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 - headers - pariinl.h (source / functions) Hit Total Coverage
Test: PARI/GP v2.14.0 lcov report (development 27775-aca467eab2) Lines: 1445 1589 90.9 %
Date: 2022-07-03 07:33:15 Functions: 640 710 90.1 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2000-2010  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             : /*********************************************************************/
      16             : /*                       MALLOC/FREE WRAPPERS                        */
      17             : /*********************************************************************/
      18             : #define BLOCK_SIGALRM_START          \
      19             : {                                    \
      20             :   int block=PARI_SIGINT_block;       \
      21             :   PARI_SIGINT_block = 2;             \
      22             :   MT_SIGINT_BLOCK(block);
      23             : 
      24             : #define BLOCK_SIGINT_START           \
      25             : {                                    \
      26             :   int block=PARI_SIGINT_block;       \
      27             :   PARI_SIGINT_block = 1;             \
      28             :   MT_SIGINT_BLOCK(block);
      29             : 
      30             : #define BLOCK_SIGINT_END             \
      31             :   PARI_SIGINT_block = block;         \
      32             :   MT_SIGINT_UNBLOCK(block);          \
      33             :   if (!block && PARI_SIGINT_pending) \
      34             :   {                                  \
      35             :     int sig = PARI_SIGINT_pending;   \
      36             :     PARI_SIGINT_pending = 0;         \
      37             :     raise(sig);                      \
      38             :   }                                  \
      39             : }
      40             : 
      41             : /*******************************************************************/
      42             : /*                                                                 */
      43             : /*                          CONSTRUCTORS                           */
      44             : /*                                                                 */
      45             : /*******************************************************************/
      46             : #define retmkfrac(x,y)\
      47             :   do { GEN _v = cgetg(3, t_FRAC);\
      48             :        gel(_v,1) = (x);\
      49             :        gel(_v,2) = (y); return _v; } while(0)
      50             : #define retmkrfrac(x,y)\
      51             :   do { GEN _v = cgetg(3, t_RFRAC);\
      52             :        gel(_v,1) = (x);\
      53             :        gel(_v,2) = (y); return _v; } while(0)
      54             : #define retmkintmod(x,y)\
      55             :   do { GEN _v = cgetg(3, t_INTMOD);\
      56             :        gel(_v,1) = (y);\
      57             :        gel(_v,2) = (x); return _v; } while(0)
      58             : #define retmkcomplex(x,y)\
      59             :   do { GEN _v = cgetg(3, t_COMPLEX);\
      60             :        gel(_v,1) = (x);\
      61             :        gel(_v,2) = (y); return _v; } while(0)
      62             : #define retmkpolmod(x,y)\
      63             :   do { GEN _v = cgetg(3, t_POLMOD);\
      64             :        gel(_v,1) = (y);\
      65             :        gel(_v,2) = (x); return _v; } while(0)
      66             : #define retmkvec(x)\
      67             :   do { GEN _v = cgetg(2, t_VEC);\
      68             :        gel(_v,1) = (x); return _v; } while(0)
      69             : #define retmkvec2(x,y)\
      70             :   do { GEN _v = cgetg(3, t_VEC);\
      71             :        gel(_v,1) = (x);\
      72             :        gel(_v,2) = (y); return _v; } while(0)
      73             : #define retmkvec3(x,y,z)\
      74             :   do { GEN _v = cgetg(4, t_VEC);\
      75             :        gel(_v,1) = (x);\
      76             :        gel(_v,2) = (y);\
      77             :        gel(_v,3) = (z); return _v; } while(0)
      78             : #define retmkqfb(x,y,z,d)\
      79             :   do { GEN _v = cgetg(5, t_QFB);\
      80             :        gel(_v,1) = (x);\
      81             :        gel(_v,2) = (y);\
      82             :        gel(_v,3) = (z);\
      83             :        gel(_v,4) = (d); return _v; } while(0)
      84             : #define retmkquad(x,y,z)\
      85             :   do { GEN _v = cgetg(4, t_QUAD);\
      86             :        gel(_v,1) = (x);\
      87             :        gel(_v,2) = (y);\
      88             :        gel(_v,3) = (z); return _v; } while(0)
      89             : #define retmkvec4(x,y,z,t)\
      90             :   do { GEN _v = cgetg(5, t_VEC);\
      91             :        gel(_v,1) = (x);\
      92             :        gel(_v,2) = (y);\
      93             :        gel(_v,3) = (z);\
      94             :        gel(_v,4) = (t); return _v; } while(0)
      95             : #define retmkvec5(x,y,z,t,u)\
      96             :   do { GEN _v = cgetg(6, t_VEC);\
      97             :        gel(_v,1) = (x);\
      98             :        gel(_v,2) = (y);\
      99             :        gel(_v,3) = (z);\
     100             :        gel(_v,4) = (t);\
     101             :        gel(_v,5) = (u); return _v; } while(0)
     102             : #define retmkcol(x)\
     103             :   do { GEN _v = cgetg(2, t_COL);\
     104             :        gel(_v,1) = (x); return _v; } while(0)
     105             : #define retmkcol2(x,y)\
     106             :   do { GEN _v = cgetg(3, t_COL);\
     107             :        gel(_v,1) = (x);\
     108             :        gel(_v,2) = (y); return _v; } while(0)
     109             : #define retmkcol3(x,y,z)\
     110             :   do { GEN _v = cgetg(4, t_COL);\
     111             :        gel(_v,1) = (x);\
     112             :        gel(_v,2) = (y);\
     113             :        gel(_v,3) = (z); return _v; } while(0)
     114             : #define retmkcol4(x,y,z,t)\
     115             :   do { GEN _v = cgetg(5, t_COL);\
     116             :        gel(_v,1) = (x);\
     117             :        gel(_v,2) = (y);\
     118             :        gel(_v,3) = (z);\
     119             :        gel(_v,4) = (t); return _v; } while(0)
     120             : #define retmkcol5(x,y,z,t,u)\
     121             :   do { GEN _v = cgetg(6, t_COL);\
     122             :        gel(_v,1) = (x);\
     123             :        gel(_v,2) = (y);\
     124             :        gel(_v,3) = (z);\
     125             :        gel(_v,4) = (t);\
     126             :        gel(_v,5) = (u); return _v; } while(0)
     127             : #define retmkcol6(x,y,z,t,u,v)\
     128             :   do { GEN _v = cgetg(7, t_COL);\
     129             :        gel(_v,1) = (x);\
     130             :        gel(_v,2) = (y);\
     131             :        gel(_v,3) = (z);\
     132             :        gel(_v,4) = (t);\
     133             :        gel(_v,5) = (u);\
     134             :        gel(_v,6) = (v); return _v; } while(0)
     135             : #define retmkmat(x)\
     136             :   do { GEN _v = cgetg(2, t_MAT);\
     137             :        gel(_v,1) = (x); return _v; } while(0)
     138             : #define retmkmat2(x,y)\
     139             :   do { GEN _v = cgetg(3, t_MAT);\
     140             :        gel(_v,1) = (x);\
     141             :        gel(_v,2) = (y); return _v; } while(0)
     142             : #define retmkmat3(x,y,z)\
     143             :   do { GEN _v = cgetg(4, t_MAT);\
     144             :        gel(_v,1) = (x);\
     145             :        gel(_v,2) = (y);\
     146             :        gel(_v,3) = (z); return _v; } while(0)
     147             : #define retmkmat4(x,y,z,t)\
     148             :   do { GEN _v = cgetg(5, t_MAT);\
     149             :        gel(_v,1) = (x);\
     150             :        gel(_v,2) = (y);\
     151             :        gel(_v,3) = (z);\
     152             :        gel(_v,4) = (t); return _v; } while(0)
     153             : #define retmkmat5(x,y,z,t,u)\
     154             :   do { GEN _v = cgetg(6, t_MAT);\
     155             :        gel(_v,1) = (x);\
     156             :        gel(_v,2) = (y);\
     157             :        gel(_v,3) = (z);\
     158             :        gel(_v,4) = (t);\
     159             :        gel(_v,5) = (u); return _v; } while(0)
     160             : 
     161             : INLINE GEN
     162     6554370 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
     163             : INLINE GEN
     164        1813 : mkintmodu(ulong x, ulong y) {
     165        1813 :   GEN v = cgetg(3,t_INTMOD);
     166        1813 :   gel(v,1) = utoipos(y);
     167        1813 :   gel(v,2) = utoi(x); return v;
     168             : }
     169             : INLINE GEN
     170     2581123 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
     171             : INLINE GEN
     172    29408177 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
     173             : INLINE GEN
     174     1205620 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
     175             : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
     176             : INLINE void
     177       18501 : Qtoss(GEN q, long *n, long *d)
     178             : {
     179       18501 :   if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
     180        5691 :   else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
     181       18501 : }
     182             : INLINE GEN
     183      769223 : sstoQ(long n, long d)
     184             : {
     185             :   ulong r;
     186             :   long g, q;
     187      769223 :   if (!n)
     188             :   {
     189       92267 :     if (!d) pari_err_INV("sstoQ",gen_0);
     190       92267 :     return gen_0;
     191             :   }
     192      676956 :   if (d < 0) { d = -d; n = -n; }
     193      676956 :   if (d == 1) return stoi(n);
     194      664034 :   r = labs(n);
     195      664034 :   if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
     196      629972 :   q = udivuu_rem(r, d, &r);
     197      629972 :   if (!r) return n > 0? utoipos(q): utoineg(q);
     198      575379 :   g = ugcd(d,r); /* gcd(n,d) */
     199      575379 :   if (g != 1) { n /= g; d /= g; }
     200      575379 :   retmkfrac(stoi(n), utoipos(d));
     201             : }
     202             : 
     203             : INLINE GEN
     204   157848191 : uutoQ(ulong n, ulong d)
     205             : {
     206             :   ulong r;
     207             :   long g, q;
     208   157848191 :   if (!n)
     209             :   {
     210        9438 :     if (!d) pari_err_INV("uutoQ",gen_0);
     211        9438 :     return gen_0;
     212             :   }
     213   157838753 :   if (d == 1) return utoipos(n);
     214   157827658 :   if (n == 1) retmkfrac(gen_1, utoipos(d));
     215   157740417 :   q = udivuu_rem(n,d,&r);
     216   157740417 :   if (!r) return utoipos(q);
     217     5114797 :   g = ugcd(d,r); /* gcd(n,d) */
     218     5114797 :   if (g != 1) { n /= g; d /= g; }
     219     5114797 :   retmkfrac(utoipos(n), utoipos(d));
     220             : }
     221             : 
     222             : INLINE GEN
     223     3720507 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
     224             : INLINE GEN
     225       10310 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
     226       10310 :   gel(v,1) = x; gel(v,2) = y; return v; }
     227             : INLINE GEN
     228           7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
     229           7 :   gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
     230             : INLINE GEN
     231    73473575 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
     232             : INLINE GEN
     233      825642 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
     234             : INLINE GEN
     235      778681 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
     236             : INLINE GEN
     237       69132 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
     238       69132 :   gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
     239             : /* vecsmall */
     240             : INLINE GEN
     241   117430881 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
     242             : INLINE GEN
     243   194457641 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
     244   194432975 :   v[1]=x; v[2]=y; return v; }
     245             : INLINE GEN
     246    93727214 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
     247    93713005 :   v[1]=x; v[2]=y; v[3]=z; return v; }
     248             : INLINE GEN
     249    13985055 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
     250    13973325 :   v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
     251             : INLINE GEN
     252      575298 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
     253      575296 :   v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
     254             : 
     255             : INLINE GEN
     256    16870238 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
     257             : /* vec */
     258             : INLINE GEN
     259    60123007 : mkvec(GEN x) { retmkvec(x); }
     260             : INLINE GEN
     261   147555248 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
     262             : INLINE GEN
     263    97334931 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
     264             : INLINE GEN
     265     5912497 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
     266             : INLINE GEN
     267    14569324 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
     268             : INLINE GEN
     269         126 : mkvecs(long x) { retmkvec(stoi(x)); }
     270             : INLINE GEN
     271      211201 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
     272             : INLINE GEN
     273      488650 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
     274             : INLINE GEN
     275          21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
     276             : INLINE GEN
