2864             : }
    2865             : GEN
    2866     1014963 : Flxq_pow(GEN x, GEN n, GEN T, ulong p)
    2867     1014963 : { return Flxq_pow_pre(x, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2868             : 
    2869             : GEN
    2870          28 : Flxq_pow_init_pre(GEN x, GEN n, long k, GEN T, ulong p, ulong pi)
    2871             : {
    2872          28 :   struct _Flxq D; set_Flxq_pre(&D, T, p, pi);
    2873          28 :   return gen_pow_init(x, n, k, (void*)&D, &_Flxq_sqr, &_Flxq_mul);
    2874             : }
    2875             : GEN
    2876           0 : Flxq_pow_init(GEN x, GEN n, long k, GEN T, ulong p)
    2877           0 : { return Flxq_pow_init_pre(x, n, k, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2878             : 
    2879             : GEN
    2880        4400 : Flxq_pow_table_pre(GEN R, GEN n, GEN T, ulong p, ulong pi)
    2881             : {
    2882        4400 :   struct _Flxq D; set_Flxq_pre(&D, T, p, pi);
    2883        4400 :   return gen_pow_table(R, n, (void*)&D, &_Flxq_one, &_Flxq_mul);
    2884             : }
    2885             : GEN
    2886           0 : Flxq_pow_table(GEN R, GEN n, GEN T, ulong p)
    2887           0 : { return Flxq_pow_table_pre(R, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2888             : 
    2889             : /* Inverse of x in Z/lZ[X]/(T) or NULL if inverse doesn't exist
    2890             :  * not stack clean. */
    2891             : GEN
    2892     5444336 : Flxq_invsafe_pre(GEN x, GEN T, ulong p, ulong pi)
    2893             : {
    2894     5444336 :   GEN V, z = Flx_extgcd_pre(get_Flx_mod(T), x, p, pi, NULL, &V);
    2895             :   ulong iz;
    2896     5444426 :   if (degpol(z)) return NULL;
    2897     5443735 :   iz = Fl_inv(uel(z,2), p);
    2898     5443757 :   return Flx_Fl_mul(V, iz, p);
    2899             : }
    2900             : GEN
    2901      418532 : Flxq_invsafe(GEN x, GEN T, ulong p)
    2902      418532 : { return Flxq_invsafe_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2903             : 
    2904             : GEN
    2905     4624441 : Flxq_inv_pre(GEN x, GEN T, ulong p, ulong pi)
    2906             : {
    2907     4624441 :   pari_sp av=avma;
    2908     4624441 :   GEN U = Flxq_invsafe_pre(x, T, p, pi);
    2909     4624393 :   if (!U) pari_err_INV("Flxq_inv",Flx_to_ZX(x));
    2910     4624365 :   return gerepileuptoleaf(av, U);
    2911             : }
    2912             : GEN
    2913      345415 : Flxq_inv(GEN x, GEN T, ulong p)
    2914      345415 : { return Flxq_inv_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2915             : 
    2916             : GEN
    2917     2183427 : Flxq_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
    2918             : {
    2919     2183427 :   pari_sp av = avma;
    2920     2183427 :   return gerepileuptoleaf(av, Flxq_mul_pre(x,Flxq_inv_pre(y,T,p,pi),T,p,pi));
    2921             : }
    2922             : GEN
    2923      220847 : Flxq_div(GEN x, GEN y, GEN T, ulong p)
    2924      220847 : { return Flxq_div_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2925             : 
    2926             : GEN
    2927    21905262 : Flxq_powers_pre(GEN x, long l, GEN T, ulong p, ulong pi)
    2928             : {
    2929    21905262 :   int use_sqr = 2*degpol(x) >= get_Flx_degree(T);
    2930    21894066 :   struct _Flxq D; set_Flxq_pre(&D, T, p, pi);
    2931    21892433 :   return gen_powers(x, l, use_sqr, (void*)&D, &_Flxq_sqr, &_Flxq_mul, &_Flxq_one);
    2932             : }
    2933             : GEN
    2934      231804 : Flxq_powers(GEN x, long l, GEN T, ulong p)
    2935      231804 : { return Flxq_powers_pre(x, l, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2936             : 
    2937             : GEN
    2938      168497 : Flxq_matrix_pow_pre(GEN y, long n, long m, GEN P, ulong l, ulong li)
    2939      168497 : { return FlxV_to_Flm(Flxq_powers_pre(y,m-1,P,l,li),n); }
    2940             : GEN
    2941         399 : Flxq_matrix_pow(GEN y, long n, long m, GEN P, ulong l)
    2942         399 : { return Flxq_matrix_pow_pre(y, n, m, P, l, SMALL_ULONG(l)? 0: get_Fl_red(l)); }
    2943             : 
    2944             : GEN
    2945    12476697 : Flx_Frobenius_pre(GEN T, ulong p, ulong pi)
    2946    12476697 : { return Flxq_powu_pre(polx_Flx(get_Flx_var(T)), p, T, p, pi); }
    2947             : GEN
    2948       82296 : Flx_Frobenius(GEN T, ulong p)
    2949       82296 : { return Flx_Frobenius_pre(T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2950             : 
    2951             : GEN
    2952       85501 : Flx_matFrobenius_pre(GEN T, ulong p, ulong pi)
    2953             : {
    2954       85501 :   long n = get_Flx_degree(T);
    2955       85501 :   return Flxq_matrix_pow_pre(Flx_Frobenius_pre(T, p, pi), n, n, T, p, pi);
    2956             : }
    2957             : GEN
    2958           0 : Flx_matFrobenius(GEN T, ulong p)
    2959           0 : { return Flx_matFrobenius_pre(T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    2960             : 
    2961             : static GEN
    2962    12436160 : Flx_blocks_Flm(GEN P, long n, long m)
    2963             : {
    2964    12436160 :   GEN z = cgetg(m+1,t_MAT);
    2965    12433525 :   long i,j, k=2, l = lg(P);
    2966    37234185 :   for(i=1; i<=m; i++)
    2967             :   {
    2968    24804938 :     GEN zi = cgetg(n+1,t_VECSMALL);
    2969    24800660 :     gel(z,i) = zi;
    2970   111560655 :     for(j=1; j<=n; j++)
    2971    86759995 :       uel(zi, j) = k==l ? 0 : uel(P,k++);
    2972             :   }
    2973    12429247 :   return z;
    2974             : }
    2975             : 
    2976             : GEN
    2977      516470 : Flx_blocks(GEN P, long n, long m)
    2978             : {
    2979      516470 :   GEN z = cgetg(m+1,t_VEC);
    2980      516255 :   long i,j, k=2, l = lg(P);
    2981     1546681 :   for(i=1; i<=m; i++)
    2982             :   {
    2983     1030702 :     GEN zi = cgetg(n+2,t_VECSMALL);
    2984     1029713 :     zi[1] = P[1];
    2985     1029713 :     gel(z,i) = zi;
    2986     6454393 :     for(j=2; j<n+2; j++)
    2987     5424680 :       uel(zi, j) = k==l ? 0 : uel(P,k++);
    2988     1029713 :     zi = Flx_renormalize(zi, n+2);
    2989             :   }
    2990      515979 :   return z;
    2991             : }
    2992             : 
    2993             : static GEN
    2994    12436348 : FlxV_to_Flm_lg(GEN x, long m, long n)
    2995             : {
    2996             :   long i;
    2997    12436348 :   GEN y = cgetg(n+1, t_MAT);
    2998    57264571 :   for (i=1; i<=n; i++) gel(y,i) = Flx_to_Flv(gel(x,i), m);
    2999    12432002 :   return y;
    3000             : }
    3001             : 
    3002             : /* allow pi = 0 (SMALL_ULONG) */
    3003             : GEN
    3004    12633603 : Flx_FlxqV_eval_pre(GEN Q, GEN x, GEN T, ulong p, ulong pi)
    3005             : {
    3006    12633603 :   pari_sp btop, av = avma;
    3007    12633603 :   long sv = get_Flx_var(T), m = get_Flx_degree(T);
    3008    12633333 :   long i, l = lg(x)-1, lQ = lgpol(Q), n,  d;
    3009             :   GEN A, B, C, S, g;
    3010    12634444 :   if (lQ == 0) return pol0_Flx(sv);
    3011    12437640 :   if (lQ <= l)
    3012             :   {
    3013     5344714 :     n = l;
    3014     5344714 :     d = 1;
    3015             :   }
    3016             :   else
    3017             :   {
    3018     7092926 :     n = l-1;
    3019     7092926 :     d = (lQ+n-1)/n;
    3020             :   }
    3021    12437640 :   A = FlxV_to_Flm_lg(x, m, n);
    3022    12435113 :   B = Flx_blocks_Flm(Q, n, d);
    3023    12432871 :   C = gerepileupto(av, Flm_mul(A, B, p));
    3024    12438519 :   g = gel(x, l);
    3025    12438519 :   if (pi && SMALL_ULONG(p)) pi = 0;
    3026    12438519 :   T = Flx_get_red_pre(T, p, pi);
    3027    12437192 :   btop = avma;
    3028    12437192 :   S = Flv_to_Flx(gel(C, d), sv);
    3029    24813945 :   for (i = d-1; i>0; i--)
    3030             :   {
    3031    12379769 :     S = Flx_add(Flxq_mul_pre(S, g, T, p, pi), Flv_to_Flx(gel(C,i), sv), p);
    3032    12378942 :     if (gc_needed(btop,1))
    3033           0 :       S = gerepileuptoleaf(btop, S);
    3034             :   }
    3035    12434176 :   return gerepileuptoleaf(av, S);
    3036             : }
    3037             : GEN
    3038        5103 : Flx_FlxqV_eval(GEN Q, GEN x, GEN T, ulong p)
    3039        5103 : { return Flx_FlxqV_eval_pre(Q, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3040             : 
    3041             : /* allow pi = 0 (SMALL_ULONG) */
    3042             : GEN
    3043     2484122 : Flx_Flxq_eval_pre(GEN Q, GEN x, GEN T, ulong p, ulong pi)
    3044             : {
    3045     2484122 :   pari_sp av = avma;
    3046             :   GEN z, V;
    3047     2484122 :   long d = degpol(Q), rtd;
    3048     2484120 :   if (d < 0) return pol0_Flx(get_Flx_var(T));
    3049     2484029 :   rtd = (long) sqrt((double)d);
    3050     2484029 :   T = Flx_get_red_pre(T, p, pi);
    3051     2484040 :   V = Flxq_powers_pre(x, rtd, T, p, pi);
    3052     2484079 :   z = Flx_FlxqV_eval_pre(Q, V, T, p, pi);
    3053     2484070 :   return gerepileupto(av, z);
    3054             : }
    3055             : GEN
    3056      787559 : Flx_Flxq_eval(GEN Q, GEN x, GEN T, ulong p)
    3057      787559 : { return Flx_Flxq_eval_pre(Q, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3058             : 
    3059             : /* allow pi = 0 (SMALL_ULONG) */
    3060             : GEN
    3061           0 : FlxC_FlxqV_eval_pre(GEN x, GEN v, GEN T, ulong p, ulong pi)
    3062           0 : { pari_APPLY_type(t_COL, Flx_FlxqV_eval_pre(gel(x,i), v, T, p, pi)) }
    3063             : GEN
    3064           0 : FlxC_FlxqV_eval(GEN x, GEN v, GEN T, ulong p)
    3065           0 : { return FlxC_FlxqV_eval_pre(x, v, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3066             : 
    3067             : /* allow pi = 0 (SMALL_ULONG) */
    3068             : GEN
    3069           0 : FlxC_Flxq_eval_pre(GEN x, GEN F, GEN T, ulong p, ulong pi)
    3070             : {
    3071           0 :   long d = brent_kung_optpow(get_Flx_degree(T)-1,lg(x)-1,1);
    3072           0 :   GEN Fp = Flxq_powers_pre(F, d, T, p, pi);
    3073           0 :   return FlxC_FlxqV_eval_pre(x, Fp, T, p, pi);
    3074             : }
    3075             : GEN
    3076           0 : FlxC_Flxq_eval(GEN x, GEN F, GEN T, ulong p)
    3077           0 : { return FlxC_Flxq_eval_pre(x, F, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3078             : 