     277       35854 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
     278             : INLINE GEN
     279      125021 : mkvec2copy(GEN x, GEN y) {
     280      125021 :   GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
     281             : /* col */
     282             : INLINE GEN
     283     5431249 : mkcol(GEN x) { retmkcol(x); }
     284             : INLINE GEN
     285    53779599 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
     286             : INLINE GEN
     287       85543 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
     288             : INLINE GEN
     289           0 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
     290             : INLINE GEN
     291         101 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
     292             : INLINE GEN
     293       11993 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
     294             : INLINE GEN
     295       36589 : mkcols(long x) { retmkcol(stoi(x)); }
     296             : INLINE GEN
     297     2761682 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
     298             : INLINE GEN
     299         294 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
     300             : INLINE GEN
     301           0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
     302             : INLINE GEN
     303       29038 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
     304             : /* mat */
     305             : INLINE GEN
     306     3764219 : mkmat(GEN x) { retmkmat(x); }
     307             : INLINE GEN
     308    36562210 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
     309             : INLINE GEN
     310       16485 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
     311             : INLINE GEN
     312           0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
     313             : INLINE GEN
     314           0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
     315             : INLINE GEN
     316      118046 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
     317             : INLINE GEN
     318           0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
     319             : INLINE GEN
     320      199451 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
     321             : INLINE GEN
     322      102741 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
     323             : INLINE long
     324      314336 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
     325             : INLINE GEN
     326       12495 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
     327             : INLINE GEN
     328     4467262 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
     329             : 
     330             : /* pol */
     331             : INLINE GEN
     332     2436268 : pol_x(long v) {
     333     2436268 :   GEN p = cgetg(4, t_POL);
     334     2436298 :   p[1] = evalsigne(1)|evalvarn(v);
     335     2436298 :   gel(p,2) = gen_0;
     336     2436298 :   gel(p,3) = gen_1; return p;
     337             : }
     338             : /* x^n, assume n >= 0 */
     339             : INLINE GEN
     340     2155396 : pol_xn(long n, long v) {
     341     2155396 :   long i, a = n+2;
     342     2155396 :   GEN p = cgetg(a+1, t_POL);
     343     2155397 :   p[1] = evalsigne(1)|evalvarn(v);
     344     5079455 :   for (i = 2; i < a; i++) gel(p,i) = gen_0;
     345     2155397 :   gel(p,a) = gen_1; return p;
     346             : }
     347             : /* x^n, no assumption on n */
     348             : INLINE GEN
     349         287 : pol_xnall(long n, long v)
     350             : {
     351         287 :   if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
     352         280 :   return pol_xn(n, v);
     353             : }
     354             : /* x^n, assume n >= 0 */
     355             : INLINE GEN
     356         210 : polxn_Flx(long n, long sv) {
     357         210 :   long i, a = n+2;
     358         210 :   GEN p = cgetg(a+1, t_VECSMALL);
     359         210 :   p[1] = sv;
     360        1022 :   for (i = 2; i < a; i++) p[i] = 0;
     361         210 :   p[a] = 1; return p;
     362             : }
     363             : INLINE GEN
     364     3200601 : pol_1(long v) {
     365     3200601 :   GEN p = cgetg(3, t_POL);
     366     3200593 :   p[1] = evalsigne(1)|evalvarn(v);
     367     3200593 :   gel(p,2) = gen_1; return p;
     368             : }
     369             : INLINE GEN
     370    33500467 : pol_0(long v)
     371             : {
     372    33500467 :   GEN x = cgetg(2,t_POL);
     373    33500458 :   x[1] = evalvarn(v); return x;
     374             : }
     375             : #define retconst_vec(n,x)\
     376             :   do { long _i, _n = (n);\
     377             :        GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
     378             :        for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
     379             :        return _v; } while(0)
     380             : INLINE GEN
     381   201138896 : const_vec(long n, GEN x) { retconst_vec(n, x); }
     382             : #define retconst_col(n,x)\
     383             :   do { long _i, _n = (n);\
     384             :        GEN _v = cgetg(_n+1, t_COL), _x = (x);\
     385             :        for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
     386             :        return _v; } while(0)
     387             : INLINE GEN
     388    37137862 : const_col(long n, GEN x) { retconst_col(n, x); }
     389             : INLINE GEN
     390    16730756 : const_vecsmall(long n, long c)
     391             : {
     392             :   long i;
     393    16730756 :   GEN V = cgetg(n+1,t_VECSMALL);
     394   593416372 :   for(i=1;i<=n;i++) V[i] = c;
     395    16730760 :   return V;
     396             : }
     397             : 
     398             : /***   ZERO   ***/
     399             : /* O(p^e) */
     400             : INLINE GEN
     401      850658 : zeropadic(GEN p, long e)
     402             : {
     403      850658 :   GEN y = cgetg(5,t_PADIC);
     404      850634 :   gel(y,4) = gen_0;
     405      850634 :   gel(y,3) = gen_1;
     406      850634 :   gel(y,2) = icopy(p);
     407      850577 :   y[1] = evalvalp(e) | _evalprecp(0);
     408      850569 :   return y;
     409             : }
     410             : INLINE GEN
     411       10220 : zeropadic_shallow(GEN p, long e)
     412             : {
     413       10220 :   GEN y = cgetg(5,t_PADIC);
     414       10220 :   gel(y,4) = gen_0;
     415       10220 :   gel(y,3) = gen_1;
     416       10220 :   gel(y,2) = p;
     417       10220 :   y[1] = evalvalp(e) | _evalprecp(0);
     418       10220 :   return y;
     419             : }
     420             : /* O(pol_x(v)^e) */
     421             : INLINE GEN
     422      135618 : zeroser(long v, long e)
     423             : {
     424      135618 :   GEN x = cgetg(2, t_SER);
     425      135618 :   x[1] = evalvalp(e) | evalvarn(v); return x;
     426             : }
     427             : INLINE int
     428     9766057 : ser_isexactzero(GEN x)
     429             : {
     430     9766057 :   if (!signe(x)) switch(lg(x))
     431             :   {
     432      130802 :     case 2: return 1;
     433        3640 :     case 3: return isexactzero(gel(x,2));
     434             :   }
     435     9631615 :   return 0;
     436             : }
     437             : /* 0 * pol_x(v) */
     438             : INLINE GEN
     439    14649135 : zeropol(long v) { return pol_0(v); }
     440             : /* vector(n) */
     441             : INLINE GEN
     442    67398940 : zerocol(long n)
     443             : {
     444    67398940 :   GEN y = cgetg(n+1,t_COL);
     445   521382702 :   long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
     446    67399217 :   return y;
     447             : }
     448             : /* vectorv(n) */
     449             : INLINE GEN
     450    25522394 : zerovec(long n)
     451             : {
     452    25522394 :   GEN y = cgetg(n+1,t_VEC);
     453   332078546 :   long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
     454    25522383 :   return y;
     455             : }
     456             : /* matrix(m, n) */
     457             : INLINE GEN
     458       91579 : zeromat(long m, long n)
     459             : {
     460       91579 :   GEN y = cgetg(n+1,t_MAT);
     461       91579 :   GEN v = zerocol(m);
     462      297272 :   long i; for (i=1; i<=n; i++) gel(y,i) = v;
     463       91580 :   return y;
     464             : }
     465             : /* = zero_zx, sv is a evalvarn()*/
     466             : INLINE GEN
     467     1147600 : zero_Flx(long sv) { return pol0_Flx(sv); }
     468             : INLINE GEN
     469    51913091 : zero_Flv(long n)
     470             : {
     471    51913091 :   GEN y = cgetg(n+1,t_VECSMALL);
     472  1029353449 :   long i; for (i=1; i<=n; i++) y[i] = 0;
     473    51913007 :   return y;
     474             : }
     475             : /* matrix(m, n) */
     476             : INLINE GEN
     477     2424425 : zero_Flm(long m, long n)
     478             : {
     479     2424425 :   GEN y = cgetg(n+1,t_MAT);
     480     2424394 :   GEN v = zero_Flv(m);
     481    15448619 :   long i; for (i=1; i<=n; i++) gel(y,i) = v;
     482     2424413 :   return y;
     483             : }
     484             : /* matrix(m, n) */
     485             : INLINE GEN
     486      221878 : zero_Flm_copy(long m, long n)
     487             : {
     488      221878 :   GEN y = cgetg(n+1,t_MAT);
     489     2263005 :   long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
     490      221873 :   return y;
     491             : }
     492             : 
     493             : INLINE GEN
     494     2933737 : zero_F2v(long m)
     495             : {
     496     2933737 :   long l = nbits2nlong(m);
     497     2933725 :   GEN v  = zero_Flv(l+1);
     498     2933718 :   v[1] = m;
     499     2933718 :   return v;
     500             : }
     501             : 
     502             : INLINE GEN
     503           0 : zero_F2m(long m, long n)
     504             : {
     505             :   long i;
     506           0 :   GEN M = cgetg(n+1, t_MAT);
     507           0 :   GEN v = zero_F2v(m);
     508           0 :   for (i = 1; i <= n; i++)
     509           0 :     gel(M,i) = v;
     510           0 :   return M;
     511             : }
     512             : 
     513             : 
     514             : INLINE GEN
     515      842979 : zero_F2m_copy(long m, long n)
     516             : {
     517             :   long i;
     518      842979 :   GEN M = cgetg(n+1, t_MAT);
     519     2007652 :   for (i = 1; i <= n; i++)
     520     1164673 :     gel(M,i)= zero_F2v(m);
     521      842979 :   return M;
     522             : }
     523             : 
     524             : /* matrix(m, n) */
     525             : INLINE GEN
     526     4949019 : zeromatcopy(long m, long n)
     527             : {
     528     4949019 :   GEN y = cgetg(n+1,t_MAT);
     529    25117484 :   long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
     530     4949056 :   return y;
     531             : }
     532             : 
     533             : INLINE GEN
     534       18235 : zerovec_block(long len)
     535             : {
     536             :   long i;
     537       18235 :   GEN blk = cgetg_block(len + 1, t_VEC);
     538      601755 :   for (i = 1; i <= len; ++i)
     539      583520 :     gel(blk, i) = gen_0;
     540       18235 :   return blk;
     541             : }
     542             : 
     543             : /* i-th vector in the standard basis */
     544             : INLINE GEN
     545     4528582 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
     546             : INLINE GEN
     547     1690643 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
     548             : INLINE GEN
     549          42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
     550             : INLINE GEN
     551       66446 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
     552             : INLINE GEN
     553     1141531 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
     554             : 
     555             : INLINE GEN
     556    18156638 : shallowcopy(GEN x)
     557    18156638 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
     558             : 
     559             : /* routines for naive growarrays */
     560             : INLINE GEN
     561    11149386 : vectrunc_init(long l)
     562             : {
     563    11149386 :   GEN z = new_chunk(l);
     564    11149250 :   z[0] = evaltyp(t_VEC) | _evallg(1); return z;
     565             : }
     566             : INLINE GEN
     567      348894 : coltrunc_init(long l)
     568             : {
     569      348894 :   GEN z = new_chunk(l);
     570      348894 :   z[0] = evaltyp(t_COL) | _evallg(1); return z;
     571             : }
     572             : INLINE void
     573   268045727 : lg_increase(GEN x) { x[0]++; }
     574             : INLINE void
     575    13863566 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
     576             : INLINE void
     577       10864 : vectrunc_append_batch(GEN x, GEN y)
     578             : {
     579       10864 :   long i, l = lg(x), ly = lg(y);
     580       10864 :   GEN z = x + l-1;
     581       36358 :   for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
     582       10864 :   setlg(x, l+ly-1);
     583       10864 : }
     584             : INLINE GEN
     585   106077956 : vecsmalltrunc_init(long l)
     586             : {
     587   106077956 :   GEN z = new_chunk(l);
     588   105978107 :   z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
     589             : }
     590             : INLINE void
     591    36435461 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
     592             : 
     593             : /*******************************************************************/
     594             : /*                                                                 */
     595             : /*                    STRING HASH FUNCTIONS                        */
     596             : /*                                                                 */
     597             : /*******************************************************************/
     598             : INLINE ulong
     599     2522630 : hash_str(const char *str)
     600             : {
     601     2522630 :   ulong hash = 5381UL, c;
     602    26032671 :   while ( (c = (ulong)*str++) )
     603    23510041 :     hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
     604     2522630 :   return hash;
     605             : }
     606             : INLINE ulong
     607    60459616 : hash_str_len(const char *str, long len)
     608             : {
     609    60459616 :   ulong hash = 5381UL;
     610             :   long i;
     611   256214956 :   for (i = 0; i < len; i++)
     612             :   {
     613   195755340 :     ulong c = (ulong)*str++;
     614   195755340 :     hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
     615             :   }
     616    60459616 :   return hash;
     617             : }
     618             : 
     619             : /*******************************************************************/
     620             : /*                                                                 */
     621             : /*                        VEC / COL / VECSMALL                     */
     622             : /*                                                                 */
     623             : /*******************************************************************/
     624             : /* shallow*/
     625             : INLINE GEN
     626       11466 : vec_shorten(GEN v, long n)
     627             : {
     628       11466 :   GEN V = cgetg(n+1, t_VEC);
     629             :   long i;
     630       12845 :   for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
     631       11466 :   return V;
     632             : }
     633             : /* shallow*/
     634             : INLINE GEN
     635       19612 : vec_lengthen(GEN v, long n)
     636             : {
     637       19612 :   GEN V = cgetg(n+1, t_VEC);
     638       19612 :   long i, l = lg(v);
     639    16748521 :   for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
     640       19612 :   return V;
     641             : }
     642             : /* shallow*/
     643             : INLINE GEN
     644     3419593 : vec_append(GEN V, GEN s)
     645             : {
     646     3419593 :   long i, l2 = lg(V);
     647     3419593 :   GEN res = cgetg(l2+1, typ(V));
     648    10705369 :   for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
     649     3419581 :   gel(res,l2) = s; return res;
     650             : }
     651             : /* shallow*/
     652             : INLINE GEN
     653      272210 : vec_prepend(GEN v, GEN s)
     654             : {
     655      272210 :   long i, l = lg(v);
     656      272210 :   GEN w = cgetg(l+1, typ(v));
     657      272210 :   gel(w,1) = s;
     658      576596 :   for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
     659      272210 :   return w;
     660             : }
     661             : /* shallow*/
     662             : INLINE GEN
     663           0 : vec_setconst(GEN v, GEN x)
     664             : {
     665           0 :   long i, l = lg(v);
     666           0 :   for (i = 1; i < l; i++) gel(v,i) = x;
     667           0 :   return v;
     668             : }
     669             : INLINE GEN
     670       51945 : vecsmall_shorten(GEN v, long n)
     671             : {
     672       51945 :   GEN V = cgetg(n+1,t_VECSMALL);
     673             :   long i;
     674      628556 :   for(i = 1; i <= n; i++) V[i] = v[i];
     675       51944 :   return V;
     676             : }
     677             : INLINE GEN
     678         469 : vecsmall_lengthen(GEN v, long n)
     679             : {
     680         469 :   long i, l = lg(v);
     681         469 :   GEN V = cgetg(n+1,t_VECSMALL);
     682       24976 :   for(i = 1; i < l; i++) V[i] = v[i];
     683         469 :   return V;
     684             : }
     685             : 
     686             : INLINE GEN
     687     4238876 : vec_to_vecsmall(GEN x)
     688    19626542 : { pari_APPLY_long(itos(gel(x,i))) }
     689             : INLINE GEN
     690      491841 : vecsmall_to_vec(GEN x)
     691     6229594 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
     692             : INLINE GEN
     693        2457 : vecsmall_to_vec_inplace(GEN z)
     694             : {
     695        2457 :   long i, l = lg(z);
     696       76867 :   for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
     697        2457 :   settyp(z, t_VEC); return z;
     698             : }
     699             : INLINE GEN
     700     6947916 : vecsmall_to_col(GEN x)
     701    57608256 : { pari_APPLY_type(t_COL, stoi(x[i])) }
     702             : 
     703             : INLINE int
     704     7071892 : vecsmall_lexcmp(GEN x, GEN y)
     705             : {
     706             :   long lx,ly,l,i;
     707     7071892 :   lx = lg(x);
     708     7071892 :   ly = lg(y); l = minss(lx,ly);
     709    30507687 :   for (i=1; i<l; i++)
     710    28880852 :     if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
     711     1626835 :   if (lx == ly) return 0;
     712       30578 :   return (lx < ly)? -1 : 1;
     713             : }
     714             : 
     715             : INLINE int
     716   108088071 : vecsmall_prefixcmp(GEN x, GEN y)
     717             : {
     718   108088071 :   long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
     719   542691324 :   for (i=1; i<l; i++)
     720   519806035 :     if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
     721    22885289 :   return 0;
     722             : }
     723             : 
     724             : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
     725             : INLINE GEN
     726      182889 : vecsmall_prepend(GEN V, long s)
     727             : {
     728      182889 :   long i, l2 = lg(V);
     729      182889 :   GEN res = cgetg(l2+1, typ(V));
     730      182889 :   res[1] = s;
     731      613249 :   for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
     732      182889 :   return res;
     733             : }
     734             : 
     735             : INLINE GEN
     736     3617352 : vecsmall_append(GEN V, long s)
     737             : {
     738     3617352 :   long i, l2 = lg(V);
     739     3617352 :   GEN res = cgetg(l2+1, t_VECSMALL);
     740     5455015 :   for (i = 1; i < l2; ++i) res[i] = V[i];
     741     3617351 :   res[l2] = s; return res;
     742             : }
     743             : 
     744             : INLINE GEN
     745     1813742 : vecsmall_concat(GEN u, GEN v)
     746             : {
     747     1813742 :   long i, l1 = lg(u)-1, l2 = lg(v)-1;
     748     1813742 :   GEN res = cgetg(l1+l2+1, t_VECSMALL);
     749    14788041 :   for (i = 1; i <= l1; ++i) res[i]    = u[i];
     750    17954793 :   for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
     751     1813741 :   return res;
     752             : }
     753             : 
     754             : /* return the number of indices where u and v are equal */
     755             : INLINE long
     756           0 : vecsmall_coincidence(GEN u, GEN v)
     757             : {
     758           0 :   long i, s = 0, l = minss(lg(u),lg(v));
     759           0 :   for(i=1; i<l; i++)
     760           0 :     if(u[i] == v[i]) s++;
     761           0 :   return s;
     762             : }
     763             : 
     764             : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
     765             : INLINE long
     766          42 : vecsmall_isin(GEN v, long x)
     767             : {
     768          42 :   long i, l = lg(v);
     769          68 :   for (i = 1; i < l; i++)
     770          52 :     if (v[i] == x) return i;
     771          16 :   return 0;
     772             : }
     773             : 
     774             : INLINE long
     775          84 : vecsmall_pack(GEN V, long base, long mod)
     776             : {
     777          84 :   long i, s = 0;
     778         273 :   for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
     779          84 :   return s;
     780             : }
     781             : 
     782             : INLINE long
     783          14 : vecsmall_indexmax(GEN x)
     784             : {
     785          14 :   long i, i0 = 1, t = x[1], lx = lg(x);
     786          56 :   for (i=2; i<lx; i++)
     787          42 :     if (x[i] > t) t = x[i0=i];
     788          14 :   return i0;
     789             : }
     790             : 
     791             : INLINE long
     792      674958 : vecsmall_max(GEN x)
     793             : {
     794      674958 :   long i, t = x[1], lx = lg(x);
     795     2028249 :   for (i=2; i<lx; i++)
     796     1353291 :     if (x[i] > t) t = x[i];
     797      674958 :   return t;
     798             : }
     799             : 
     800             : INLINE long
     801          14 : vecsmall_indexmin(GEN x)
     802             : {
     803          14 :   long i, i0 = 1, t = x[1], lx =lg(x);
     804          56 :   for (i=2; i<lx; i++)
     805          42 :     if (x[i] < t) t = x[i0=i];
     806          14 :   return i0;
     807             : }
     808             : 
     809             : INLINE long
     810        1435 : vecsmall_min(GEN x)
     811             : {
     812        1435 :   long i, t = x[1], lx =lg(x);
     813       10045 :   for (i=2; i<lx; i++)
     814        8610 :     if (x[i] < t) t = x[i];
     815        1435 :   return t;
     816             : }
     817             : 
     818             : INLINE int
     819    34671394 : ZV_isscalar(GEN x)
     820             : {
     821    34671394 :   long l = lg(x);
     822    59683150 :   while (--l > 1)
     823    59236146 :     if (signe(gel(x, l))) return 0;
     824      447004 :   return 1;
     825             : }
     826             : INLINE int
     827    36350183 : QV_isscalar(GEN x)
     828             : {
     829    36350183 :   long lx = lg(x),i;
     830    43323682 :   for (i=2; i<lx; i++)
     831    41646740 :     if (!isintzero(gel(x, i))) return 0;
     832     1676942 :   return 1;
     833             : }
     834             : INLINE int
     835        9357 : RgV_isscalar(GEN x)
     836             : {
     837        9357 :   long lx = lg(x),i;
     838       11196 :   for (i=2; i<lx; i++)
     839       11154 :     if (!gequal0(gel(x, i))) return 0;
     840          42 :   return 1;
     841             : }
     842             : INLINE int
     843           0 : RgX_isscalar(GEN x)
     844             : {
     845             :   long i;
     846           0 :   for (i=lg(x)-1; i>2; i--)
     847           0 :     if (!gequal0(gel(x, i))) return 0;
     848           0 :   return 1;
     849             : }
     850             : INLINE long
     851    25077893 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
     852             : INLINE GEN
     853         140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
     854             : 
     855             : INLINE int
     856       63677 : RgX_is_rational(GEN x)
     857             : {
     858             :   long i;
     859      296441 :   for (i = lg(x)-1; i > 1; i--)
     860      281349 :     if (!is_rational_t(typ(gel(x,i)))) return 0;
     861       15092 :   return 1;
     862             : }
     863             : INLINE int
     864    11683684 : RgX_is_ZX(GEN x)
     865             : {
     866             :   long i;
     867    49960922 :   for (i = lg(x)-1; i > 1; i--)
     868    38334819 :     if (typ(gel(x,i)) != t_INT) return 0;
     869    11626103 :   return 1;
     870             : }
     871             : INLINE int
     872      333359 : RgX_is_QX(GEN x)
     873             : {
     874      333359 :   long k = lg(x)-1;
     875     1232150 :   for ( ; k>1; k--)
     876      899050 :     if (!is_rational_t(typ(gel(x,k)))) return 0;
     877      333100 :   return 1;
     878             : }
     879             : INLINE int
     880     2466555 : RgX_is_monomial(GEN x)
     881             : {
     882             :   long i;
     883     2466555 :   if (!signe(x)) return 0;
     884     6082646 :   for (i=lg(x)-2; i>1; i--)
     885     3686440 :     if (!isexactzero(gel(x,i))) return 0;
     886     2396206 :   return 1;
     887             : }
     888             : INLINE int
     889    30108516 : RgV_is_ZV(GEN x)
     890             : {
     891             :   long i;
     892   120311763 :   for (i = lg(x)-1; i > 0; i--)
     893    90232318 :     if (typ(gel(x,i)) != t_INT) return 0;
     894    30079445 :   return 1;
     895             : }
     896             : INLINE int
     897      110264 : RgV_is_QV(GEN x)
     898             : {
     899             :   long i;
     900      527926 :   for (i = lg(x)-1; i > 0; i--)
     901      420617 :     if (!is_rational_t(typ(gel(x,i)))) return 0;
     902      107309 :   return 1;
     903             : }
     904             : INLINE long
     905      108892 : RgV_isin_i(GEN v, GEN x, long n)
     906             : {
     907             :   long i;
     908     1031205 :   for (i = 1; i <= n; i++)
     909     1025416 :     if (gequal(gel(v,i), x)) return i;
     910        5789 :   return 0;
     911             : }
     912             : INLINE long
     913      108892 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
     914             : 
     915             : /********************************************************************/
     916             : /**                                                                **/
     917             : /**            Dynamic arrays implementation                       **/
     918             : /**                                                                **/
     919             : /********************************************************************/
     920             : INLINE void **
     921  1243750711 : pari_stack_base(pari_stack *s) { return s->data; }
     922             : 
     923             : INLINE void
     924     3870462 : pari_stack_init(pari_stack *s, size_t size, void **data)
     925             : {
     926     3870462 :   s->data = data;
     927     3870462 :   *data = NULL;
     928     3870462 :   s->n = 0;
     929     3870462 :   s->alloc = 0;