    3079             : #if 0
    3080             : static struct bb_algebra Flxq_algebra = { _Flxq_red, _Flx_add, _Flx_sub,
    3081             :               _Flxq_mul, _Flxq_sqr, _Flxq_one, _Flxq_zero};
    3082             : #endif
    3083             : 
    3084             : static GEN
    3085      389109 : Flxq_autpow_sqr(void *E, GEN x)
    3086             : {
    3087      389109 :   struct _Flxq *D = (struct _Flxq*)E;
    3088      389109 :   return Flx_Flxq_eval_pre(x, x, D->T, D->p, D->pi);
    3089             : }
    3090             : static GEN
    3091       20734 : Flxq_autpow_msqr(void *E, GEN x)
    3092             : {
    3093       20734 :   struct _Flxq *D = (struct _Flxq*)E;
    3094       20734 :   return Flx_FlxqV_eval_pre(Flxq_autpow_sqr(E, x), D->aut, D->T, D->p, D->pi);
    3095             : }
    3096             : 
    3097             : GEN
    3098      307189 : Flxq_autpow_pre(GEN x, ulong n, GEN T, ulong p, ulong pi)
    3099             : {
    3100      307189 :   pari_sp av = avma;
    3101             :   struct _Flxq D;
    3102             :   long d;
    3103      307189 :   if (n==0) return Flx_rem_pre(polx_Flx(x[1]), T, p, pi);
    3104      307182 :   if (n==1) return Flx_rem_pre(x, T, p, pi);
    3105      306692 :   set_Flxq_pre(&D, T, p, pi);
    3106      306692 :   d = brent_kung_optpow(get_Flx_degree(T), hammingl(n)-1, 1);
    3107      306692 :   D.aut = Flxq_powers_pre(x, d, T, p, D.pi);
    3108      306692 :   x = gen_powu_fold_i(x,n,(void*)&D,Flxq_autpow_sqr,Flxq_autpow_msqr);
    3109      306692 :   return gerepilecopy(av, x);
    3110             : }
    3111             : GEN
    3112           7 : Flxq_autpow(GEN x, ulong n, GEN T, ulong p)
    3113           7 : { return Flxq_autpow_pre(x, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3114             : 
    3115             : GEN
    3116        1705 : Flxq_autpowers(GEN x, ulong l, GEN T, ulong p)
    3117             : {
    3118        1705 :   long d, vT = get_Flx_var(T), dT = get_Flx_degree(T);
    3119             :   ulong i, pi;
    3120        1705 :   pari_sp av = avma;
    3121        1705 :   GEN xp, V = cgetg(l+2,t_VEC);
    3122        1705 :   gel(V,1) = polx_Flx(vT); if (l==0) return V;
    3123        1705 :   gel(V,2) = gcopy(x); if (l==1) return V;
    3124        1705 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    3125        1705 :   T = Flx_get_red_pre(T, p, pi);
    3126        1705 :   d = brent_kung_optpow(dT-1, l-1, 1);
    3127        1705 :   xp = Flxq_powers_pre(x, d, T, p, pi);
    3128        7188 :   for(i = 3; i < l+2; i++)
    3129        5483 :     gel(V,i) = Flx_FlxqV_eval_pre(gel(V,i-1), xp, T, p, pi);
    3130        1705 :   return gerepilecopy(av, V);
    3131             : }
    3132             : 
    3133             : static GEN
    3134      591678 : Flxq_autsum_mul(void *E, GEN x, GEN y)
    3135             : {
    3136      591678 :   struct _Flxq *D = (struct _Flxq*)E;
    3137      591678 :   GEN T = D->T;
    3138      591678 :   ulong p = D->p, pi = D->pi;
    3139      591678 :   GEN phi1 = gel(x,1), a1 = gel(x,2);
    3140      591678 :   GEN phi2 = gel(y,1), a2 = gel(y,2);
    3141      591678 :   ulong d = brent_kung_optpow(maxss(degpol(phi1),degpol(a1)),2,1);
    3142      591678 :   GEN V2 = Flxq_powers_pre(phi2, d, T, p, pi);
    3143      591678 :   GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
    3144      591678 :   GEN aphi = Flx_FlxqV_eval_pre(a1, V2, T, p, pi);
    3145      591678 :   GEN a3 = Flxq_mul_pre(aphi, a2, T, p, pi);
    3146      591678 :   return mkvec2(phi3, a3);
    3147             : }
    3148             : static GEN
    3149      381076 : Flxq_autsum_sqr(void *E, GEN x)
    3150      381076 : { return Flxq_autsum_mul(E, x, x); }
    3151             : 
    3152             : static GEN
    3153      317636 : Flxq_autsum_pre(GEN x, ulong n, GEN T, ulong p, ulong pi)
    3154             : {
    3155      317636 :   pari_sp av = avma;
    3156      317636 :   struct _Flxq D; set_Flxq_pre(&D, T, p, pi);
    3157      317636 :   x = gen_powu_i(x,n,(void*)&D,Flxq_autsum_sqr,Flxq_autsum_mul);
    3158      317636 :   return gerepilecopy(av, x);
    3159             : }
    3160             : GEN
    3161           0 : Flxq_autsum(GEN x, ulong n, GEN T, ulong p)
    3162           0 : { return Flxq_autsum_pre(x, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3163             : 
    3164             : static GEN
    3165      674336 : Flxq_auttrace_mul(void *E, GEN x, GEN y)
    3166             : {
    3167      674336 :   struct _Flxq *D = (struct _Flxq*)E;
    3168      674336 :   GEN T = D->T;
    3169      674336 :   ulong p = D->p, pi = D->pi;
    3170      674336 :   GEN phi1 = gel(x,1), a1 = gel(x,2);
    3171      674336 :   GEN phi2 = gel(y,1), a2 = gel(y,2);
    3172      674336 :   ulong d = brent_kung_optpow(maxss(degpol(phi1),degpol(a1)),2,1);
    3173      674350 :   GEN V1 = Flxq_powers_pre(phi1, d, T, p, pi);
    3174      674296 :   GEN phi3 = Flx_FlxqV_eval_pre(phi2, V1, T, p, pi);
    3175      674332 :   GEN aphi = Flx_FlxqV_eval_pre(a2, V1, T, p, pi);
    3176      674333 :   GEN a3 = Flx_add(a1, aphi, p);
    3177      674332 :   return mkvec2(phi3, a3);
    3178             : }
    3179             : 
    3180             : static GEN
    3181      548646 : Flxq_auttrace_sqr(void *E, GEN x)
    3182      548646 : { return Flxq_auttrace_mul(E, x, x); }
    3183             : 
    3184             : GEN
    3185      819970 : Flxq_auttrace_pre(GEN x, ulong n, GEN T, ulong p, ulong pi)
    3186             : {
    3187      819970 :   pari_sp av = avma;
    3188             :   struct _Flxq D;
    3189      819970 :   set_Flxq_pre(&D, T, p, pi);
    3190      819974 :   x = gen_powu_i(x,n,(void*)&D,Flxq_auttrace_sqr,Flxq_auttrace_mul);
    3191      819957 :   return gerepilecopy(av, x);
    3192             : }
    3193             : GEN
    3194           0 : Flxq_auttrace(GEN x, ulong n, GEN T, ulong p)
    3195           0 : { return Flxq_auttrace_pre(x, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3196             : 
    3197             : static long
    3198      862204 : bounded_order(ulong p, GEN b, long k)
    3199             : {
    3200      862204 :   GEN a = modii(utoipos(p), b);
    3201             :   long i;
    3202     2089981 :   for(i = 1; i < k; i++)
    3203             :   {
    3204     1614933 :     if (equali1(a)) return i;
    3205     1227780 :     a = modii(muliu(a,p),b);
    3206             :   }
    3207      475048 :   return 0;
    3208             : }
    3209             : 
    3210             : /*
    3211             :   n = (p^d-a)\b
    3212             :   b = bb*p^vb
    3213             :   p^k = 1 [bb]
    3214             :   d = m*k+r+vb
    3215             :   u = (p^k-1)/bb;
    3216             :   v = (p^(r+vb)-a)/b;
    3217             :   w = (p^(m*k)-1)/(p^k-1)
    3218             :   n = p^r*w*u+v
    3219             :   w*u = p^vb*(p^(m*k)-1)/b
    3220             :   n = p^(r+vb)*(p^(m*k)-1)/b+(p^(r+vb)-a)/b
    3221             : */
    3222             : 
    3223             : static GEN
    3224    26012361 : Flxq_pow_Frobenius(GEN x, GEN n, GEN aut, GEN T, ulong p, ulong pi)
    3225             : {
    3226    26012361 :   pari_sp av=avma;
    3227    26012361 :   long d = get_Flx_degree(T);
    3228    26012382 :   GEN an = absi_shallow(n), z, q;
    3229    26012358 :   if (abscmpiu(an,p)<0 || cmpis(an,d)<=0) return Flxq_pow_pre(x, n, T, p, pi);
    3230      862580 :   q = powuu(p, d);
    3231      862579 :   if (dvdii(q, n))
    3232             :   {
    3233         353 :     long vn = logint(an, utoipos(p));
    3234         353 :     GEN autvn = vn==1 ? aut: Flxq_autpow_pre(aut,vn,T,p,pi);
    3235         353 :     z = Flx_Flxq_eval_pre(x,autvn,T,p,pi);
    3236             :   } else
    3237             :   {
    3238      862227 :     GEN b = diviiround(q, an), a = subii(q, mulii(an,b));
    3239             :     GEN bb, u, v, autk;
    3240      862226 :     long vb = Z_lvalrem(b,p,&bb);
    3241      862227 :     long m, r, k = is_pm1(bb)? 1: bounded_order(p,bb,d);
    3242      862224 :     if (!k || d-vb < k) return Flxq_pow_pre(x,n, T,p,pi);
    3243      387169 :     m = (d-vb)/k; r = (d-vb)%k;
    3244      387169 :     u = diviiexact(subiu(powuu(p,k),1),bb);
    3245      387169 :     v = diviiexact(subii(powuu(p,r+vb),a),b);
    3246      387169 :     autk = k==1 ? aut: Flxq_autpow_pre(aut,k,T,p,pi);
    3247      387169 :     if (r)
    3248             :     {
    3249       95471 :       GEN autr = r==1 ? aut: Flxq_autpow_pre(aut,r,T,p,pi);
    3250       95471 :       z = Flx_Flxq_eval_pre(x,autr,T,p,pi);
    3251      291698 :     } else z = x;
    3252      387169 :     if (m > 1) z = gel(Flxq_autsum_pre(mkvec2(autk, z), m, T, p, pi), 2);
    3253      387169 :     if (!is_pm1(u)) z = Flxq_pow_pre(z, u, T, p, pi);
    3254      387169 :     if (signe(v)) z = Flxq_mul_pre(z, Flxq_pow_pre(x, v, T, p, pi), T, p, pi);
    3255             :   }
    3256      387522 :   return gerepileupto(av,signe(n)>0 ? z : Flxq_inv_pre(z,T,p,pi));
    3257             : }
    3258             : 
    3259             : static GEN
    3260    26004872 : _Flxq_pow(void *data, GEN x, GEN n)
    3261             : {
    3262    26004872 :   struct _Flxq *D = (struct _Flxq*)data;
    3263    26004872 :   return Flxq_pow_Frobenius(x, n, D->aut, D->T, D->p, D->pi);
    3264             : }
    3265             : 
    3266             : static GEN
    3267      363815 : _Flxq_rand(void *data)
    3268             : {
    3269      363815 :   pari_sp av=avma;
    3270      363815 :   struct _Flxq *D = (struct _Flxq*)data;
    3271             :   GEN z;
    3272             :   do
    3273             :   {
    3274      367214 :     set_avma(av);
    3275      367214 :     z = random_Flx(get_Flx_degree(D->T),get_Flx_var(D->T),D->p);
    3276      367215 :   } while (lgpol(z)==0);
    3277      363816 :   return z;
    3278             : }
    3279             : 
    3280             : /* discrete log in FpXQ for a in Fp^*, g in FpXQ^* of order ord */
    3281             : static GEN
    3282       28970 : Fl_Flxq_log(ulong a, GEN g, GEN o, GEN T, ulong p)
    3283             : {
    3284       28970 :   pari_sp av = avma;
    3285             :   GEN q,n_q,ord,ordp, op;
    3286             : 
    3287       28970 :   if (a == 1UL) return gen_0;
    3288             :   /* p > 2 */
    3289             : 
    3290       28970 :   ordp = utoi(p - 1);