     930     3870462 :   s->size = size;
     931     3870462 : }
     932             : 
     933             : INLINE void
     934  1240172917 : pari_stack_alloc(pari_stack *s, long nb)
     935             : {
     936  1240172917 :   void **sdat = pari_stack_base(s);
     937  1240092253 :   long alloc = s->alloc;
     938  1240092253 :   if (s->n+nb <= alloc) return;
     939     1486151 :   if (!alloc)
     940     1389429 :     alloc = nb;
     941             :   else
     942             :   {
     943      197403 :     while (s->n+nb > alloc) alloc <<= 1;
     944             :   }
     945     1486151 :   pari_realloc_ip(sdat,alloc*s->size);
     946     1496465 :   s->alloc = alloc;
     947             : }
     948             : 
     949             : INLINE long
     950  1153543571 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
     951             : 
     952             : INLINE void
     953     3608092 : pari_stack_delete(pari_stack *s)
     954             : {
     955     3608092 :   void **sdat = pari_stack_base(s);
     956     3602204 :   if (*sdat) pari_free(*sdat);
     957     3624255 : }
     958             : 
     959             : INLINE void
     960        5557 : pari_stack_pushp(pari_stack *s, void *u)
     961             : {
     962        5557 :   long n = pari_stack_new(s);
     963        5557 :   void **sdat =(void**) *pari_stack_base(s);
     964        5557 :   sdat[n] = u;
     965        5557 : }
     966             : 
     967             : /*******************************************************************/
     968             : /*                                                                 */
     969             : /*                            EXTRACT                              */
     970             : /*                                                                 */
     971             : /*******************************************************************/
     972             : INLINE GEN
     973   582420563 : vecslice(GEN A, long y1, long y2)
     974             : {
     975   582420563 :   long i,lB = y2 - y1 + 2;
     976   582420563 :   GEN B = cgetg(lB, typ(A));
     977  2584532428 :   for (i=1; i<lB; i++) B[i] = A[y1-1+i];
     978   582409824 :   return B;
     979             : }
     980             : INLINE GEN
     981     2071779 : vecslicepermute(GEN A, GEN p, long y1, long y2)
     982             : {
     983     2071779 :   long i,lB = y2 - y1 + 2;
     984     2071779 :   GEN B = cgetg(lB, typ(A));
     985    31495362 :   for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
     986     2071759 :   return B;
     987             : }
     988             : /* rowslice(rowpermute(A,p), x1, x2) */
     989             : INLINE GEN
     990      167626 : rowslicepermute(GEN x, GEN p, long j1, long j2)
     991      725311 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
     992             : 
     993             : INLINE GEN
     994    64511275 : rowslice(GEN x, long j1, long j2)
     995   593566592 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
     996             : 
     997             : INLINE GEN
     998     9385418 : matslice(GEN A, long x1, long x2, long y1, long y2)
     999     9385418 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
    1000             : 
    1001             : /* shallow, remove coeff of index j */
    1002             : INLINE GEN
    1003         210 : rowsplice(GEN x, long j)
    1004        1036 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
    1005             : 
    1006             : /* shallow, remove coeff of index j */
    1007             : INLINE GEN
    1008      353919 : vecsplice(GEN a, long j)
    1009             : {
    1010      353919 :   long i, k, l = lg(a);
    1011             :   GEN b;
    1012      353919 :   if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
    1013      353919 :   b = cgetg(l-1, typ(a));
    1014     1498109 :   for (i = k = 1; i < l; i++)
    1015     1144191 :     if (i != j) gel(b, k++) = gel(a,i);
    1016      353918 :   return b;
    1017             : }
    1018             : /* shallow */
    1019             : INLINE GEN
    1020        1036 : RgM_minor(GEN a, long i, long j)
    1021             : {
    1022        1036 :   GEN b = vecsplice(a, j);
    1023        1036 :   long k, l = lg(b);
    1024        4242 :   for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
    1025        1036 :   return b;
    1026             : }
    1027             : 
    1028             : /* A[x0,] */
    1029             : INLINE GEN
    1030      474034 : row(GEN x, long j)
    1031     4402149 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
    1032             : INLINE GEN
    1033     9877316 : Flm_row(GEN x, long j)
    1034   242639836 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
    1035             : /* A[x0,] */
    1036             : INLINE GEN
    1037      204988 : rowcopy(GEN x, long j)
    1038     2105509 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
    1039             : /* A[x0, x1..x2] */
    1040             : INLINE GEN
    1041         987 : row_i(GEN A, long x0, long x1, long x2)
    1042             : {
    1043         987 :   long i, lB = x2 - x1 + 2;
    1044         987 :   GEN B  = cgetg(lB, t_VEC);
    1045        2989 :   for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
    1046         987 :   return B;
    1047             : }
    1048             : 
    1049             : INLINE GEN
    1050      398643 : vecreverse(GEN A)
    1051             : {
    1052             :   long i, l;
    1053      398643 :   GEN B = cgetg_copy(A, &l);
    1054     1187137 :   for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
    1055      398643 :   return B;
    1056             : }
    1057             : 
    1058             : INLINE GEN
    1059        2961 : vecsmall_reverse(GEN A)
    1060             : {
    1061             :   long i, l;
    1062        2961 :   GEN B = cgetg_copy(A, &l);
    1063       11669 :   for (i=1; i<l; i++) B[i] = A[l-i];
    1064        2961 :   return B;
    1065             : }
    1066             : 
    1067             : INLINE void
    1068        2321 : vecreverse_inplace(GEN y)
    1069             : {
    1070        2321 :   long l = lg(y), lim = l>>1, i;
    1071        7615 :   for (i = 1; i <= lim; i++)
    1072             :   {
    1073        5294 :     GEN z = gel(y,i);
    1074        5294 :     gel(y,i)    = gel(y,l-i);
    1075        5294 :     gel(y,l-i) = z;
    1076             :   }
    1077        2321 : }
    1078             : 
    1079             : INLINE GEN
    1080    75676066 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
    1081             : 
    1082             : INLINE GEN
    1083    11510292 : vecpermute(GEN A, GEN x)
    1084    97545915 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
    1085             : 
    1086             : INLINE GEN
    1087    10070491 : rowpermute(GEN x, GEN p)
    1088    88105161 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
    1089             :                                               : vecpermute(gel(x, i), p))
    1090             : }
    1091             : /*******************************************************************/
    1092             : /*                                                                 */
    1093             : /*                          PERMUTATIONS                           */
    1094             : /*                                                                 */
    1095             : /*******************************************************************/
    1096             : INLINE GEN
    1097     2102125 : identity_zv(long n)
    1098             : {
    1099     2102125 :   GEN v = cgetg(n+1, t_VECSMALL);
    1100             :   long i;
    1101    25998721 :   for (i = 1; i <= n; i++) v[i] = i;
    1102     2102085 :   return v;
    1103             : }
    1104             : INLINE GEN
    1105        4242 : identity_ZV(long n)
    1106             : {
    1107        4242 :   GEN v = cgetg(n+1, t_VEC);
    1108             :   long i;
    1109       51541 :   for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
    1110        4242 :   return v;
    1111             : }
    1112             : /* identity permutation */
    1113             : INLINE GEN
    1114     2077821 : identity_perm(long n) { return identity_zv(n); }
    1115             : 
    1116             : /* assume d <= n */
    1117             : INLINE GEN
    1118       98483 : cyclic_perm(long n, long d)
    1119             : {
    1120       98483 :   GEN perm = cgetg(n+1, t_VECSMALL);
    1121             :   long i;
    1122      504098 :   for (i = 1; i <= n-d; i++) perm[i] = i+d;
    1123      225029 :   for (     ; i <= n;   i++) perm[i] = i-n+d;
    1124       98483 :   return perm;
    1125             : }
    1126             : 
    1127             : /* Multiply (compose) two permutations */
    1128             : INLINE GEN
    1129    77870569 : perm_mul(GEN s, GEN x)
    1130  1000545885 : { pari_APPLY_long(s[x[i]]) }
    1131             : 
    1132             : INLINE GEN
    1133         728 : perm_sqr(GEN x)
    1134       18284 : { pari_APPLY_long(x[x[i]]) }
    1135             : 
    1136             : /* Compute the inverse (reciprocal) of a permutation. */
    1137             : INLINE GEN
    1138     2692623 : perm_inv(GEN x)
    1139             : {
    1140             :   long i, lx;
    1141     2692623 :   GEN y = cgetg_copy(x, &lx);
    1142    37979896 :   for (i=1; i<lx; i++) y[ x[i] ] = i;
    1143     2692618 :   return y;
    1144             : }
    1145             : /* Return s*t*s^-1 */
    1146             : INLINE GEN
    1147      418257 : perm_conj(GEN s, GEN t)
    1148             : {
    1149             :   long i, l;
    1150      418257 :   GEN v = cgetg_copy(s, &l);
    1151     6857683 :   for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
    1152      418257 :   return v;
    1153             : }
    1154             : 
    1155             : INLINE void
    1156   367145602 : pari_free(void *pointer)
    1157             : {
    1158   367145602 :   BLOCK_SIGINT_START;
    1159   367208248 :   free(pointer);
    1160   367208248 :   BLOCK_SIGINT_END;
    1161   367211500 : }
    1162             : INLINE void*
    1163   589586429 : pari_malloc(size_t size)
    1164             : {
    1165   589586429 :   if (size)
    1166             :   {
    1167             :     char *tmp;
    1168   589588162 :     BLOCK_SIGINT_START;
    1169   589666021 :     tmp = (char*)malloc(size);
    1170   589666021 :     BLOCK_SIGINT_END;
    1171   589665862 :     if (!tmp) pari_err(e_MEM);
    1172   589681587 :     return tmp;
    1173             :   }
    1174           0 :   return NULL;
    1175             : }
    1176             : INLINE void*
    1177        1792 : pari_realloc(void *pointer, size_t size)
    1178             : {
    1179             :   char *tmp;
    1180             : 
    1181        1792 :   BLOCK_SIGINT_START;
    1182        1792 :   if (!pointer) tmp = (char *) malloc(size);
    1183        1792 :   else tmp = (char *) realloc(pointer,size);
    1184        1792 :   BLOCK_SIGINT_END;
    1185        1792 :   if (!tmp) pari_err(e_MEM);
    1186        1792 :   return tmp;
    1187             : }
    1188             : INLINE void
    1189     1491469 : pari_realloc_ip(void **pointer, size_t size)
    1190             : {
    1191             :   char *tmp;
    1192     1491469 :   BLOCK_SIGINT_START;
    1193     1490348 :   if (!*pointer) tmp = (char *) malloc(size);
    1194      102752 :   else tmp = (char *) realloc(*pointer,size);
    1195     1490348 :   if (!tmp) pari_err(e_MEM);
    1196     1490348 :   *pointer = tmp;
    1197     1490348 :   BLOCK_SIGINT_END;
    1198     1486282 : }
    1199             : 
    1200             : INLINE void*
    1201       43870 : pari_calloc(size_t size)
    1202             : {
    1203       43870 :   void *t = pari_malloc(size);
    1204       43870 :   memset(t, 0, size); return t;
    1205             : }
    1206             : INLINE GEN
    1207        8059 : cgetalloc(long t, size_t l)
    1208             : { /* evallg may raise e_OVERFLOW, which would leak x */
    1209        8059 :   ulong x0 = evaltyp(t) | evallg(l);
    1210        8059 :   GEN x = (GEN)pari_malloc(l * sizeof(long));
    1211        8059 :   x[0] = x0; return x;
    1212             : }
    1213             : 
    1214             : /*******************************************************************/
    1215             : /*                                                                 */
    1216             : /*                       GARBAGE COLLECTION                        */
    1217             : /*                                                                 */
    1218             : /*******************************************************************/
    1219             : /* copy integer x as if we had set_avma(av) */
    1220             : INLINE GEN
    1221  6373869910 : icopy_avma(GEN x, pari_sp av)
    1222             : {
    1223  6373869910 :   long i = lgefint(x), lx = i;
    1224  6373869910 :   GEN y = ((GEN)av) - i;
    1225 42882100338 :   while (--i > 0) y[i] = x[i];
    1226  6373869910 :   y[0] = evaltyp(t_INT)|evallg(lx);
    1227  6377834999 :   return y;
    1228             : }
    1229             : /* copy leaf x as if we had set_avma(av) */
    1230             : INLINE GEN
    1231   434456213 : leafcopy_avma(GEN x, pari_sp av)
    1232             : {
    1233   434456213 :   long i = lg(x);
    1234   434456213 :   GEN y = ((GEN)av) - i;
    1235  2729598874 :   while (--i > 0) y[i] = x[i];
    1236   434456213 :   y[0] = x[0] & (~CLONEBIT);
    1237   434456213 :   return y;
    1238             : }
    1239             : INLINE GEN
    1240  1027550986 : gerepileuptoleaf(pari_sp av, GEN x)
    1241             : {
    1242             :   long lx;
    1243             :   GEN q;
    1244             : 
    1245  1027550986 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1246  1026905060 :   lx = lg(x);
    1247  1026905060 :   q = ((GEN)av) - lx;