    3291       28970 :   ord  = get_arith_Z(o);
    3292       28970 :   if (!ord) ord = T? subiu(powuu(p, get_FpX_degree(T)), 1): ordp;
    3293       28970 :   if (a == p - 1) /* -1 */
    3294        7501 :     return gerepileuptoint(av, shifti(ord,-1));
    3295       21469 :   ordp = gcdii(ordp, ord);
    3296       21469 :   op = typ(o)==t_MAT ? famat_Z_gcd(o, ordp) : ordp;
    3297             : 
    3298       21469 :   q = NULL;
    3299       21469 :   if (T)
    3300             :   { /* we want < g > = Fp^* */
    3301       21469 :     if (!equalii(ord,ordp)) {
    3302       10566 :       q = diviiexact(ord,ordp);
    3303       10566 :       g = Flxq_pow(g,q,T,p);
    3304             :     }
    3305             :   }
    3306       21469 :   n_q = Fp_log(utoi(a), utoipos(uel(g,2)), op, utoipos(p));
    3307       21469 :   if (lg(n_q)==1) return gerepileuptoleaf(av, n_q);
    3308       21469 :   if (q) n_q = mulii(q, n_q);
    3309       21469 :   return gerepileuptoint(av, n_q);
    3310             : }
    3311             : 
    3312             : static GEN
    3313      692488 : Flxq_easylog(void* E, GEN a, GEN g, GEN ord)
    3314             : {
    3315      692488 :   struct _Flxq *f = (struct _Flxq *)E;
    3316      692488 :   GEN T = f->T;
    3317      692488 :   ulong p = f->p;
    3318      692488 :   long d = get_Flx_degree(T);
    3319      692488 :   if (Flx_equal1(a)) return gen_0;
    3320      534252 :   if (Flx_equal(a,g)) return gen_1;
    3321      164852 :   if (!degpol(a))
    3322       28970 :     return Fl_Flxq_log(uel(a,2), g, ord, T, p);
    3323      135882 :   if (typ(ord)!=t_INT || d <= 4 || d == 6 || abscmpiu(ord,1UL<<27)<0)
    3324      135854 :     return NULL;
    3325          28 :   return Flxq_log_index(a, g, ord, T, p);
    3326             : }
    3327             : 
    3328             : static const struct bb_group Flxq_star={_Flxq_mul,_Flxq_pow,_Flxq_rand,hash_GEN,Flx_equal,Flx_equal1,Flxq_easylog};
    3329             : 
    3330             : const struct bb_group *
    3331      441087 : get_Flxq_star(void **E, GEN T, ulong p)
    3332             : {
    3333      441087 :   struct _Flxq *e = (struct _Flxq *) stack_malloc(sizeof(struct _Flxq));
    3334      441086 :   e->T = T; e->p  = p; e->pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    3335      441086 :   e->aut =  Flx_Frobenius_pre(T, p, e->pi);
    3336      441088 :   *E = (void*)e; return &Flxq_star;
    3337             : }
    3338             : 
    3339             : GEN
    3340       95497 : Flxq_order(GEN a, GEN ord, GEN T, ulong p)
    3341             : {
    3342             :   void *E;
    3343       95497 :   const struct bb_group *S = get_Flxq_star(&E,T,p);
    3344       95497 :   return gen_order(a,ord,E,S);
    3345             : }
    3346             : 
    3347             : GEN
    3348      158384 : Flxq_log(GEN a, GEN g, GEN ord, GEN T, ulong p)
    3349             : {
    3350             :   void *E;
    3351      158384 :   pari_sp av = avma;
    3352      158384 :   const struct bb_group *S = get_Flxq_star(&E,T,p);
    3353      158384 :   GEN v = get_arith_ZZM(ord), F = gmael(v,2,1);
    3354      158384 :   if (Flxq_log_use_index(gel(F,lg(F)-1), T, p))
    3355       24590 :     v = mkvec2(gel(v, 1), ZM_famat_limit(gel(v, 2), int2n(27)));
    3356      158384 :   return gerepileuptoleaf(av, gen_PH_log(a, g, v, E, S));
    3357             : }
    3358             : 
    3359             : GEN
    3360      190273 : Flxq_sqrtn(GEN a, GEN n, GEN T, ulong p, GEN *zeta)
    3361             : {
    3362      190273 :   if (!lgpol(a))
    3363             :   {
    3364        3066 :     if (signe(n) < 0) pari_err_INV("Flxq_sqrtn",a);
    3365        3059 :     if (zeta)
    3366           0 :       *zeta=pol1_Flx(get_Flx_var(T));
    3367        3059 :     return pol0_Flx(get_Flx_var(T));
    3368             :   }
    3369             :   else
    3370             :   {
    3371             :     void *E;
    3372      187207 :     pari_sp av = avma;
    3373      187207 :     const struct bb_group *S = get_Flxq_star(&E,T,p);
    3374      187207 :     GEN o = subiu(powuu(p,get_Flx_degree(T)), 1);
    3375      187202 :     GEN s = gen_Shanks_sqrtn(a,n,o,zeta,E,S);
    3376      187207 :     if (!s) return gc_NULL(av);
    3377      184365 :     return gc_all(av, zeta?2:1, &s, zeta);
    3378             :   }
    3379             : }
    3380             : 
    3381             : GEN
    3382      164388 : Flxq_sqrt(GEN a, GEN T, ulong p)
    3383      164388 : { return Flxq_sqrtn(a, gen_2, T, p, NULL); }
    3384             : 
    3385             : /* assume T irreducible mod p */
    3386             : int
    3387      364126 : Flxq_issquare(GEN x, GEN T, ulong p)
    3388             : {
    3389      364126 :   if (lgpol(x) == 0 || p == 2) return 1;
    3390      361011 :   return krouu(Flxq_norm(x,T,p), p) == 1;
    3391             : }
    3392             : 
    3393             : /* assume T irreducible mod p */
    3394             : int
    3395           0 : Flxq_is2npower(GEN x, long n, GEN T, ulong p)
    3396             : {
    3397             :   pari_sp av;
    3398             :   GEN m;
    3399           0 :   if (n==1) return Flxq_issquare(x, T, p);
    3400           0 :   if (lgpol(x) == 0 || p == 2) return 1;
    3401           0 :   av = avma;
    3402           0 :   m = shifti(subiu(powuu(p, get_Flx_degree(T)), 1), -n);
    3403           0 :   return gc_bool(av, Flx_equal1(Flxq_pow(x, m, T, p)));
    3404             : }
    3405             : 
    3406             : GEN
    3407      113589 : Flxq_lroot_fast_pre(GEN a, GEN sqx, GEN T, long p, ulong pi)
    3408             : {
    3409      113589 :   pari_sp av=avma;
    3410      113589 :   GEN A = Flx_splitting(a,p);
    3411      113589 :   return gerepileuptoleaf(av, FlxqV_dotproduct_pre(A,sqx,T,p,pi));
    3412             : }
    3413             : GEN
    3414           0 : Flxq_lroot_fast(GEN a, GEN sqx, GEN T, long p)
    3415           0 : { return Flxq_lroot_fast_pre(a, sqx, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3416             : 
    3417             : GEN
    3418       25053 : Flxq_lroot_pre(GEN a, GEN T, long p, ulong pi)
    3419             : {
    3420       25053 :   pari_sp av=avma;
    3421       25053 :   long n = get_Flx_degree(T), d = degpol(a);
    3422             :   GEN sqx, V;
    3423       25053 :   if (n==1) return leafcopy(a);
    3424       25053 :   if (n==2) return Flxq_powu_pre(a, p, T, p, pi);
    3425       25053 :   sqx = Flxq_autpow_pre(Flx_Frobenius_pre(T, p, pi), n-1, T, p, pi);
    3426       25053 :   if (d==1 && a[2]==0 && a[3]==1) return gerepileuptoleaf(av, sqx);
    3427           0 :   if (d>=p)
    3428             :   {
    3429           0 :     V = Flxq_powers_pre(sqx,p-1,T,p,pi);
    3430           0 :     return gerepileuptoleaf(av, Flxq_lroot_fast_pre(a,V,T,p,pi));
    3431             :   } else
    3432           0 :     return gerepileuptoleaf(av, Flx_Flxq_eval_pre(a,sqx,T,p,pi));
    3433             : }
    3434             : GEN
    3435           0 : Flxq_lroot(GEN a, GEN T, long p)
    3436           0 : { return Flxq_lroot_pre(a, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3437             : 
    3438             : ulong
    3439      397773 : Flxq_norm(GEN x, GEN TB, ulong p)
    3440             : {
    3441      397773 :   GEN T = get_Flx_mod(TB);
    3442      397773 :   ulong y = Flx_resultant(T, x, p), L = Flx_lead(T);
    3443      397773 :   if (L==1 || lgpol(x)==0) return y;
    3444           0 :   return Fl_div(y, Fl_powu(L, (ulong)degpol(x), p), p);
    3445             : }
    3446             : 
    3447             : ulong
    3448        3359 : Flxq_trace(GEN x, GEN TB, ulong p)
    3449             : {
    3450        3359 :   pari_sp av = avma;
    3451             :   ulong t;
    3452        3359 :   GEN T = get_Flx_mod(TB);
    3453        3359 :   long n = degpol(T)-1;
    3454        3359 :   GEN z = Flxq_mul(x, Flx_deriv(T, p), TB, p);
    3455        3359 :   t = degpol(z)<n ? 0 : Fl_div(z[2+n],T[3+n],p);
    3456        3359 :   return gc_ulong(av, t);
    3457             : }
    3458             : 
    3459             : /*x must be reduced*/
    3460             : GEN
    3461        3626 : Flxq_charpoly(GEN x, GEN TB, ulong p)
    3462             : {
    3463        3626 :   pari_sp ltop=avma;
    3464        3626 :   GEN T = get_Flx_mod(TB);
    3465        3626 :   long vs = evalvarn(fetch_var());
    3466        3626 :   GEN xm1 = deg1pol_shallow(pol1_Flx(x[1]),Flx_neg(x,p),vs);
    3467        3626 :   GEN r = Flx_FlxY_resultant(T, xm1, p);
    3468        3626 :   r[1] = x[1];
    3469        3626 :   (void)delete_var(); return gerepileupto(ltop, r);
    3470             : }
    3471             : 
    3472             : /* Computing minimal polynomial :                         */
    3473             : /* cf Shoup 'Efficient Computation of Minimal Polynomials */
    3474             : /*          in Algebraic Extensions of Finite Fields'     */
    3475             : 
    3476             : /* Let v a linear form, return the linear form z->v(tau*z)
    3477             :    that is, v*(M_tau) */
    3478             : 
    3479             : static GEN
    3480     1442909 : Flxq_transmul_init(GEN tau, GEN T, ulong p, ulong pi)
    3481             : {
    3482             :   GEN bht;
    3483     1442909 :   GEN h, Tp = get_Flx_red(T, &h);
    3484     1442896 :   long n = degpol(Tp), vT = Tp[1];
    3485     1442896 :   GEN ft = Flx_recipspec(Tp+2, n+1, n+1);
    3486     1442879 :   GEN bt = Flx_recipspec(tau+2, lgpol(tau), n);
    3487     1442877 :   ft[1] = vT; bt[1] = vT;
    3488     1442877 :   if (h)
    3489        2688 :     bht = Flxn_mul_pre(bt, h, n-1, p, pi);
    3490             :   else
    3491             :   {
    3492     1440189 :     GEN bh = Flx_div_pre(Flx_shift(tau, n-1), T, p, pi);
    3493     1440183 :     bht = Flx_recipspec(bh+2, lgpol(bh), n-1);
    3494     1440185 :     bht[1] = vT;
    3495             :   }
    3496     1442873 :   return mkvec3(bt, bht, ft);
    3497             : }
    3498             : 
    3499             : static GEN
    3500     3489614 : Flxq_transmul(GEN tau, GEN a, long n, ulong p, ulong pi)
    3501             : {
    3502     3489614 :   pari_sp ltop = avma;
    3503             :   GEN t1, t2, t3, vec;
    3504     3489614 :   GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
    3505     3489614 :   if (lgpol(a)==0) return pol0_Flx(a[1]);
    3506     3461924 :   t2  = Flx_shift(Flx_mul_pre(bt, a, p, pi),1-n);