    1248  1026905060 :   set_avma((pari_sp)q);
    1249 10586326504 :   while (--lx >= 0) q[lx] = x[lx];
    1250  1026845569 :   return q;
    1251             : }
    1252             : INLINE GEN
    1253  2916055140 : gerepileuptoint(pari_sp av, GEN x)
    1254             : {
    1255  2916055140 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1256  2553025650 :   set_avma((pari_sp)icopy_avma(x, av));
    1257  2556395775 :   return (GEN)avma;
    1258             : }
    1259             : INLINE GEN
    1260  1537706384 : gerepileupto(pari_sp av, GEN x)
    1261             : {
    1262  1537706384 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1263  1367950841 :   switch(typ(x))
    1264             :   { /* non-default = !is_recursive_t(tq) */
    1265   412497369 :     case t_INT: return gerepileuptoint(av, x);
    1266   320618275 :     case t_REAL:
    1267             :     case t_STR:
    1268   320618275 :     case t_VECSMALL: return gerepileuptoleaf(av,x);
    1269   634837627 :     default:
    1270             :       /* NB: x+i --> ((long)x) + i*sizeof(long) */
    1271   634837627 :       return gerepile(av, (pari_sp) (x+lg(x)), x);
    1272             :   }
    1273             : }
    1274             : 
    1275             : /* gerepileupto(av, gcopy(x)) */
    1276             : INLINE GEN
    1277   140454517 : gerepilecopy(pari_sp av, GEN x)
    1278             : {
    1279   140454517 :   if (is_recursive_t(typ(x)))
    1280             :   {
    1281   134073014 :     GENbin *p = copy_bin(x);
    1282   134088855 :     set_avma(av); return bin_copy(p);
    1283             :   }
    1284             :   else
    1285             :   {
    1286     6382123 :     set_avma(av);
    1287     6382164 :     if (x < (GEN)av) {
    1288     4636939 :       if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
    1289     4636941 :       x = leafcopy_avma(x, av);
    1290     4636958 :       set_avma((pari_sp)x);
    1291             :     } else
    1292     1745228 :       x = leafcopy(x);
    1293     6382191 :     return x;
    1294             :   }
    1295             : }
    1296             : 
    1297             : INLINE void
    1298    28111905 : guncloneNULL(GEN x) { if (x) gunclone(x); }
    1299             : INLINE void
    1300      944343 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
    1301             : 
    1302             : /* Takes an array of pointers to GENs, of length n. Copies all
    1303             :  * objects to contiguous locations and cleans up the stack between
    1304             :  * av and avma. */
    1305             : INLINE void
    1306      938357 : gerepilemany(pari_sp av, GEN* gptr[], int n)
    1307             : {
    1308             :   int i;
    1309     3745199 :   for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
    1310      938008 :   set_avma(av);
    1311     3745909 :   for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1312      938574 : }
    1313             : 
    1314             : INLINE void
    1315    11420931 : gerepileall(pari_sp av, int n, ...)
    1316             : {
    1317             :   int i;
    1318    11420931 :   va_list a; va_start(a, n);
    1319    11420931 :   if (n < 10)
    1320             :   {
    1321             :     GEN *gptr[10];
    1322    34538082 :     for (i=0; i<n; i++)
    1323    23116885 :     { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
    1324    11421197 :     set_avma(av);
    1325    34538434 :     for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1326             : 
    1327             :   }
    1328             :   else
    1329             :   {
    1330           1 :     GEN **gptr = (GEN**)  pari_malloc(n*sizeof(GEN*));
    1331           0 :     for (i=0; i<n; i++)
    1332           0 :     { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
    1333           0 :     set_avma(av);
    1334           0 :     for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1335           0 :     pari_free(gptr);
    1336             :   }
    1337    11421648 :   va_end(a);
    1338    11421648 : }
    1339             : 
    1340             : /* assume 1 <= n < 10 */
    1341             : INLINE GEN
    1342    70429329 : gc_all(pari_sp av, int n, ...)
    1343             : {
    1344             :   int i;
    1345             :   GEN *v[10];
    1346    70429329 :   va_list a; va_start(a, n);
    1347   241588205 :   for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
    1348    70429726 :   set_avma(av);
    1349   241589154 :   for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
    1350    70430089 :   return *v[0];
    1351             : }
    1352             : 
    1353             : INLINE void
    1354     2195687 : gerepilecoeffs(pari_sp av, GEN x, int n)
    1355             : {
    1356             :   int i;
    1357    26131622 :   for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
    1358     2196238 :   set_avma(av);
    1359    26133115 :   for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
    1360     2195941 : }
    1361             : 
    1362             : /* p from copy_bin. Copy p->x back to stack, then destroy p */
    1363             : INLINE GEN
    1364   355148053 : bin_copy(GENbin *p)
    1365             : {
    1366             :   GEN x, y, base;
    1367             :   long dx, len;
    1368             : 
    1369   355148053 :   x   = p->x; if (!x) { pari_free(p); return gen_0; }
    1370   327013270 :   len = p->len;
    1371   327013270 :   base= p->base; dx = x - base;
    1372   327013270 :   y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
    1373   327007480 :   y += dx;
    1374   327007480 :   p->rebase(y, ((ulong)y-(ulong)x));
    1375   327007127 :   pari_free(p); return y;
    1376             : }
    1377             : 
    1378             : INLINE GEN
    1379   682157133 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
    1380             : 
    1381             : INLINE void
    1382   111007172 : cgiv(GEN x)
    1383             : {
    1384   111007172 :   pari_sp av = (pari_sp)(x+lg(x));
    1385   111007172 :   if (isonstack((GEN)av)) set_avma(av);
    1386   111009922 : }
    1387             : 
    1388             : INLINE void
    1389     1547506 : killblock(GEN x) { gunclone(x); }
    1390             : 
    1391             : INLINE int
    1392   319153516 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
    1393             : 
    1394             : /*******************************************************************/
    1395             : /*                                                                 */
    1396             : /*                    CONVERSION / ASSIGNMENT                      */
    1397             : /*                                                                 */
    1398             : /*******************************************************************/
    1399             : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
    1400             : INLINE GEN
    1401    17639168 : cxcompotor(GEN z, long prec)
    1402             : {
    1403    17639168 :   switch(typ(z))
    1404             :   {
    1405    11192553 :     case t_INT:  return itor(z, prec);
    1406      289429 :     case t_FRAC: return fractor(z, prec);
    1407     6157513 :     case t_REAL: return rtor(z, prec);
    1408           0 :     default: pari_err_TYPE("cxcompotor",z);
    1409             :              return NULL; /* LCOV_EXCL_LINE */
    1410             :   }
    1411             : }
    1412             : INLINE GEN
    1413     8805020 : cxtofp(GEN x, long prec)
    1414     8805020 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
    1415             : 
    1416             : INLINE GEN
    1417      275452 : cxtoreal(GEN q)
    1418      275452 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
    1419             : 
    1420             : INLINE double
    1421    55381935 : gtodouble(GEN x)
    1422             : {
    1423    55381935 :   if (typ(x)!=t_REAL) {
    1424     6007946 :     pari_sp av = avma;
    1425     6007946 :     x = gtofp(x, DEFAULTPREC);
    1426     6007263 :     if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
    1427     6007263 :     set_avma(av);
    1428             :   }
    1429    55381122 :   return rtodbl(x);
    1430             : }
    1431             : 
    1432             : INLINE int
    1433     8926208 : gisdouble(GEN x, double *g)
    1434             : {
    1435     8926208 :   if (typ(x)!=t_REAL) {
    1436      146817 :     pari_sp av = avma;
    1437      146817 :     x = gtofp(x, DEFAULTPREC);
    1438      146814 :     if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
    1439      146814 :     set_avma(av);
    1440             :   }
    1441     8926194 :   if (expo(x) >= 0x3ff) return 0;
    1442     8926194 :   *g = rtodbl(x); return 1;
    1443             : }
    1444             : 
    1445             : INLINE long
    1446    73835003 : gtos(GEN x) {
    1447    73835003 :   if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
    1448    73834996 :   return itos(x);
    1449             : }
    1450             : 
    1451             : INLINE ulong
    1452      102510 : gtou(GEN x) {
    1453      102510 :   if (typ(x) != t_INT || signe(x)<0)
    1454           7 :     pari_err_TYPE("gtou [integer >=0 expected]",x);
    1455      102503 :   return itou(x);
    1456             : }
    1457             : 
    1458             : INLINE GEN
    1459    40800646 : absfrac(GEN x)
    1460             : {
    1461    40800646 :   GEN y = cgetg(3, t_FRAC);
    1462    40800672 :   gel(y,1) = absi(gel(x,1));
    1463    40800666 :   gel(y,2) = icopy(gel(x,2)); return y;
    1464             : }
    1465             : INLINE GEN
    1466       43890 : absfrac_shallow(GEN x)
    1467       43890 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
    1468             : INLINE GEN
    1469     7091833 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
    1470             : INLINE GEN
    1471      159347 : Q_abs_shallow(GEN x)
    1472      159347 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
    1473             : INLINE GEN
    1474       12754 : R_abs_shallow(GEN x)
    1475       12754 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
    1476             : INLINE GEN
    1477           0 : R_abs(GEN x)
    1478           0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
    1479             : 
    1480             : /* Force z to be of type real/complex with floating point components */
    1481             : INLINE GEN
    1482    74638253 : gtofp(GEN z, long prec)
    1483             : {
    1484    74638253 :   switch(typ(z))
    1485             :   {
    1486    42171224 :     case t_INT:  return itor(z, prec);
    1487     4091773 :     case t_FRAC: return fractor(z, prec);
    1488    19838282 :     case t_REAL: return rtor(z, prec);
    1489     8544798 :     case t_COMPLEX: {
    1490     8544798 :       GEN a = gel(z,1), b = gel(z,2);
    1491     8544798 :       if (isintzero(b)) return cxcompotor(a, prec);
    1492     8544808 :       if (isintzero(a)) {
    1493        8308 :         GEN y = cgetg(3, t_COMPLEX);
    1494        8308 :         b = cxcompotor(b, prec);
    1495        8308 :         gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
    1496        8308 :         gel(y,2) = b; return y;
    1497             :       }
    1498     8536460 :       return cxtofp(z, prec);
    1499             :     }
    1500           0 :     case t_QUAD: return quadtofp(z, prec);
    1501           0 :     default: pari_err_TYPE("gtofp",z);
    1502             :              return NULL; /* LCOV_EXCL_LINE */
    1503             :   }
    1504             : }
    1505             : /* Force z to be of type real / int */
    1506             : INLINE GEN
    1507       22428 : gtomp(GEN z, long prec)
    1508             : {
    1509       22428 :   switch(typ(z))
    1510             :   {
    1511          42 :     case t_INT:  return z;
    1512       22386 :     case t_FRAC: return fractor(z, prec);
    1513           0 :     case t_REAL: return rtor(z, prec);
    1514           0 :     case t_QUAD: z = quadtofp(z, prec);
    1515           0 :                  if (typ(z) == t_REAL) return z;
    1516           0 :     default: pari_err_TYPE("gtomp",z);
    1517             :              return NULL; /* LCOV_EXCL_LINE */
    1518             :   }
    1519             : }
    1520             : 
    1521             : INLINE GEN
    1522     4686227 : RgX_gtofp(GEN x, long prec)
    1523             : {
    1524             :   long l;
    1525     4686227 :   GEN y = cgetg_copy(x, &l);
    1526    26548274 :   while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
    1527     4684083 :   y[1] = x[1]; return y;
    1528             : }
    1529             : INLINE GEN
    1530     3122222 : RgC_gtofp(GEN x, long prec)
    1531    25453961 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
    1532             : 
    1533             : INLINE GEN
    1534          49 : RgV_gtofp(GEN x, long prec)
    1535        4746 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
    1536             : 
    1537             : INLINE GEN
    1538      584088 : RgM_gtofp(GEN x, long prec)
    1539     3080352 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
    1540             : 
    1541             : INLINE GEN
    1542         574 : RgC_gtomp(GEN x, long prec)
    1543       23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
    1544             : 
    1545             : INLINE GEN
    1546          21 : RgM_gtomp(GEN x, long prec)
    1547         595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
    1548             : 
    1549             : INLINE GEN
    1550       57604 : RgX_fpnorml2(GEN x, long prec)
    1551             : {
    1552       57604 :   pari_sp av = avma;
    1553       57604 :   return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
    1554             : }
    1555             : INLINE GEN
    1556      615234 : RgC_fpnorml2(GEN x, long prec)
    1557             : {
    1558      615234 :   pari_sp av = avma;
    1559      615234 :   return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