    3507     3461640 :   if (lgpol(bht)==0) return gerepileuptoleaf(ltop, t2);
    3508     2617872 :   t1  = Flx_shift(Flx_mul_pre(ft, a, p, pi),-n);
    3509     2617916 :   t3  = Flxn_mul_pre(t1, bht, n-1, p, pi);
    3510     2617867 :   vec = Flx_sub(t2, Flx_shift(t3, 1), p);
    3511     2617869 :   return gerepileuptoleaf(ltop, vec);
    3512             : }
    3513             : 
    3514             : GEN
    3515      668359 : Flxq_minpoly_pre(GEN x, GEN T, ulong p, ulong pi)
    3516             : {
    3517      668359 :   pari_sp ltop = avma;
    3518      668359 :   long vT = get_Flx_var(T), n = get_Flx_degree(T);
    3519             :   GEN v_x;
    3520      668351 :   GEN g = pol1_Flx(vT), tau = pol1_Flx(vT);
    3521      668326 :   T = Flx_get_red_pre(T, p, pi);
    3522      668325 :   v_x = Flxq_powers_pre(x, usqrt(2*n), T, p, pi);
    3523     1389772 :   while (lgpol(tau) != 0)
    3524             :   {
    3525             :     long i, j, m, k1;
    3526             :     GEN M, v, tr, g_prime, c;
    3527      721434 :     if (degpol(g) == n) { tau = pol1_Flx(vT); g = pol1_Flx(vT); }
    3528      721438 :     v = random_Flx(n, vT, p);
    3529      721470 :     tr = Flxq_transmul_init(tau, T, p, pi);
    3530      721441 :     v = Flxq_transmul(tr, v, n, p, pi);
    3531      721465 :     m = 2*(n-degpol(g));
    3532      721465 :     k1 = usqrt(m);
    3533      721466 :     tr = Flxq_transmul_init(gel(v_x,k1+1), T, p, pi);
    3534      721441 :     c = cgetg(m+2,t_VECSMALL);
    3535      721367 :     c[1] = vT;
    3536     3489468 :     for (i=0; i<m; i+=k1)
    3537             :     {
    3538     2767997 :       long mj = minss(m-i, k1);
    3539    11229952 :       for (j=0; j<mj; j++)
    3540     8461478 :         uel(c,m+1-(i+j)) = Flx_dotproduct_pre(v, gel(v_x,j+1), p, pi);
    3541     2768474 :       v = Flxq_transmul(tr, v, n, p, pi);
    3542             :     }
    3543      721471 :     c = Flx_renormalize(c, m+2);
    3544             :     /* now c contains <v,x^i> , i = 0..m-1  */
    3545      721465 :     M = Flx_halfgcd_pre(monomial_Flx(1, m, vT), c, p, pi);
    3546      721478 :     g_prime = gmael(M, 2, 2);
    3547      721478 :     if (degpol(g_prime) < 1) continue;
    3548      710780 :     g = Flx_mul_pre(g, g_prime, p, pi);
    3549      710764 :     tau = Flxq_mul_pre(tau, Flx_FlxqV_eval_pre(g_prime, v_x, T,p,pi), T,p,pi);
    3550             :   }
    3551      668305 :   g = Flx_normalize(g,p);
    3552      668354 :   return gerepileuptoleaf(ltop,g);
    3553             : }
    3554             : GEN
    3555       40590 : Flxq_minpoly(GEN x, GEN T, ulong p)
    3556       40590 : { return Flxq_minpoly_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3557             : 
    3558             : GEN
    3559          20 : Flxq_conjvec(GEN x, GEN T, ulong p)
    3560             : {
    3561          20 :   long i, l = 1+get_Flx_degree(T);
    3562          20 :   GEN z = cgetg(l,t_COL);
    3563          20 :   struct _Flxq D; set_Flxq(&D, T, p);
    3564          20 :   gel(z,1) = Flx_copy(x);
    3565          88 :   for (i=2; i<l; i++) gel(z,i) = _Flxq_powu(&D, gel(z,i-1), p);
    3566          20 :   return z;
    3567             : }
    3568             : 
    3569             : GEN
    3570        7166 : gener_Flxq(GEN T, ulong p, GEN *po)
    3571             : {
    3572        7166 :   long i, j, vT = get_Flx_var(T), f = get_Flx_degree(T);
    3573             :   ulong p_1, pi;
    3574             :   GEN g, L, L2, o, q, F;
    3575             :   pari_sp av0, av;
    3576             : 
    3577        7166 :   if (f == 1) {
    3578             :     GEN fa;
    3579          28 :     o = utoipos(p-1);
    3580          28 :     fa = Z_factor(o);
    3581          28 :     L = gel(fa,1);
    3582          28 :     L = vecslice(L, 2, lg(L)-1); /* remove 2 for efficiency */
    3583          28 :     g = Fl_to_Flx(pgener_Fl_local(p, vec_to_vecsmall(L)), vT);
    3584          28 :     if (po) *po = mkvec2(o, fa);
    3585          28 :     return g;
    3586             :   }
    3587             : 
    3588        7138 :   av0 = avma; p_1 = p - 1;
    3589        7138 :   q = diviuexact(subiu(powuu(p,f), 1), p_1);
    3590             : 
    3591        7138 :   L = cgetg(1, t_VECSMALL);
    3592        7138 :   if (p > 3)
    3593             :   {
    3594        2343 :     ulong t = p_1 >> vals(p_1);
    3595        2343 :     GEN P = gel(factoru(t), 1);
    3596        2343 :     L = cgetg_copy(P, &i);
    3597        3738 :     while (--i) L[i] = p_1 / P[i];
    3598             :   }
    3599        7138 :   o = factor_pn_1(utoipos(p),f);
    3600        7138 :   L2 = leafcopy( gel(o, 1) );
    3601       19093 :   for (i = j = 1; i < lg(L2); i++)
    3602             :   {
    3603       11955 :     if (umodui(p_1, gel(L2,i)) == 0) continue;
    3604        6460 :     gel(L2,j++) = diviiexact(q, gel(L2,i));
    3605             :   }
    3606        7138 :   setlg(L2, j); pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    3607        7138 :   F = Flx_Frobenius_pre(T, p, pi);
    3608       17737 :   for (av = avma;; set_avma(av))
    3609       10599 :   {
    3610             :     GEN tt;
    3611       17737 :     g = random_Flx(f, vT, p);
    3612       17737 :     if (degpol(g) < 1) continue;
    3613       12089 :     if (p == 2) tt = g;
    3614             :     else
    3615             :     {
    3616        8890 :       ulong t = Flxq_norm(g, T, p);
    3617        8890 :       if (t == 1 || !is_gener_Fl(t, p, p_1, L)) continue;
    3618        4782 :       tt = Flxq_powu_pre(g, p_1>>1, T, p, pi);
    3619             :     }
    3620       14576 :     for (i = 1; i < j; i++)
    3621             :     {
    3622        7438 :       GEN a = Flxq_pow_Frobenius(tt, gel(L2,i), F, T, p, pi);
    3623        7438 :       if (!degpol(a) && uel(a,2) == p_1) break;
    3624             :     }
    3625        7981 :     if (i == j) break;
    3626             :   }
    3627        7138 :   if (!po)
    3628             :   {
    3629         180 :     set_avma((pari_sp)g);
    3630         180 :     g = gerepileuptoleaf(av0, g);
    3631             :   }
    3632             :   else {
    3633        6958 :     *po = mkvec2(subiu(powuu(p,f), 1), o);
    3634        6958 :     gerepileall(av0, 2, &g, po);
    3635             :   }
    3636        7138 :   return g;
    3637             : }
    3638             : 
    3639             : static GEN
    3640      557727 : _Flxq_neg(void *E, GEN x)
    3641      557727 : { struct _Flxq *s = (struct _Flxq *)E;
    3642      557727 :   return Flx_neg(x,s->p); }
    3643             : 
    3644             : static GEN
    3645     1528908 : _Flxq_rmul(void *E, GEN x, GEN y)
    3646     1528908 : { struct _Flxq *s = (struct _Flxq *)E;
    3647     1528908 :   return Flx_mul_pre(x,y,s->p,s->pi); }
    3648             : 
    3649             : static GEN
    3650       19035 : _Flxq_inv(void *E, GEN x)
    3651       19035 : { struct _Flxq *s = (struct _Flxq *)E;
    3652       19035 :   return Flxq_inv(x,s->T,s->p); }
    3653             : 
    3654             : static int
    3655      164940 : _Flxq_equal0(GEN x) { return lgpol(x)==0; }
    3656             : 
    3657             : static GEN
    3658       24793 : _Flxq_s(void *E, long x)
    3659       24793 : { struct _Flxq *s = (struct _Flxq *)E;
    3660       24793 :   ulong u = x<0 ? s->p+x: (ulong)x;
    3661       24793 :   return Fl_to_Flx(u, get_Flx_var(s->T));
    3662             : }
    3663             : 
    3664             : static const struct bb_field Flxq_field={_Flxq_red,_Flx_add,_Flxq_rmul,_Flxq_neg,
    3665             :                                          _Flxq_inv,_Flxq_equal0,_Flxq_s};
    3666             : 
    3667       67922 : const struct bb_field *get_Flxq_field(void **E, GEN T, ulong p)
    3668             : {
    3669       67922 :   GEN z = new_chunk(sizeof(struct _Flxq));
    3670       67922 :   set_Flxq((struct _Flxq *)z, T, p); *E = (void*)z; return &Flxq_field;
    3671             : }
    3672             : 
    3673             : /***********************************************************************/
    3674             : /**                               Flxn                                **/
    3675             : /***********************************************************************/
    3676             : 
    3677             : GEN
    3678       54342 : Flx_invLaplace(GEN x, ulong p)
    3679             : {
    3680       54342 :   long i, d = degpol(x);
    3681             :   ulong t;
    3682             :   GEN y;
    3683       54333 :   if (d <= 1) return Flx_copy(x);
    3684       54333 :   t = Fl_inv(factorial_Fl(d, p), p);
    3685       54384 :   y = cgetg(d+3, t_VECSMALL);
    3686       54326 :   y[1] = x[1];
    3687     1328834 :   for (i=d; i>=2; i--)
    3688             :   {
    3689     1274464 :     uel(y,i+2) = Fl_mul(uel(x,i+2), t, p);
    3690     1274492 :     t = Fl_mul(t, i, p);
    3691             :   }
    3692       54370 :   uel(y,3) = uel(x,3);
    3693       54370 :   uel(y,2) = uel(x,2);
    3694       54370 :   return y;
    3695             : }
    3696             : 
    3697             : GEN
    3698       27333 : Flx_Laplace(GEN x, ulong p)
    3699             : {
    3700       27333 :   long i, d = degpol(x);
    3701       27330 :   ulong t = 1;
    3702             :   GEN y;
    3703       27330 :   if (d <= 1) return Flx_copy(x);
    3704       27330 :   y = cgetg(d+3, t_VECSMALL);
    3705       27319 :   y[1] = x[1];
    3706       27319 :   uel(y,2) = uel(x,2);
    3707       27319 :   uel(y,3) = uel(x,3);
    3708      757670 :   for (i=2; i<=d; i++)
    3709             :   {
    3710      730324 :     t = Fl_mul(t, i%p, p);
    3711      730336 :     uel(y,i+2) = Fl_mul(uel(x,i+2), t, p);
    3712             :   }
    3713       27346 :   return y;
    3714             : }
    3715             : 
    3716             : GEN
    3717     5731170 : Flxn_red(GEN a, long n)
    3718             : {
    3719     5731170 :   long i, L, l = lg(a);
    3720             :   GEN  b;
    3721     5731170 :   if (l == 2 || !n) return zero_Flx(a[1]);
    3722     5342108 :   L = n+2; if (L > l) L = l;
    3723     5342108 :   b = cgetg(L, t_VECSMALL); b[1] = a[1];
    3724    51678557 :   for (i=2; i<L; i++) b[i] = a[i];
    3725     5338442 :   return Flx_renormalize(b,L);
    3726             : }
    3727             : 
    3728             : GEN
    3729     4620668 : Flxn_mul_pre(GEN a, GEN b, long n, ulong p, ulong pi)