    1560             : }
    1561             : INLINE GEN
    1562       18616 : RgM_fpnorml2(GEN x, long prec)
    1563             : {
    1564       18616 :   pari_sp av = avma;
    1565       18616 :   return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
    1566             : }
    1567             : 
    1568             : /* y a t_REAL */
    1569             : INLINE void
    1570      216244 : affgr(GEN x, GEN y)
    1571             : {
    1572             :   pari_sp av;
    1573      216244 :   switch(typ(x)) {
    1574        5992 :     case t_INT:  affir(x,y); break;
    1575      210252 :     case t_REAL: affrr(x,y); break;
    1576           0 :     case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
    1577           0 :     case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
    1578           0 :     default: pari_err_TYPE2("=",x,y);
    1579             :   }
    1580      216244 : }
    1581             : 
    1582             : INLINE GEN
    1583      245073 : affc_fixlg(GEN x, GEN res)
    1584             : {
    1585      245073 :   if (typ(x) == t_COMPLEX)
    1586             :   {
    1587      212849 :     affrr_fixlg(gel(x,1), gel(res,1));
    1588      212849 :     affrr_fixlg(gel(x,2), gel(res,2));
    1589             :   }
    1590             :   else
    1591             :   {
    1592       32224 :     set_avma((pari_sp)(res+3));
    1593       32223 :     res = cgetr(realprec(gel(res,1)));
    1594       32229 :     affrr_fixlg(x, res);
    1595             :   }
    1596      245076 :   return res;
    1597             : }
    1598             : 
    1599             : INLINE GEN
    1600           0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
    1601             : 
    1602             : /*******************************************************************/
    1603             : /*                                                                 */
    1604             : /*                          LENGTH CONVERSIONS                     */
    1605             : /*                                                                 */
    1606             : /*******************************************************************/
    1607             : INLINE long
    1608       38405 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
    1609             : INLINE long
    1610       30052 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
    1611             : INLINE long
    1612        8353 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
    1613             : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
    1614             :  * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
    1615             :  *   addl, shrl instead of subl, sarl, addl */
    1616             : INLINE long
    1617    11350914 : nbits2nlong(long x) {
    1618    11350914 :   return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1619             : }
    1620             : 
    1621             : INLINE long
    1622   513328645 : nbits2extraprec(long x) {
    1623   513328645 :   return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1624             : }
    1625             : 
    1626             : /* Fast implementation of 2 + nbits2nlong(x) */
    1627             : INLINE long
    1628   178962864 : nbits2prec(long x) {
    1629   178962864 :   return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1630             : }
    1631             : INLINE long
    1632   314935555 : nbits2lg(long x) {
    1633   314935555 :   return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1634             : }
    1635             : /* ceil(x / sizeof(long)) */
    1636             : INLINE long
    1637   100152232 : nchar2nlong(long x) {
    1638   100152232 :   return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
    1639             : }
    1640             : INLINE long
    1641  2142935364 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
    1642             : INLINE double
    1643     2866907 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
    1644             : INLINE double
    1645      586430 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
    1646             : INLINE long
    1647    99669334 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
    1648             : INLINE long
    1649  1911147730 : bit_accuracy(long x) { return prec2nbits(x); }
    1650             : INLINE long
    1651       10152 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
    1652             : INLINE long
    1653         228 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
    1654             : INLINE long
    1655        4774 : precdbl(long x) {return (x - 1) << 1;}
    1656             : INLINE long
    1657  6051820377 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
    1658             : INLINE long
    1659  5948357062 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
    1660             : 
    1661             : /*********************************************************************/
    1662             : /**                                                                 **/
    1663             : /**                      OPERATIONS MODULO m                        **/
    1664             : /**                                                                 **/
    1665             : /*********************************************************************/
    1666             : /* Assume m > 0, more efficient if 0 <= a, b < m */
    1667             : 
    1668             : INLINE GEN
    1669    45843593 : Fp_red(GEN a, GEN m) { return modii(a, m); }
    1670             : INLINE GEN
    1671   109532415 : Fp_add(GEN a, GEN b, GEN m)
    1672             : {
    1673   109532415 :   pari_sp av=avma;
    1674   109532415 :   GEN p = addii(a,b);
    1675   107964697 :   long s = signe(p);
    1676   107964697 :   if (!s) return p; /* = gen_0 */
    1677    97057354 :   if (s > 0) /* general case */
    1678             :   {
    1679    97075003 :     GEN t = subii(p, m);
    1680    96714030 :     s = signe(t);
    1681    96714030 :     if (!s) return gc_const(av, gen_0);
    1682    89240020 :     if (s < 0) return gc_const((pari_sp)p, p);
    1683    44915973 :     if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
    1684     3001949 :     p = remii(t, m);
    1685             :   }
    1686             :   else
    1687      226384 :     p = modii(p, m);
    1688     3228443 :   return gerepileuptoint(av, p);
    1689             : }
    1690             : INLINE GEN
    1691   113808811 : Fp_sub(GEN a, GEN b, GEN m)
    1692             : {
    1693   113808811 :   pari_sp av=avma;
    1694   113808811 :   GEN p = subii(a,b);
    1695   111720382 :   long s = signe(p);
    1696   111720382 :   if (!s) return p; /* = gen_0 */
    1697   100199284 :   if (s > 0)
    1698             :   {
    1699    45009634 :     if (cmpii(p, m) < 0) return p; /* general case ! */
    1700     1251763 :     p = remii(p, m);
    1701             :   }
    1702             :   else
    1703             :   {
    1704    55189650 :     GEN t = addii(p, m);
    1705    56971723 :     if (!s) return gc_const(av, gen_0);
    1706    57016827 :     if (s > 0) return gerepileuptoint(av, t); /* general case ! */
    1707    57016827 :     p = modii(t, m);
    1708             :   }
    1709    58551332 :   return gerepileuptoint(av, p);
    1710             : }
    1711             : INLINE GEN
    1712    16916210 : Fp_neg(GEN b, GEN m)
    1713             : {
    1714    16916210 :   pari_sp av = avma;
    1715    16916210 :   long s = signe(b);
    1716             :   GEN p;
    1717    16916210 :   if (!s) return gen_0;
    1718    12940165 :   if (s > 0)
    1719             :   {
    1720    11826938 :     p = subii(m, b);
    1721    11824570 :     if (signe(p) >= 0) return p; /* general case ! */
    1722      382852 :     p = modii(p, m);
    1723             :   } else
    1724     1114179 :     p = remii(negi(b), m);
    1725     1497234 :   return gerepileuptoint(av, p);
    1726             : }
    1727             : 
    1728             : INLINE GEN
    1729       63925 : Fp_halve(GEN a, GEN p)
    1730             : {
    1731       63925 :   if (mpodd(a)) a = addii(a,p);
    1732       63925 :   return shifti(a,-1);
    1733             : }
    1734             : 
    1735             : /* assume 0 <= u < p and ps2 = p>>1 */
    1736             : INLINE GEN
    1737    58859903 : Fp_center(GEN u, GEN p, GEN ps2)
    1738    58859903 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
    1739             : /* same without copy */
    1740             : INLINE GEN
    1741    12199735 : Fp_center_i(GEN u, GEN p, GEN ps2)
    1742    12199735 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
    1743             : 
    1744             : /* x + y*z mod p */
    1745             : INLINE GEN
    1746    10746406 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
    1747             : {
    1748             :   pari_sp av;
    1749    10746406 :   if (!signe(y) || !signe(z)) return Fp_red(x, p);
    1750    10418292 :   if (!signe(x)) return Fp_mul(z,y, p);
    1751     9418307 :   av = avma;
    1752     9418307 :   return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
    1753             : }
    1754             : 
    1755             : INLINE GEN
    1756   170520099 : Fp_mul(GEN a, GEN b, GEN m)
    1757             : {
    1758   170520099 :   pari_sp av=avma;
    1759             :   GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1760   170520099 :   (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
    1761   170526262 :   p = mulii(a,b);
    1762   170628818 :   set_avma(av); return modii(p,m);
    1763             : }
    1764             : INLINE GEN
    1765    67571453 : Fp_sqr(GEN a, GEN m)
    1766             : {
    1767    67571453 :   pari_sp av=avma;
    1768             :   GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1769    67571453 :   (void)new_chunk((lg(a)+lg(m))<<1);
    1770    67749676 :   p = sqri(a);
    1771    65061920 :   set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
    1772             : }
    1773             : INLINE GEN
    1774    79143608 : Fp_mulu(GEN a, ulong b, GEN m)
    1775             : {
    1776    79143608 :   long l = lgefint(m);
    1777    79143608 :   if (l == 3)
    1778             :   {
    1779    44837796 :     ulong mm = m[2];
    1780    44837796 :     return utoi( Fl_mul(umodiu(a, mm), b, mm) );
    1781             :   } else {
    1782    34305812 :     pari_sp av = avma;
    1783             :     GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1784    34305812 :     (void)new_chunk(lg(a)+1+(l<<1));
    1785    34298064 :     p = muliu(a,b);
    1786    32445100 :     set_avma(av); return modii(p,m);
    1787             :   }
    1788             : }
    1789             : INLINE GEN
    1790       17290 : Fp_muls(GEN a, long b, GEN m)
    1791             : {
    1792       17290 :   long l = lgefint(m);
    1793       17290 :   if (l == 3)
    1794             :   {
    1795        3058 :     ulong mm = m[2];
    1796        3058 :     if (b < 0)
    1797             :     {
    1798        3058 :       ulong t = Fl_mul(umodiu(a, mm), -b, mm);
    1799        3058 :       return t? utoipos(mm - t): gen_0;
    1800             :     }
    1801             :     else
    1802           0 :       return utoi( Fl_mul(umodiu(a, mm), b, mm) );
    1803             :   } else {
    1804       14232 :     pari_sp av = avma;
    1805             :     GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1806       14232 :     (void)new_chunk(lg(a)+1+(l<<1));
    1807       14232 :     p = mulis(a,b);
    1808       14232 :     set_avma(av); return modii(p,m);
    1809             :   }
    1810             : }
    1811             : 
    1812             : INLINE GEN
    1813    24065753 : Fp_inv(GEN a, GEN m)
    1814             : {
    1815             :   GEN res;
    1816    24065753 :   if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
    1817    24065084 :   return res;
    1818             : }
    1819             : INLINE GEN
    1820      778242 : Fp_invsafe(GEN a, GEN m)
    1821             : {
    1822             :   GEN res;
    1823      778242 :   if (! invmod(a,m,&res)) return NULL;
    1824      778161 :   return res;
    1825             : }
    1826             : INLINE GEN
    1827     1462407 : Fp_div(GEN a, GEN b, GEN m)
    1828             : {
    1829     1462407 :   pari_sp av = avma;
    1830             :   GEN p;
    1831     1462407 :   if (lgefint(b) == 3)
    1832             :   {
    1833      489849 :     a = Fp_divu(a, b[2], m);
    1834      489849 :     if (signe(b) < 0) a = Fp_neg(a, m);
    1835      489849 :     return a;
    1836             :   }
    1837             :   /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1838      972558 :   (void)new_chunk(lg(a)+(lg(m)<<1));
    1839      972558 :   p = mulii(a, Fp_inv(b,m));
    1840      972558 :   set_avma(av); return modii(p,m);
    1841             : }
    1842             : INLINE GEN
    1843     1654989 : Fp_divu(GEN x, ulong a, GEN p)
    1844             : {
    1845     1654989 :   pari_sp av = avma;
    1846             :   ulong b;
    1847     1654989 :   if (lgefint(p) == 3)
    1848             :   {
    1849     1356786 :     ulong pp = p[2], xp = umodiu(x, pp);
    1850     1356786 :     return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
    1851             :   }
    1852      298203 :   x = Fp_red(x, p);
    1853      298202 :   b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
    1854      298207 :   return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
    1855             : }
    1856             : 
    1857             : INLINE GEN
    1858     1140743 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
    1859             : 
    1860             : INLINE GEN
    1861     1904617 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1862             : 
    1863             : INLINE long
    1864     2472672 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
    1865             : 
    1866             : INLINE long