    3730     4620668 : { return Flxn_red(Flx_mul_pre(a, b, p, pi), n); }
    3731             : GEN
    3732       75203 : Flxn_mul(GEN a, GEN b, long n, ulong p)
    3733       75203 : { return Flxn_mul_pre(a, b, n, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3734             : 
    3735             : GEN
    3736           0 : Flxn_sqr_pre(GEN a, long n, ulong p, ulong pi)
    3737           0 : { return Flxn_red(Flx_sqr_pre(a, p, pi), n); }
    3738             : GEN
    3739           0 : Flxn_sqr(GEN a, long n, ulong p)
    3740           0 : { return Flxn_sqr_pre(a, n, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3741             : 
    3742             : /* (f*g) \/ x^n */
    3743             : static GEN
    3744      937741 : Flx_mulhigh_i(GEN f, GEN g, long n, ulong p, ulong pi)
    3745      937741 : { return Flx_shift(Flx_mul_pre(f, g, p, pi),-n); }
    3746             : 
    3747             : static GEN
    3748      516414 : Flxn_mulhigh(GEN f, GEN g, long n2, long n, ulong p, ulong pi)
    3749             : {
    3750      516414 :   GEN F = Flx_blocks(f, n2, 2), fl = gel(F,1), fh = gel(F,2);
    3751      516099 :   return Flx_add(Flx_mulhigh_i(fl, g, n2, p, pi),
    3752             :                  Flxn_mul_pre(fh, g, n - n2, p, pi), p);
    3753             : }
    3754             : 
    3755             : /* g==NULL -> assume g==1 */
    3756             : GEN
    3757       55152 : Flxn_div_pre(GEN g, GEN f, long e, ulong p, ulong pi)
    3758             : {
    3759       55152 :   pari_sp av = avma, av2;
    3760             :   ulong mask;
    3761             :   GEN W;
    3762       55152 :   long n = 1;
    3763       55152 :   if (lg(f) <= 2) pari_err_INV("Flxn_inv",f);
    3764       55152 :   W = Fl_to_Flx(Fl_inv(uel(f,2),p), f[1]);
    3765       55146 :   mask = quadratic_prec_mask(e);
    3766       55162 :   av2 = avma;
    3767      258769 :   for (;mask>1;)
    3768             :   {
    3769             :     GEN u, fr;
    3770      203593 :     long n2 = n;
    3771      203593 :     n<<=1; if (mask & 1) n--;
    3772      203593 :     mask >>= 1;
    3773      203593 :     fr = Flxn_red(f, n);
    3774      203456 :     if (mask>1 || !g)
    3775             :     {
    3776      149381 :       u = Flxn_mul_pre(W, Flxn_mulhigh(fr, W, n2, n, p, pi), n-n2, p, pi);
    3777      149707 :       W = Flx_sub(W, Flx_shift(u, n2), p);
    3778             :     } else
    3779             :     {
    3780       54075 :       GEN y = Flxn_mul_pre(g, W, n, p, pi), yt =  Flxn_red(y, n-n2);
    3781       54076 :       u = Flxn_mul_pre(yt, Flxn_mulhigh(fr,  W, n2, n, p, pi), n-n2, p, pi);
    3782       54084 :       W = Flx_sub(y, Flx_shift(u, n2), p);
    3783             :     }
    3784      203600 :     if (gc_needed(av2,2))
    3785             :     {
    3786           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"Flxn_div, e = %ld", n);
    3787           0 :       W = gerepileupto(av2, W);
    3788             :     }
    3789             :   }
    3790       55176 :   return gerepileupto(av, W);
    3791             : }
    3792             : GEN
    3793       55122 : Flxn_div(GEN g, GEN f, long e, ulong p)
    3794       55122 : { return Flxn_div_pre(g, f, e, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    3795             : 
    3796             : GEN
    3797        1032 : Flxn_inv(GEN f, long e, ulong p)
    3798        1032 : { return Flxn_div(NULL, f, e, p); }
    3799             : 
    3800             : GEN
    3801      109372 : Flxn_expint(GEN h, long e, ulong p)
    3802             : {
    3803      109372 :   pari_sp av = avma, av2;
    3804      109372 :   long v = h[1], n=1;
    3805      109372 :   GEN f = pol1_Flx(v), g = pol1_Flx(v);
    3806      109336 :   ulong mask = quadratic_prec_mask(e), pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    3807      109352 :   av2 = avma;
    3808      422594 :   for (;mask>1;)
    3809             :   {
    3810             :     GEN u, w;
    3811      422523 :     long n2 = n;
    3812      422523 :     n<<=1; if (mask & 1) n--;
    3813      422523 :     mask >>= 1;
    3814      422523 :     u = Flxn_mul_pre(g, Flx_mulhigh_i(f, Flxn_red(h, n2-1), n2-1, p,pi), n-n2, p,pi);
    3815      422503 :     u = Flx_add(u, Flx_shift(Flxn_red(h, n-1), 1-n2), p);
    3816      422546 :     w = Flxn_mul_pre(f, Flx_integXn(u, n2-1, p), n-n2, p, pi);
    3817      422513 :     f = Flx_add(f, Flx_shift(w, n2), p);
    3818      422635 :     if (mask<=1) break;
    3819      313278 :     u = Flxn_mul_pre(g, Flxn_mulhigh(f, g, n2, n, p, pi), n-n2, p, pi);
    3820      313244 :     g = Flx_sub(g, Flx_shift(u, n2), p);
    3821      313242 :     if (gc_needed(av2,2))
    3822             :     {
    3823           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flxn_exp, e = %ld", n);
    3824           0 :       gerepileall(av2, 2, &f, &g);
    3825             :     }
    3826             :   }
    3827      109428 :   return gerepileupto(av, f);
    3828             : }
    3829             : 
    3830             : GEN
    3831           0 : Flxn_exp(GEN h, long e, ulong p)
    3832             : {
    3833           0 :   if (degpol(h)<1 || uel(h,2)!=0)
    3834           0 :     pari_err_DOMAIN("Flxn_exp","valuation", "<", gen_1, h);
    3835           0 :   return Flxn_expint(Flx_deriv(h, p), e, p);
    3836             : }
    3837             : 
    3838             : INLINE GEN
    3839      217181 : Flxn_recip(GEN x, long n)
    3840             : {
    3841      217181 :   GEN z=Flx_recipspec(x+2,lgpol(x),n);
    3842      217035 :   z[1]=x[1];
    3843      217035 :   return z;
    3844             : }
    3845             : 
    3846             : GEN
    3847       54067 : Flx_Newton(GEN P, long n, ulong p)
    3848             : {
    3849       54067 :   pari_sp av = avma;
    3850       54067 :   long d = degpol(P);
    3851       54064 :   GEN dP = Flxn_recip(Flx_deriv(P, p), d);
    3852       53974 :   GEN Q = Flxn_div(dP, Flxn_recip(P, d+1), n, p);
    3853       54041 :   return gerepileuptoleaf(av, Q);
    3854             : }
    3855             : 
    3856             : GEN
    3857      109368 : Flx_fromNewton(GEN P, ulong p)
    3858             : {
    3859      109368 :   pari_sp av = avma;
    3860      109368 :   ulong n = Flx_constant(P)+1;
    3861      109367 :   GEN z = Flx_neg(Flx_shift(P, -1), p);
    3862      109372 :   GEN Q = Flxn_recip(Flxn_expint(z, n, p), n);
    3863      109347 :   return gerepileuptoleaf(av, Q);
    3864             : }
    3865             : 
    3866             : static long
    3867         483 : newtonlogint(ulong n, ulong pp)
    3868             : {
    3869         483 :   long s = 0;
    3870        2107 :   while (n > pp)
    3871             :   {
    3872        1624 :     s += ulogint(n, pp);
    3873        1624 :     n = (n+1)>>1;
    3874             :   }
    3875         483 :   return s;
    3876             : }
    3877             : 
    3878             : static void
    3879       12500 : init_invlaplace(long d, ulong p, GEN *pt_P, GEN *pt_V)
    3880             : {
    3881             :   long i;
    3882             :   ulong e;
    3883       12500 :   GEN P = cgetg(d+1, t_VECSMALL);
    3884       12500 :   GEN V = cgetg(d+1, t_VECSMALL);
    3885     1389427 :   for (i=1, e=1; i<=d; i++, e++)
    3886             :   {
    3887     1376927 :     if (e==p)
    3888             :     {
    3889      455590 :       e = 0;
    3890      455590 :       V[i] = u_lvalrem(i, p, &uel(P,i));
    3891             :     } else
    3892             :     {
    3893      921337 :       V[i] = 0; uel(P,i) = i;
    3894             :     }
    3895             :   }
    3896       12500 :   *pt_P = P; *pt_V = V;
    3897       12500 : }
    3898             : 
    3899             : /* return p^val * FpX_invLaplace(1+x+...x^(n-1), q), with q a power of p and
    3900             :  * val large enough to compensate for the power of p in the factorials */
    3901             : 
    3902             : static GEN
    3903         483 : ZpX_invLaplace_init(long n, GEN q, ulong p, long v, long sv)
    3904             : {
    3905         483 :   pari_sp av = avma;
    3906         483 :   long i, d = n-1, w;
    3907             :   GEN y, W, E, t;
    3908         483 :   init_invlaplace(d, p, &E, &W);
    3909         483 :   t = Fp_inv(FpV_prod(Flv_to_ZV(E), q), q);
    3910         483 :   w = zv_sum(W);
    3911         483 :   if (v > w) t = Fp_mul(t, powuu(p, v-w), q);
    3912         483 :   y = cgetg(d+3,t_POL);
    3913         483 :   y[1] = evalsigne(1) | sv;
    3914       21728 :   for (i=d; i>=1; i--)
    3915             :   {
    3916       21245 :     gel(y,i+2) = t;
    3917       21245 :     t = Fp_mulu(t, uel(E,i), q);
    3918       21245 :     if (uel(W,i)) t = Fp_mul(t, powuu(p, uel(W,i)), q);
    3919             :   }
    3920         483 :   gel(y,2) = t;
    3921         483 :   return gerepilecopy(av, ZX_renormalize(y, d+3));
    3922             : }
    3923             : 
    3924             : static GEN
    3925       27513 : Flx_composedsum(GEN P, GEN Q, ulong p)
    3926             : {
    3927       27513 :   long n = 1 + degpol(P)*degpol(Q);
    3928       27513 :   ulong lead = Fl_mul(Fl_powu(Flx_lead(P), degpol(Q), p),
    3929       27510 :                       Fl_powu(Flx_lead(Q), degpol(P), p), p);
    3930             :   GEN R;
    3931       27515 :   if (p >= (ulong)n)
    3932             :   {
    3933       27032 :     GEN Pl = Flx_invLaplace(Flx_Newton(P,n,p), p);
    3934       27040 :     GEN Ql = Flx_invLaplace(Flx_Newton(Q,n,p), p);
    3935       27037 :     GEN L  = Flx_Laplace(Flxn_mul(Pl, Ql, n, p), p);
    3936       27041 :     R = Flx_fromNewton(L, p);
    3937             :   } else
    3938             :   {
    3939         483 :     long v = factorial_lval(n-1, p);
    3940         483 :     long w = 1 + newtonlogint(n-1, p);
    3941         483 :     GEN pv = powuu(p, v);
    3942         483 :     GEN qf = powuu(p, w), q = mulii(pv, qf), q2 = mulii(q, pv);
    3943         483 :     GEN iL = ZpX_invLaplace_init(n, q, p, v, P[1]);
    3944         483 :     GEN Pl = FpX_convol(iL, FpX_Newton(Flx_to_ZX(P), n, qf), q);
    3945         483 :     GEN Ql = FpX_convol(iL, FpX_Newton(Flx_to_ZX(Q), n, qf), q);
    3946         483 :     GEN Ln = ZX_Z_divexact(FpXn_mul(Pl, Ql, n, q2), pv);
    3947         483 :     GEN L  = ZX_Z_divexact(FpX_Laplace(Ln, q), pv);
    3948         483 :     R = ZX_to_Flx(FpX_fromNewton(L, qf), p);
    3949             :   }
    3950       27515 :   return Flx_Fl_mul(R, lead, p);
    3951             : }
    3952             : 
    3953             : GEN
    3954       27513 : Flx_direct_compositum(GEN a, GEN b, ulong p)
    3955       27513 : { return Flx_composedsum(a, b, p); }
    3956             : 
    3957             : static GEN
    3958        3812 : _Flx_direct_compositum(void *E, GEN a, GEN b)
    3959        3812 : { return Flx_direct_compositum(a, b, (ulong)E); }
    3960             : 
    3961             : GEN
    3962       28769 : FlxV_direct_compositum(GEN V, ulong p)
    3963       28769 : { return gen_product(V, (void *)p, &_Flx_direct_compositum); }
    3964             : 
    3965             : /* (x+1)^n mod p; assume 2 <= n < 2p prime */
    3966             : static GEN
    3967           0 : Fl_Xp1_powu(ulong n, ulong p, long v)
    3968             : {
    3969           0 :   ulong k, d = (n + 1) >> 1;
    3970           0 :   GEN C, V = identity_zv(d);
    3971             : 
    3972           0 :   Flv_inv_inplace(V, p); /* could restrict to odd integers in [3,d] */
    3973           0 :   C = cgetg(n+3, t_VECSMALL);
    3974           0 :   C[1] = v;
    3975           0 :   uel(C,2) = 1UL;
    3976           0 :   uel(C,3) = n%p;
    3977           0 :   uel(C,4) = Fl_mul(odd(n)? n: n-1, n >> 1, p);
    3978             :     /* binom(n,k) = binom(n,k-1) * (n-k+1) / k */
    3979           0 :   if (SMALL_ULONG(p))
    3980           0 :     for (k = 3; k <= d; k++)
    3981           0 :       uel(C,k+2) = Fl_mul(Fl_mul(n-k+1, uel(C,k+1), p), uel(V,k), p);
    3982             :   else
    3983             :   {
    3984           0 :     ulong pi  = get_Fl_red(p);
    3985           0 :     for (k = 3; k <= d; k++)
    3986           0 :       uel(C,k+2) = Fl_mul_pre(Fl_mul(n-k+1, uel(C,k+1), p), uel(V,k), p, pi);
    3987             :   }
    3988           0 :   for (   ; k <= n; k++) uel(C,2+k) = uel(C,2+n-k);
    3989           0 :   return C; /* normalized */
    3990             : }
    3991             : 
    3992             : /* p arbitrary */
    3993             : GEN
    3994       28194 : Flx_translate1_basecase(GEN P, ulong p)
    3995             : {
    3996       28194 :   GEN R = Flx_copy(P);
    3997       28194 :   long i, k, n = degpol(P);
    3998      654732 :   for (i = 1; i <= n; i++)
    3999    14846488 :     for (k = n-i; k < n; k++) uel(R,k+2) = Fl_add(uel(R,k+2), uel(R,k+3), p);
    4000       28194 :   return R;
    4001             : }
    4002             : 
    4003             : static int
    4004       41359 : translate_basecase(long n, ulong p)
    4005             : {
    4006             : #ifdef LONG_IS_64BIT
    4007       36066 :   if (p <= 19) return n < 40;
    4008       29910 :   if (p < 1UL<<30) return n < 58;
    4009           0 :   if (p < 1UL<<59) return n < 100;
    4010           0 :   if (p < 1UL<<62) return n < 120;
    4011           0 :   if (p < 1UL<<63) return n < 240;
    4012           0 :   return n < 250;
    4013             : #else
    4014        5293 :   if (p <= 13) return n < 18;
    4015        4136 :   if (p <= 17) return n < 22;
    4016        4078 :   if (p <= 29) return n < 39;
    4017        3886 :   if (p <= 67) return n < 69;
    4018        3667 :   if (p < 1UL<< 15) return n < 80;
    4019        2047 :   if (p < 1UL<< 16) return n < 100;
    4020           0 :   if (p < 1UL<< 28) return n < 300;
    4021           0 :   return n < 650;
    4022             : #endif
    4023             : }
    4024             : /* assume p prime */
    4025             : GEN
    4026       16100 : Flx_translate1(GEN P, ulong p)
    4027             : {
    4028       16100 :   long d, n = degpol(P);
    4029             :   GEN R, Q, S;
    4030       16100 :   if (translate_basecase(n, p)) return Flx_translate1_basecase(P, p);
    4031             :   /* n > 0 */
    4032        1148 :   d = n >> 1;
    4033        1148 :   if ((ulong)n < p)
    4034             :   {
    4035           0 :     R = Flx_translate1(Flxn_red(P, d), p);
    4036           0 :     Q = Flx_translate1(Flx_shift(P, -d), p);
    4037           0 :     S = Fl_Xp1_powu(d, p, P[1]);
    4038           0 :     return Flx_add(Flx_mul(Q, S, p), R, p);
    4039             :   }
    4040             :   else
    4041             :   {
    4042             :     ulong q;
    4043        1148 :     if ((ulong)d > p) (void)ulogintall(d, p, &q); else q = p;
    4044        1148 :     R = Flx_translate1(Flxn_red(P, q), p);
    4045        1148 :     Q = Flx_translate1(Flx_shift(P, -q), p);
    4046        1148 :     S = Flx_add(Flx_shift(Q, q), Q, p);
    4047        1148 :     return Flx_add(S, R, p); /* P(x+1) = Q(x+1) (x^q+1) + R(x+1) */
    4048             :   }
    4049             : }
    4050             : 
    4051             : static GEN
    4052       12017 : zl_Xp1_powu(ulong n, ulong p, ulong q, long e, long vs)
    4053             : {
    4054       12017 :   ulong k, d = n >> 1, c, v = 0;
    4055       12017 :   GEN C, V, W, U = upowers(p, e-1);
    4056       12017 :   init_invlaplace(d, p, &V, &W);
    4057       12017 :   Flv_inv_inplace(V, q);
    4058       12017 :   C = cgetg(n+3, t_VECSMALL);
    4059       12017 :   C[1] = vs;
    4060       12017 :   uel(C,2) = 1UL;
    4061       12017 :   uel(C,3) = n%q;
    4062       12017 :   v = u_lvalrem(n, p, &c);
    4063     1355682 :   for (k = 2; k <= d; k++)
    4064             :   {
    4065             :     ulong w;
    4066     1343665 :     v += u_lvalrem(n-k+1, p, &w) - W[k];
    4067     1343665 :     c = Fl_mul(Fl_mul(w%q, c, q), uel(V,k), q);
    4068     1343665 :     uel(C,2+k) = v >= (ulong)e ? 0: v==0 ? c : Fl_mul(c, uel(U, v+1), q);
    4069             :   }
    4070     1374521 :   for (   ; k <= n; k++) uel(C,2+k) = uel(C,2+n-k);
    4071       12017 :   return C; /* normalized */
    4072             : }
    4073             : 
    4074             : GEN
    4075       25259 : zlx_translate1(GEN P, ulong p, long e)
    4076             : {
    4077       25259 :   ulong d, q = upowuu(p,e), n = degpol(P);
    4078             :   GEN R, Q, S;
    4079       25259 :   if (translate_basecase(n, q)) return Flx_translate1_basecase(P, q);
    4080             :   /* n > 0 */
    4081       12017 :   d = n >> 1;
    4082       12017 :   R = zlx_translate1(Flxn_red(P, d), p, e);
    4083       12017 :   Q = zlx_translate1(Flx_shift(P, -d), p, e);
    4084       12017 :   S = zl_Xp1_powu(d, p, q, e, P[1]);
    4085       12017 :   return Flx_add(Flx_mul(Q, S, q), R, q);
    4086             : }
    4087             : 
    4088             : /***********************************************************************/
    4089             : /**                               Fl2                                 **/
    4090             : /***********************************************************************/
    4091             : /* Fl2 objects are Flv of length 2 [a,b] representing a+bsqrt(D) for
    4092             :  * a nonsquare D. */
    4093             : 
    4094             : INLINE GEN
    4095     6674290 : mkF2(ulong a, ulong b) { return mkvecsmall2(a,b); }
    4096             : 
    4097             : /* allow pi = 0 */
    4098             : GEN
    4099     1792172 : Fl2_mul_pre(GEN x, GEN y, ulong D, ulong p, ulong pi)
    4100             : {
    4101             :   ulong xaya, xbyb, Db2, mid, z1, z2;
    4102     1792172 :   ulong x1 = x[1], x2 = x[2], y1 = y[1], y2 = y[2];
    4103     1792172 :   if (pi)
    4104             :   {
    4105     1792533 :     xaya = Fl_mul_pre(x1,y1,p,pi);
    4106     1793041 :     if (x2==0 && y2==0) return mkF2(xaya,0);
    4107     1734203 :     if (x2==0) return mkF2(xaya,Fl_mul_pre(x1,y2,p,pi));
    4108     1712136 :     if (y2==0) return mkF2(xaya,Fl_mul_pre(x2,y1,p,pi));
    4109     1711923 :     xbyb = Fl_mul_pre(x2,y2,p,pi);
    4110     1711887 :     mid = Fl_mul_pre(Fl_add(x1,x2,p), Fl_add(y1,y2,p),p,pi);
    4111     1712036 :     Db2 = Fl_mul_pre(D, xbyb, p,pi);
    4112             :   }
    4113           0 :   else if (p & HIGHMASK)
    4114             :   {
    4115           0 :     xaya = Fl_mul(x1,y1,p);
    4116           0 :     if (x2==0 && y2==0) return mkF2(xaya,0);
    4117           0 :     if (x2==0) return mkF2(xaya,Fl_mul(x1,y2,p));
    4118           0 :     if (y2==0) return mkF2(xaya,Fl_mul(x2,y1,p));
    4119           0 :     xbyb = Fl_mul(x2,y2,p);
    4120           0 :     mid = Fl_mul(Fl_add(x1,x2,p), Fl_add(y1,y2,p),p);
    4121           0 :     Db2 = Fl_mul(D, xbyb, p);
    4122             :   }
    4123             :   else
    4124             :   {
    4125           0 :     xaya = (x1 * y1) % p;
    4126           0 :     if (x2==0 && y2==0) return mkF2(xaya,0);
    4127           0 :     if (x2==0) return mkF2(xaya, (x1 * y2) % p);
    4128           0 :     if (y2==0) return mkF2(xaya, (x2 * y1) % p);
    4129           0 :     xbyb = (x2 * y2) % p;
    4130           0 :     mid = (Fl_add(x1,x2,p) * Fl_add(y1,y2,p)) % p;
    4131           0 :     Db2 = (D * xbyb) % p;
    4132             :   }
    4133     1711965 :   z1 = Fl_add(xaya,Db2,p);
    4134     1711860 :   z2 = Fl_sub(mid,Fl_add(xaya,xbyb,p),p);
    4135     1711809 :   return mkF2(z1,z2);
    4136             : }
    4137             : 
    4138             : /* allow pi = 0 */
    4139             : GEN
    4140     4523983 : Fl2_sqr_pre(GEN x, ulong D, ulong p, ulong pi)
    4141             : {
    4142     4523983 :   ulong a = x[1], b = x[2];
    4143             :   ulong a2, Db2, ab;
    4144     4523983 :   if (pi)
    4145             :   {
    4146     4524699 :     a2 = Fl_sqr_pre(a,p,pi);
    4147     4528162 :     if (b==0) return mkF2(a2,0);
    4148     4342298 :     Db2= Fl_mul_pre(D, Fl_sqr_pre(b,p,pi), p,pi);
    4149     4342397 :     ab = Fl_mul_pre(a,b,p,pi);
    4150             :   }
    4151           0 :   else if (p & HIGHMASK)
    4152             :   {
    4153           0 :     a2 = Fl_sqr(a,p);
    4154           0 :     if (b==0) return mkF2(a2,0);
    4155           0 :     Db2= Fl_mul(D, Fl_sqr(b,p), p);
    4156           0 :     ab = Fl_mul(a,b,p);
    4157             :   }
    4158             :   else
    4159             :   {
    4160           0 :     a2 = (a * a) % p;
    4161           0 :     if (b==0) return mkF2(a2,0);
    4162           0 :     Db2= (D * ((b * b) % p)) % p;
    4163           0 :     ab = (a * b) % p;
    4164             :   }
    4165     4341570 :   return mkF2(Fl_add(a2,Db2,p), Fl_double(ab,p));