    1867     1927959 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
    1868             : 
    1869             : INLINE GEN
    1870         406 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1871             : 
    1872             : INLINE long
    1873      376187 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1874             : 
    1875             : INLINE long
    1876      201481 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1877             : 
    1878             : INLINE GEN
    1879    23837352 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1880             : 
    1881             : INLINE long
    1882    64297038 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
    1883             : 
    1884             : INLINE long
    1885    83069649 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1886             : 
    1887             : INLINE GEN
    1888        7956 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1889             : 
    1890             : INLINE long
    1891      234932 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1892             : 
    1893             : INLINE long
    1894      290934 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1895             : 
    1896             : INLINE GEN
    1897     2634571 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1898             : 
    1899             : INLINE long
    1900     6528389 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1901             : 
    1902             : INLINE long
    1903     5236940 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1904             : 
    1905             : INLINE GEN
    1906      146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1907             : 
    1908             : INLINE long
    1909       34808 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1910             : 
    1911             : INLINE long
    1912        2259 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1913             : 
    1914             : /*******************************************************************/
    1915             : /*                                                                 */
    1916             : /*                        ADDMULII / SUBMULII                      */
    1917             : /*                                                                 */
    1918             : /*******************************************************************/
    1919             : /* x - y*z */
    1920             : INLINE GEN
    1921    43298157 : submulii(GEN x, GEN y, GEN z)
    1922             : {
    1923    43298157 :   long lx = lgefint(x), ly, lz;
    1924             :   pari_sp av;
    1925             :   GEN t;
    1926    43298157 :   if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
    1927    38377115 :   ly = lgefint(y);
    1928    38377115 :   if (ly == 2) return icopy(x);
    1929    36320274 :   lz = lgefint(z);
    1930    36320274 :   av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
    1931    36320274 :   t = mulii(z, y);
    1932    36320274 :   set_avma(av); return subii(x,t);
    1933             : }
    1934             : /* y*z - x */
    1935             : INLINE GEN
    1936     2694365 : mulsubii(GEN y, GEN z, GEN x)
    1937             : {
    1938     2694365 :   long lx = lgefint(x), ly, lz;
    1939             :   pari_sp av;
    1940             :   GEN t;
    1941     2694365 :   if (lx == 2) return mulii(z,y);
    1942     1671125 :   ly = lgefint(y);
    1943     1671125 :   if (ly == 2) return negi(x);
    1944     1497259 :   lz = lgefint(z);
    1945     1497259 :   av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
    1946     1497311 :   t = mulii(z, y);
    1947     1497251 :   set_avma(av); return subii(t,x);
    1948             : }
    1949             : 
    1950             : /* x - u*y */
    1951             : INLINE GEN
    1952        7693 : submuliu(GEN x, GEN y, ulong u)
    1953             : {
    1954             :   pari_sp av;
    1955        7693 :   long ly = lgefint(y);
    1956        7693 :   if (ly == 2) return icopy(x);
    1957        7693 :   av = avma;
    1958        7693 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1959        7693 :   y = mului(u,y);
    1960        7693 :   set_avma(av); return subii(x, y);
    1961             : }
    1962             : /* x + u*y */
    1963             : INLINE GEN
    1964      306275 : addmuliu(GEN x, GEN y, ulong u)
    1965             : {
    1966             :   pari_sp av;
    1967      306275 :   long ly = lgefint(y);
    1968      306275 :   if (ly == 2) return icopy(x);
    1969      306275 :   av = avma;
    1970      306275 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1971      306275 :   y = mului(u,y);
    1972      306272 :   set_avma(av); return addii(x, y);
    1973             : }
    1974             : /* x - u*y */
    1975             : INLINE GEN
    1976   147898423 : submuliu_inplace(GEN x, GEN y, ulong u)
    1977             : {
    1978             :   pari_sp av;
    1979   147898423 :   long ly = lgefint(y);
    1980   147898423 :   if (ly == 2) return x;
    1981   102364770 :   av = avma;
    1982   102364770 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1983   102372098 :   y = mului(u,y);
    1984   102369339 :   set_avma(av); return subii(x, y);
    1985             : }
    1986             : /* x + u*y */
    1987             : INLINE GEN
    1988   144962161 : addmuliu_inplace(GEN x, GEN y, ulong u)
    1989             : {
    1990             :   pari_sp av;
    1991   144962161 :   long ly = lgefint(y);
    1992   144962161 :   if (ly == 2) return x;
    1993   101355413 :   av = avma;
    1994   101355413 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1995   101362239 :   y = mului(u,y);
    1996   101359787 :   set_avma(av); return addii(x, y);
    1997             : }
    1998             : /* ux + vy */
    1999             : INLINE GEN
    2000    32647936 : lincombii(GEN u, GEN v, GEN x, GEN y)
    2001             : {
    2002    32647936 :   long lx = lgefint(x), ly;
    2003             :   GEN p1, p2;
    2004             :   pari_sp av;
    2005    32647936 :   if (lx == 2) return mulii(v,y);
    2006    18876448 :   ly = lgefint(y);
    2007    18876448 :   if (ly == 2) return mulii(u,x);
    2008    16331845 :   av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
    2009    16335615 :   p1 = mulii(u,x);
    2010    16333303 :   p2 = mulii(v,y);
    2011    16333299 :   set_avma(av); return addii(p1,p2);
    2012             : }
    2013             : 
    2014             : /*******************************************************************/
    2015             : /*                                                                 */
    2016             : /*                          GEN SUBTYPES                           */
    2017             : /*                                                                 */
    2018             : /*******************************************************************/
    2019             : 
    2020             : INLINE int
    2021  3980748349 : is_const_t(long t) { return (t < t_POLMOD); }
    2022             : INLINE int
    2023        6841 : is_extscalar_t(long t) { return (t <= t_POL); }
    2024             : INLINE int
    2025     8214474 : is_intreal_t(long t) { return (t <= t_REAL); }
    2026             : INLINE int
    2027   583818277 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
    2028             : INLINE int
    2029    84755746 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
    2030             : INLINE int
    2031           0 : is_qfb_t(long t) { return (t == t_QFB); }
    2032             : INLINE int
    2033     3648490 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
    2034             : INLINE int
    2035     1180237 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
    2036             : INLINE int
    2037  6851599147 : is_recursive_t(long t) { return lontyp[t]; }
    2038             : INLINE int
    2039   224514309 : is_scalar_t(long t) { return (t < t_POL); }
    2040             : INLINE int
    2041     1426950 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
    2042             : 
    2043             : INLINE int
    2044    56152610 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
    2045             : 
    2046             : /*******************************************************************/
    2047             : /*                                                                 */
    2048             : /*                         TRANSCENDENTAL                          */
    2049             : /*                                                                 */
    2050             : /*******************************************************************/
    2051             : INLINE GEN
    2052    57501263 : sqrtr(GEN x) {
    2053    57501263 :   long s = signe(x);
    2054    57501263 :   if (s == 0) return real_0_bit(expo(x) >> 1);
    2055    57468173 :   if (s >= 0) return sqrtr_abs(x);
    2056      259841 :   retmkcomplex(gen_0, sqrtr_abs(x));
    2057             : }
    2058             : INLINE GEN
    2059           0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
    2060             : INLINE GEN
    2061           0 : cbrtr(GEN x) {
    2062           0 :   long s = signe(x);
    2063             :   GEN r;
    2064           0 :   if (s == 0) return real_0_bit(expo(x) / 3);
    2065           0 :   r = cbrtr_abs(x);
    2066           0 :   if (s < 0) togglesign(r);
    2067           0 :   return r;
    2068             : }
    2069             : INLINE GEN
    2070     1090529 : sqrtnr(GEN x, long n) {
    2071     1090529 :   long s = signe(x);
    2072             :   GEN r;
    2073     1090529 :   if (s == 0) return real_0_bit(expo(x) / n);
    2074     1090529 :   r = sqrtnr_abs(x, n);
    2075     1090556 :   if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
    2076     1090556 :   return r;
    2077             : }
    2078             : INLINE long
    2079      598249 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
    2080             : INLINE ulong
    2081     2814161 : ulogint(ulong B, ulong y)
    2082             : {
    2083             :   ulong r;
    2084             :   long e;
    2085     2814161 :   if (y == 2) return expu(B);
    2086     2758206 :   r = y;
    2087     2758206 :   for (e=1;; e++)
    2088             :   { /* here, r = y^e, r2 = y^(e-1) */
    2089     8387923 :     if (r >= B) return r == B? e: e-1;
    2090     5631200 :     r = umuluu_or_0(y, r);
    2091     5631281 :     if (!r) return e;
    2092             :   }
    2093             : }
    2094             : 
    2095             : /*******************************************************************/
    2096             : /*                                                                 */
    2097             : /*                         MISCELLANEOUS                           */
    2098             : /*                                                                 */
    2099             : /*******************************************************************/
    2100     8214382 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
    2101  2507154937 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
    2102    14790366 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
    2103     4347315 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
    2104  1011539648 : INLINE int equali1(GEN n)
    2105  1011539648 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
    2106   136870507 : INLINE int equalim1(GEN n)
    2107   136870507 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
    2108             : /* works only for POSITIVE integers */
    2109  2466051719 : INLINE int is_pm1(GEN n)
    2110  2466051719 : { return lgefint(n) == 3 && n[2] == 1; }
    2111   480451791 : INLINE int is_bigint(GEN n)
    2112   480451791 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
    2113             : 
    2114  1831241035 : INLINE int odd(long x) { return x & 1; }
    2115    62349906 : INLINE int both_odd(long x, long y) { return x & y & 1; }
    2116             : 
    2117             : INLINE int
    2118  6151326030 : isonstack(GEN x)
    2119  6151326030 : { return ((pari_sp)x >= pari_mainstack->bot
    2120  6151326030 :        && (pari_sp)x <  pari_mainstack->top); }
    2121             : 
    2122             : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
    2123             : INLINE double
    2124    60318063 : dbllog2r(GEN x)
    2125    60318063 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
    2126             : 
    2127             : INLINE GEN
    2128     1318649 : mul_content(GEN cx, GEN cy)
    2129             : {
    2130     1318649 :   if (!cx) return cy;
    2131      540549 :   if (!cy) return cx;
    2132      346729 :   return gmul(cx,cy);
    2133             : }
    2134             : INLINE GEN
    2135           0 : inv_content(GEN c) { return c? ginv(c): NULL; }
    2136             : INLINE GEN
    2137       36358 : div_content(GEN cx, GEN cy)
    2138             : {
    2139       36358 :   if (!cy) return cx;
    2140       35308 :   if (!cx) return ginv(cy);
    2141        7214 :   return gdiv(cx,cy);
    2142             : }
    2143             : INLINE GEN
    2144     5306980 : mul_denom(GEN dx, GEN dy)
    2145             : {
    2146     5306980 :   if (!dx) return dy;
    2147     1586959 :   if (!dy) return dx;
    2148      643080 :   return mulii(dx,dy);
    2149             : }
    2150             : 
    2151             : /* POLYNOMIALS */
    2152             : INLINE GEN
    2153     1284116 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
    2154             : INLINE GEN
    2155    77389057 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
    2156             : INLINE ulong
    2157      652673 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
    2158             : INLINE ulong
    2159       38629 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
    2160             : INLINE long
    2161  4489339576 : degpol(GEN x) { return lg(x)-3; }
    2162             : INLINE long