    4166             : }
    4167             : 
    4168             : /* allow pi = 0 */
    4169             : ulong
    4170       67340 : Fl2_norm_pre(GEN x, ulong D, ulong p, ulong pi)
    4171             : {
    4172       67340 :   ulong a = x[1], b = x[2], a2;
    4173       67340 :   if (pi)
    4174             :   {
    4175       67340 :     a2 = Fl_sqr_pre(a,p,pi);
    4176       67340 :     return b? Fl_sub(a2, Fl_mul_pre(D, Fl_sqr_pre(b, p,pi), p,pi), p): a2;
    4177             :   }
    4178           0 :   else if (p & HIGHMASK)
    4179             :   {
    4180           0 :     a2 = Fl_sqr(a,p);
    4181           0 :     return b? Fl_sub(a2, Fl_mul(D, Fl_sqr(b, p), p), p): a2;
    4182             :   }
    4183             :   else
    4184             :   {
    4185           0 :     a2 = (a * a) % p;
    4186           0 :     return b? Fl_sub(a2, (D * ((b * b) % p)) % p, p): a2;
    4187             :   }
    4188             : }
    4189             : 
    4190             : /* allow pi = 0 */
    4191             : GEN
    4192      177208 : Fl2_inv_pre(GEN x, ulong D, ulong p, ulong pi)
    4193             : {
    4194      177208 :   ulong a = x[1], b = x[2], n, ni;
    4195      177208 :   if (b == 0) return mkF2(Fl_inv(a,p), 0);
    4196      151107 :   b = Fl_neg(b, p);
    4197      151107 :   if (pi)
    4198             :   {
    4199      151107 :     n = Fl_sub(Fl_sqr_pre(a, p,pi),
    4200             :                Fl_mul_pre(D, Fl_sqr_pre(b, p,pi), p,pi), p);
    4201      151107 :     ni = Fl_inv(n,p);
    4202      151112 :     return mkF2(Fl_mul_pre(a, ni, p,pi), Fl_mul_pre(b, ni, p,pi));
    4203             :   }
    4204           0 :   else if (p & HIGHMASK)
    4205             :   {
    4206           0 :     n = Fl_sub(Fl_sqr(a, p), Fl_mul(D, Fl_sqr(b, p), p), p);
    4207           0 :     ni = Fl_inv(n,p);
    4208           0 :     return mkF2(Fl_mul(a, ni, p), Fl_mul(b, ni, p));
    4209             :   }
    4210             :   else
    4211             :   {
    4212           0 :     n = Fl_sub((a * a) % p, (D * ((b * b) % p)) % p, p);
    4213           0 :     ni = Fl_inv(n,p);
    4214           0 :     return mkF2((a * ni) % p, (b * ni) % p);
    4215             :   }
    4216             : }
    4217             : 
    4218             : int
    4219      404404 : Fl2_equal1(GEN x) { return x[1]==1 && x[2]==0; }
    4220             : 
    4221             : struct _Fl2 {
    4222             :   ulong p, pi, D;
    4223             : };
    4224             : 
    4225             : static GEN
    4226     4523019 : _Fl2_sqr(void *data, GEN x)
    4227             : {
    4228     4523019 :   struct _Fl2 *D = (struct _Fl2*)data;
    4229     4523019 :   return Fl2_sqr_pre(x, D->D, D->p, D->pi);
    4230             : }
    4231             : static GEN
    4232     1763828 : _Fl2_mul(void *data, GEN x, GEN y)
    4233             : {
    4234     1763828 :   struct _Fl2 *D = (struct _Fl2*)data;
    4235     1763828 :   return Fl2_mul_pre(x,y, D->D, D->p, D->pi);
    4236             : }
    4237             : 
    4238             : /* n-Power of x in Z/pZ[X]/(T), as t_VECSMALL; allow pi = 0 */
    4239             : GEN
    4240      604436 : Fl2_pow_pre(GEN x, GEN n, ulong D, ulong p, ulong pi)
    4241             : {
    4242      604436 :   pari_sp av = avma;
    4243             :   struct _Fl2 d;
    4244             :   GEN y;
    4245      604436 :   long s = signe(n);
    4246      604436 :   if (!s) return mkF2(1,0);
    4247      535611 :   if (s < 0)
    4248      177208 :     x = Fl2_inv_pre(x,D,p,pi);
    4249      535602 :   if (is_pm1(n)) return s < 0 ? x : zv_copy(x);
    4250      394590 :   d.p = p; d.pi = pi; d.D=D;
    4251      394590 :   y = gen_pow_i(x, n, (void*)&d, &_Fl2_sqr, &_Fl2_mul);
    4252      394585 :   return gerepileuptoleaf(av, y);
    4253             : }
    4254             : 
    4255             : static GEN
    4256      604406 : _Fl2_pow(void *data, GEN x, GEN n)
    4257             : {
    4258      604406 :   struct _Fl2 *D = (struct _Fl2*)data;
    4259      604406 :   return Fl2_pow_pre(x, n, D->D, D->p, D->pi);
    4260             : }
    4261             : 
    4262             : static GEN
    4263      102658 : _Fl2_rand(void *data)
    4264             : {
    4265      102658 :   struct _Fl2 *D = (struct _Fl2*)data;
    4266      102658 :   ulong a = random_Fl(D->p), b=random_Fl(D->p-1)+1;
    4267      102659 :   return mkF2(a,b);
    4268             : }
    4269             : 
    4270             : static const struct bb_group Fl2_star={_Fl2_mul, _Fl2_pow, _Fl2_rand,
    4271             :        hash_GEN, zv_equal, Fl2_equal1, NULL};
    4272             : 
    4273             : /* allow pi = 0 */
    4274             : GEN
    4275       68824 : Fl2_sqrtn_pre(GEN a, GEN n, ulong D, ulong p, ulong pi, GEN *zeta)
    4276             : {
    4277             :   struct _Fl2 E;
    4278             :   GEN o;
    4279       68824 :   if (a[1]==0 && a[2]==0)
    4280             :   {
    4281           0 :     if (signe(n) < 0) pari_err_INV("Flxq_sqrtn",a);
    4282           0 :     if (zeta) *zeta=mkF2(1,0);
    4283           0 :     return zv_copy(a);
    4284             :   }
    4285       68824 :   E.p=p; E.pi = pi; E.D = D;
    4286       68824 :   o = subiu(powuu(p,2), 1);
    4287       68825 :   return gen_Shanks_sqrtn(a,n,o,zeta,(void*)&E,&Fl2_star);
    4288             : }
    4289             : 
    4290             : /* allow pi = 0 */
    4291             : GEN
    4292       10402 : Flx_Fl2_eval_pre(GEN x, GEN y, ulong D, ulong p, ulong pi)
    4293             : {
    4294             :   GEN p1;
    4295       10402 :   long i = lg(x)-1;
    4296       10402 :   if (i <= 2)
    4297        2065 :     return mkF2(i == 2? x[2]: 0, 0);
    4298        8337 :   p1 = mkF2(x[i], 0);
    4299       36456 :   for (i--; i>=2; i--)
    4300             :   {
    4301       28119 :     p1 = Fl2_mul_pre(p1, y, D, p, pi);
    4302       28119 :     uel(p1,1) = Fl_add(uel(p1,1), uel(x,i), p);
    4303             :   }
    4304        8337 :   return p1;
    4305             : }
    4306             : 
    4307             : /***********************************************************************/
    4308             : /**                               FlxV                                **/
    4309             : /***********************************************************************/
    4310             : /* FlxV are t_VEC with Flx coefficients. */
    4311             : 
    4312             : GEN
    4313       34482 : FlxV_Flc_mul(GEN V, GEN W, ulong p)
    4314             : {
    4315       34482 :   pari_sp ltop=avma;
    4316             :   long i;
    4317       34482 :   GEN z = Flx_Fl_mul(gel(V,1),W[1],p);
    4318      257068 :   for(i=2;i<lg(V);i++)
    4319      222586 :     z=Flx_add(z,Flx_Fl_mul(gel(V,i),W[i],p),p);
    4320       34482 :   return gerepileuptoleaf(ltop,z);
    4321             : }
    4322             : 
    4323             : GEN
    4324           0 : ZXV_to_FlxV(GEN x, ulong p)
    4325           0 : { pari_APPLY_type(t_VEC, ZX_to_Flx(gel(x,i), p)) }
    4326             : 
    4327             : GEN
    4328     3768422 : ZXT_to_FlxT(GEN x, ulong p)
    4329             : {
    4330     3768422 :   if (typ(x) == t_POL)
    4331     3708428 :     return ZX_to_Flx(x, p);
    4332             :   else
    4333      196795 :     pari_APPLY_type(t_VEC, ZXT_to_FlxT(gel(x,i), p))
    4334             : }
    4335             : 
    4336             : GEN
    4337      169704 : FlxV_to_Flm(GEN x, long n)
    4338      919882 : { pari_APPLY_type(t_MAT, Flx_to_Flv(gel(x,i), n)) }
    4339             : 
    4340             : GEN
    4341           0 : FlxV_red(GEN x, ulong p)
    4342           0 : { pari_APPLY_type(t_VEC, Flx_red(gel(x,i), p)) }
    4343             : 
    4344             : GEN
    4345      309209 : FlxT_red(GEN x, ulong p)
    4346             : {
    4347      309209 :   if (typ(x) == t_VECSMALL)
    4348      208048 :     return Flx_red(x, p);
    4349             :   else
    4350      339427 :     pari_APPLY_type(t_VEC, FlxT_red(gel(x,i), p))
    4351             : }
    4352             : 
    4353             : GEN
    4354      113589 : FlxqV_dotproduct_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
    4355             : {
    4356      113589 :   long i, lx = lg(x);
    4357             :   pari_sp av;
    4358             :   GEN c;
    4359      113589 :   if (lx == 1) return pol0_Flx(get_Flx_var(T));
    4360      113589 :   av = avma; c = Flx_mul_pre(gel(x,1),gel(y,1), p, pi);
    4361      464499 :   for (i=2; i<lx; i++) c = Flx_add(c, Flx_mul_pre(gel(x,i),gel(y,i), p, pi), p);
    4362      113589 :   return gerepileuptoleaf(av, Flx_rem_pre(c,T,p,pi));
    4363             : }
    4364             : GEN
    4365           0 : FlxqV_dotproduct(GEN x, GEN y, GEN T, ulong p)
    4366           0 : { return FlxqV_dotproduct_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
    4367             : 
    4368             : GEN
    4369        2108 : FlxqX_dotproduct(GEN x, GEN y, GEN T, ulong p)
    4370             : {
    4371        2108 :   long i, l = minss(lg(x), lg(y));
    4372             :   ulong pi;
    4373             :   pari_sp av;
    4374             :   GEN c;
    4375        2108 :   if (l == 2) return pol0_Flx(get_Flx_var(T));
    4376        2108 :   av = avma; pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    4377        2108 :   c = Flx_mul_pre(gel(x,2),gel(y,2), p, pi);
    4378        6780 :   for (i=3; i<l; i++) c = Flx_add(c, Flx_mul_pre(gel(x,i),gel(y,i), p, pi), p);
    4379        2108 :   return gerepileuptoleaf(av, Flx_rem_pre(c,T,p,pi));
    4380             : }
    4381             : 
    4382             : /* allow pi = 0 */
    4383             : GEN
    4384      250755 : FlxC_eval_powers_pre(GEN z, GEN x, ulong p, ulong pi)
    4385             : {
    4386      250755 :   long i, l = lg(z);
    4387      250755 :   GEN y = cgetg(l, t_VECSMALL);
    4388    12724217 :   for (i=1; i<l; i++) uel(y,i) = Flx_eval_powers_pre(gel(z,i), x, p, pi);
    4389      251009 :   return y;
    4390             : }
    4391             : 
    4392             : /***********************************************************************/
    4393             : /**                               FlxM                                **/
    4394             : /***********************************************************************/
    4395             : /* allow pi = 0 */
    4396             : GEN
    4397       19404 : FlxM_eval_powers_pre(GEN z, GEN x, ulong p, ulong pi)
    4398             : {
    4399       19404 :   long i, l = lg(z);
    4400       19404 :   GEN y = cgetg(l, t_MAT);
    4401      270162 :   for (i=1; i<l; i++) gel(y,i) = FlxC_eval_powers_pre(gel(z,i), x, p, pi);
    4402       19404 :   return y;
    4403             : }
    4404             : 
    4405             : GEN
    4406           0 : zero_FlxC(long n, long sv)
    4407             : {
    4408           0 :   GEN x = cgetg(n + 1, t_COL), z = zero_Flx(sv);
    4409             :   long i;
    4410           0 :   for (i = 1; i <= n; i++) gel(x, i) = z;
    4411           0 :   return x;
    4412             : }
    4413             : 
    4414             : GEN
    4415           0 : FlxC_neg(GEN x, ulong p)
    4416           0 : { pari_APPLY_type(t_COL, Flx_neg(gel(x, i), p)) }
    4417             : 
    4418             : GEN
    4419           0 : FlxC_sub(GEN x, GEN y, ulong p)
    4420           0 : { pari_APPLY_type(t_COL, Flx_sub(gel(x, i), gel(y, i), p)) }
    4421             : 
    4422             : GEN
    4423           0 : zero_FlxM(long r, long c, long sv)
    4424             : {
    4425           0 :   GEN x = cgetg(c + 1, t_MAT), z = zero_FlxC(r, sv);
    4426             :   long j;
    4427           0 :   for (j = 1; j <= c; j++) gel(x, j) = z;
    4428           0 :   return x;
    4429             : }
    4430             : 
    4431             : GEN
    4432           0 : FlxM_neg(GEN x, ulong p)
    4433           0 : { pari_APPLY_same(FlxC_neg(gel(x, i), p)) }
    4434             : 
    4435             : GEN
    4436           0 : FlxM_sub(GEN x, GEN y, ulong p)
    4437           0 : { pari_APPLY_same(FlxC_sub(gel(x, i), gel(y,i), p)) }
    4438             : 
    4439             : GEN
    4440           0 : FlxqC_Flxq_mul(GEN x, GEN y, GEN T, ulong p)
    4441           0 : { pari_APPLY_type(t_COL, Flxq_mul(gel(x, i), y, T, p)) }
    4442             : 
    4443             : GEN
    4444           0 : FlxqM_Flxq_mul(GEN x, GEN y, GEN T, ulong p)
    4445           0 : { pari_APPLY_same(FlxqC_Flxq_mul(gel(x, i), y, T, p)) }
    4446             : 
    4447             : static GEN
    4448       54700 : FlxM_pack_ZM(GEN M, GEN (*pack)(GEN, long)) {
    4449             :   long i, j, l, lc;
    4450       54700 :   GEN N = cgetg_copy(M, &l), x;
    4451       54700 :   if (l == 1)
    4452           0 :     return N;
    4453       54700 :   lc = lgcols(M);
    4454      269372 :   for (j = 1; j < l; j++) {
    4455      214672 :     gel(N, j) = cgetg(lc, t_COL);
    4456     1107480 :     for (i = 1; i < lc; i++) {
    4457      892808 :       x = gcoeff(M, i, j);
    4458      892808 :       gcoeff(N, i, j) = pack(x + 2, lgpol(x));
    4459             :     }
    4460             :   }
    4461       54700 :   return N;
    4462             : }
    4463             : 
    4464             : static GEN
    4465      839129 : kron_pack_Flx_spec_half(GEN x, long l) {
    4466      839129 :   if (l == 0) return gen_0;
    4467      480287 :   return Flx_to_int_halfspec(x, l);
    4468             : }
    4469             : 
    4470             : static GEN
    4471       50290 : kron_pack_Flx_spec(GEN x, long l) {
    4472             :   long i;
    4473             :   GEN w, y;
    4474       50290 :   if (l == 0)
    4475        9482 :     return gen_0;
    4476       40808 :   y = cgetipos(l + 2);
    4477      150922 :   for (i = 0, w = int_LSW(y); i < l; i++, w = int_nextW(w))
    4478      110114 :     *w = x[i];
    4479       40808 :   return y;
    4480             : }
    4481             : 
    4482             : static GEN
    4483        3389 : kron_pack_Flx_spec_2(GEN x, long l) { return Flx_eval2BILspec(x, 2, l); }
    4484             : 
    4485             : static GEN
    4486           0 : kron_pack_Flx_spec_3(GEN x, long l) { return Flx_eval2BILspec(x, 3, l); }
    4487             : 
    4488             : static GEN
    4489       42080 : kron_unpack_Flx(GEN z, ulong p)
    4490             : {
    4491       42080 :   long i, l = lgefint(z);
    4492       42080 :   GEN x = cgetg(l, t_VECSMALL), w;
    4493      198461 :   for (w = int_LSW(z), i = 2; i < l; w = int_nextW(w), i++)
    4494      156381 :     x[i] = ((ulong) *w) % p;
    4495       42080 :   return Flx_renormalize(x, l);
    4496             : }
    4497             : 
    4498             : static GEN
    4499        2930 : kron_unpack_Flx_2(GEN x, ulong p) {
    4500        2930 :   long d = (lgefint(x)-1)/2 - 1;
    4501        2930 :   return Z_mod2BIL_Flx_2(x, d, p);
    4502             : }
    4503             : 
    4504             : static GEN
    4505           0 : kron_unpack_Flx_3(GEN x, ulong p) {
    4506           0 :   long d = lgefint(x)/3 - 1;
    4507           0 :   return Z_mod2BIL_Flx_3(x, d, p);
    4508             : }
    4509             : 
    4510             : static GEN
    4511      118539 : FlxM_pack_ZM_bits(GEN M, long b)
    4512             : {
    4513             :   long i, j, l, lc;
    4514      118539 :   GEN N = cgetg_copy(M, &l), x;
    4515      118539 :   if (l == 1)
    4516           0 :     return N;
    4517      118539 :   lc = lgcols(M);
    4518      492013 :   for (j = 1; j < l; j++) {
    4519      373474 :     gel(N, j) = cgetg(lc, t_COL);
    4520     5974153 :     for (i = 1; i < lc; i++) {
    4521     5600679 :       x = gcoeff(M, i, j);
    4522     5600679 :       gcoeff(N, i, j) = kron_pack_Flx_spec_bits(x + 2, b, lgpol(x));
    4523             :     }
    4524             :   }
    4525      118539 :   return N;
    4526             : }
    4527             : 
    4528             : static GEN
    4529       27350 : ZM_unpack_FlxqM(GEN M, GEN T, ulong p, ulong pi, GEN (*unpack)(GEN, ulong))
    4530             : {
    4531       27350 :   long i, j, l, lc, sv = get_Flx_var(T);
    4532       27350 :   GEN N = cgetg_copy(M, &l), x;
    4533       27350 :   if (l == 1)
    4534           0 :     return N;
    4535       27350 :   lc = lgcols(M);
    4536      161343 :   for (j = 1; j < l; j++) {
    4537      133993 :     gel(N, j) = cgetg(lc, t_COL);
    4538      762713 :     for (i = 1; i < lc; i++) {
    4539      628720 :       x = unpack(gcoeff(M, i, j), p);
    4540      628720 :       x[1] = sv;
    4541      628720 :       gcoeff(N, i, j) = Flx_rem_pre(x, T, p, pi);
    4542             :     }
    4543             :   }
    4544       27350 :   return N;
    4545             : }
    4546             : 
    4547             : static GEN
    4548       59310 : ZM_unpack_FlxqM_bits(GEN M, long b, GEN T, ulong p, ulong pi)
    4549             : {
    4550       59310 :   long i, j, l, lc, sv = get_Flx_var(T);
    4551       59310 :   GEN N = cgetg_copy(M, &l), x;
    4552       59310 :   if (l == 1)
    4553           0 :     return N;
    4554       59310 :   lc = lgcols(M);
    4555       59310 :   if (b < BITS_IN_LONG) {
    4556      202047 :     for (j = 1; j < l; j++) {
    4557      144420 :       gel(N, j) = cgetg(lc, t_COL);
    4558     3254377 :       for (i = 1; i < lc; i++) {
    4559     3109957 :         x = kron_unpack_Flx_bits_narrow(gcoeff(M, i, j), b, p);
    4560     3109957 :         x[1] = sv;
    4561     3109957 :         gcoeff(N, i, j) = Flx_rem_pre(x, T, p, pi);
    4562             :       }
    4563             :     }
    4564             :   } else {
    4565        1683 :     ulong pi = get_Fl_red(p);
    4566        9844 :     for (j = 1; j < l; j++) {
    4567        8161 :       gel(N, j) = cgetg(lc, t_COL);
    4568      175361 :       for (i = 1; i < lc; i++) {
    4569      167200 :         x = kron_unpack_Flx_bits_wide(gcoeff(M, i, j), b, p, pi);
    4570      167200 :         x[1] = sv;
    4571      167200 :         gcoeff(N, i, j) = Flx_rem_pre(x, T, p, pi);
    4572             :       }
    4573             :     }
    4574             :   }
    4575       59310 :   return N;
    4576             : }
    4577             : 
    4578             : GEN
    4579       86660 : FlxqM_mul_Kronecker(GEN A, GEN B, GEN T, ulong p)
    4580             : {
    4581       86660 :   pari_sp av = avma;
    4582       86660 :   long b, d = get_Flx_degree(T), n = lg(A) - 1;
    4583             :   GEN C, D, z;
    4584             :   GEN (*pack)(GEN, long), (*unpack)(GEN, ulong);
    4585       86660 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    4586       86660 :   int is_sqr = A==B;
    4587             : 
    4588       86660 :   z = muliu(muliu(sqru(p - 1), d), n);
    4589       86660 :   b = expi(z) + 1;
    4590             :   /* only do expensive bit-packing if it saves at least 1 limb */
    4591       86660 :   if (b <= BITS_IN_HALFULONG)
    4592       82485 :   { if (nbits2nlong(d*b) == (d + 1)/2) b = BITS_IN_HALFULONG; }
    4593             :   else
    4594             :   {
    4595        4175 :     long l = lgefint(z) - 2;
    4596        4175 :     if (nbits2nlong(d*b) == d*l) b = l*BITS_IN_LONG;
    4597             :   }
    4598       86660 :   set_avma(av);
    4599             : 
    4600       86660 :   switch (b) {
    4601       26581 :   case BITS_IN_HALFULONG:
    4602       26581 :     pack = kron_pack_Flx_spec_half;
    4603       26581 :     unpack = int_to_Flx_half;
    4604       26581 :     break;
    4605         720 :   case BITS_IN_LONG:
    4606         720 :     pack = kron_pack_Flx_spec;
    4607         720 :     unpack = kron_unpack_Flx;
    4608         720 :     break;
    4609          49 :   case 2*BITS_IN_LONG:
    4610          49 :     pack = kron_pack_Flx_spec_2;
    4611          49 :     unpack = kron_unpack_Flx_2;
    4612          49 :     break;
    4613           0 :   case 3*BITS_IN_LONG:
    4614           0 :     pack = kron_pack_Flx_spec_3;
    4615           0 :     unpack = kron_unpack_Flx_3;
    4616           0 :     break;
    4617       59310 :   default:
    4618       59310 :     A = FlxM_pack_ZM_bits(A, b);
    4619       59310 :     B = is_sqr? A: FlxM_pack_ZM_bits(B, b);
    4620       59310 :     C = ZM_mul(A, B);
    4621       59310 :     D = ZM_unpack_FlxqM_bits(C, b, T, p, pi);
    4622       59310 :     return gerepilecopy(av, D);
    4623             :   }
    4624       27350 :   A = FlxM_pack_ZM(A, pack);
    4625       27350 :   B = is_sqr? A: FlxM_pack_ZM(B, pack);
    4626       27350 :   C = ZM_mul(A, B);
    4627       27350 :   D = ZM_unpack_FlxqM(C, T, p, pi, unpack);
    4628       27350 :   return gerepilecopy(av, D);
    4629             : }

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