    2163  2286644079 : lgpol(GEN x) { return lg(x)-2; }
    2164             : INLINE long
    2165   282260630 : lgcols(GEN x) { return lg(gel(x,1)); }
    2166             : INLINE long
    2167   131586716 : nbrows(GEN x) { return lg(gel(x,1))-1; }
    2168             : INLINE GEN
    2169           0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
    2170             : 
    2171             : INLINE GEN
    2172     1429849 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
    2173             : INLINE GEN
    2174      576784 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
    2175             : 
    2176             : INLINE GEN
    2177    96466850 : RgX_copy(GEN x)
    2178             : {
    2179             :   long lx, i;
    2180    96466850 :   GEN y = cgetg_copy(x, &lx); y[1] = x[1];
    2181   351324338 :   for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
    2182    96466883 :   return y;
    2183             : }
    2184             : /* have to use ulong to avoid silly warnings from gcc "assuming signed
    2185             :  * overflow does not occur" */
    2186             : INLINE GEN
    2187     2243253 : RgX_coeff(GEN x, long n)
    2188             : {
    2189     2243253 :   ulong l = lg(x);
    2190     2243253 :   return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
    2191             : }
    2192             : INLINE GEN
    2193      345537 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
    2194             : INLINE GEN
    2195     6840303 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
    2196             : INLINE GEN
    2197        1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
    2198             : INLINE GEN
    2199      104610 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
    2200             : INLINE GEN
    2201     4514358 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
    2202             : INLINE GEN
    2203    22658290 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
    2204             : INLINE GEN
    2205     1265801 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
    2206             : INLINE GEN
    2207           0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
    2208             : INLINE GEN
    2209    92976962 : pol0_Flx(long sv) { return mkvecsmall(sv); }
    2210             : INLINE GEN
    2211    50980584 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
    2212             : INLINE GEN
    2213    34602612 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
    2214             : INLINE GEN
    2215           0 : zero_zx(long sv) { return zero_Flx(sv); }
    2216             : INLINE GEN
    2217           0 : polx_zx(long sv) { return polx_Flx(sv); }
    2218             : INLINE GEN
    2219           0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
    2220             : INLINE GEN
    2221       14042 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
    2222             : INLINE GEN
    2223        1357 : zero_F2x(long sv) { return zero_Flx(sv); }
    2224             : INLINE GEN
    2225    11861497 : pol0_F2x(long sv) { return pol0_Flx(sv); }
    2226             : INLINE GEN
    2227     3293580 : pol1_F2x(long sv) { return pol1_Flx(sv); }
    2228             : INLINE GEN
    2229     1009864 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
    2230             : INLINE int
    2231     1031867 : F2x_equal1(GEN x) { return Flx_equal1(x); }
    2232             : INLINE int
    2233     3382243 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
    2234             : INLINE GEN
    2235    56877877 : F2x_copy(GEN x) { return leafcopy(x); }
    2236             : INLINE GEN
    2237        4074 : F2v_copy(GEN x) { return leafcopy(x); }
    2238             : INLINE GEN
    2239     2358304 : Flv_copy(GEN x) { return leafcopy(x); }
    2240             : INLINE GEN
    2241   163213724 : Flx_copy(GEN x) { return leafcopy(x); }
    2242             : INLINE GEN
    2243     4101144 : vecsmall_copy(GEN x) { return leafcopy(x); }
    2244             : INLINE int
    2245     7829468 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
    2246             : INLINE int
    2247       19366 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
    2248             : INLINE int
    2249     5721913 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
    2250             : 
    2251             : INLINE GEN
    2252   122627606 : ZX_renormalize(GEN x, long lx)    { return ZXX_renormalize(x,lx); }
    2253             : INLINE GEN
    2254    98698608 : FpX_renormalize(GEN x, long lx)   { return ZXX_renormalize(x,lx); }
    2255             : INLINE GEN
    2256      676857 : FpXX_renormalize(GEN x, long lx)  { return ZXX_renormalize(x,lx); }
    2257             : INLINE GEN
    2258     4251191 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
    2259             : INLINE GEN
    2260   113905170 : F2x_renormalize(GEN x, long lx)   { return Flx_renormalize(x,lx); }
    2261             : INLINE GEN
    2262       38393 : F2v_to_F2x(GEN x, long sv) {
    2263       38393 :   GEN y = leafcopy(x);
    2264       38393 :   y[1] = sv; F2x_renormalize(y, lg(y)); return y;
    2265             : }
    2266             : 
    2267             : INLINE long
    2268         378 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
    2269             : 
    2270             : INLINE long
    2271        4655 : gval(GEN x, long v)
    2272        4655 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
    2273             : 
    2274             : INLINE void
    2275      490087 : RgX_shift_inplace_init(long v)
    2276      490087 : { if (v) (void)cgetg(v, t_VECSMALL); }
    2277             : /* shift polynomial in place. assume v free cells have been left before x */
    2278             : INLINE GEN
    2279      490087 : RgX_shift_inplace(GEN x, long v)
    2280             : {
    2281             :   long i, lx;
    2282             :   GEN z;
    2283      490087 :   if (!v) return x;
    2284      253165 :   lx = lg(x);
    2285      253165 :   if (lx == 2) return x;
    2286      253165 :   z = x + lx;
    2287             :   /* stackdummy's from normalizepol */
    2288      253165 :   while (lg(z) != v) z += lg(z);
    2289      253165 :   z += v;
    2290     4654452 :   for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
    2291      675883 :   for (i = 0;  i < v; i++) gel(--z,0) = gen_0;
    2292      253165 :   z -= 2;
    2293      253165 :   z[1] = x[1];
    2294      253165 :   z[0] = evaltyp(t_POL) | evallg(lx+v);
    2295      253165 :   stackdummy((pari_sp)z, (pari_sp)x); return z;
    2296             : }
    2297             : 
    2298             : 
    2299             : /* LINEAR ALGEBRA */
    2300             : INLINE GEN
    2301      486780 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
    2302             : INLINE GEN
    2303     6934102 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
    2304             : INLINE GEN
    2305     3418316 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
    2306             : INLINE GEN
    2307           0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
    2308             : INLINE GEN
    2309      104139 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
    2310             : INLINE GEN
    2311           0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
    2312             : INLINE GEN
    2313           0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
    2314             : INLINE GEN
    2315    28143648 : zero_zv(long x) { return zero_Flv(x); }
    2316             : INLINE GEN
    2317         266 : zm_transpose(GEN x) { return Flm_transpose(x); }
    2318             : INLINE GEN
    2319           0 : zm_copy(GEN x) { return Flm_copy(x); }
    2320             : INLINE GEN
    2321     2130826 : zv_copy(GEN x) { return Flv_copy(x); }
    2322             : INLINE GEN
    2323           0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
    2324             : 
    2325             : INLINE GEN
    2326     9973365 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
    2327             : INLINE GEN
    2328      313773 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
    2329             : INLINE GEN
    2330     2514573 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
    2331             : INLINE void
    2332     9173252 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
    2333             : INLINE GEN
    2334    18045332 : RgM_shallowcopy(GEN x)
    2335             : {
    2336             :   long l;
    2337    18045332 :   GEN y = cgetg_copy(x, &l);
    2338    93707065 :   while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
    2339    18045088 :   return y;
    2340             : }
    2341             : INLINE GEN
    2342      199285 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
    2343             : 
    2344             : INLINE GEN
    2345           0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
    2346             : 
    2347             : INLINE GEN
    2348     5773084 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
    2349             : 
    2350             : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
    2351             :  * x,y are ZV of the same length */
    2352             : INLINE int
    2353       23240 : ZV_dvd(GEN x, GEN y)
    2354             : {
    2355       23240 :   long i, l = lg(x);
    2356       36722 :   for (i=1; i < l; i++)
    2357       29575 :     if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
    2358        7147 :   return 1;
    2359             : }
    2360             : 
    2361             : /* Fq */
    2362             : INLINE GEN
    2363     2563488 : Fq_red(GEN x, GEN T, GEN p)
    2364     2563488 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
    2365             : INLINE GEN
    2366      101219 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
    2367             : {
    2368             :   (void) p;
    2369      101219 :   return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
    2370             : }
    2371             : INLINE GEN
    2372         756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
    2373             : 
    2374             : INLINE GEN
    2375       14624 : gener_Fq_local(GEN T, GEN p, GEN L)
    2376           0 : { return T? gener_FpXQ_local(T,p, L)
    2377       14624 :           : pgener_Fp_local(p, L); }
    2378             : 
    2379             : /* FpXQX */
    2380             : INLINE GEN
    2381        4417 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
    2382             : INLINE GEN
    2383      163871 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
    2384             : INLINE GEN
    2385       33376 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
    2386             : 
    2387             : INLINE GEN
    2388       20006 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    2389       20006 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
    2390             : 
    2391             : /* FqX */
    2392             : INLINE GEN
    2393       25144 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
    2394             : INLINE GEN
    2395      105343 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
    2396             : INLINE GEN
    2397       24313 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
    2398             : INLINE GEN
    2399       66458 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
    2400             : INLINE GEN
    2401      546195 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
    2402      546195 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
    2403             : INLINE GEN
    2404      404743 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
    2405      404743 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
    2406             : INLINE GEN
    2407      364867 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
    2408      364867 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
    2409             : INLINE GEN
    2410       17510 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
    2411       17510 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
    2412             : INLINE GEN
    2413       69678 : FqX_sqr(GEN x, GEN T, GEN p)
    2414       69678 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
    2415             : INLINE GEN
    2416        1281 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
    2417        1281 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
    2418             : INLINE GEN
    2419       18774 : FqX_halve(GEN x, GEN T, GEN p)
    2420       18774 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
    2421             : INLINE GEN
    2422       38884 : FqX_div(GEN x, GEN y, GEN T, GEN p)
    2423       38884 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
    2424             : INLINE GEN
    2425        6081 : FqX_get_red(GEN S, GEN T, GEN p)
    2426        6081 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
    2427             : INLINE GEN
    2428       31086 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
    2429       31086 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
    2430             : INLINE GEN
    2431           0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
    2432           0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
    2433             : INLINE GEN
    2434        5936 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
    2435        5936 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
    2436             : INLINE GEN
    2437           0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
    2438           0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
    2439             : INLINE GEN
    2440      260911 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
    2441      260911 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
    2442             : INLINE GEN
    2443      425995 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
    2444      425995 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
    2445             : INLINE GEN
    2446        3969 : FqX_normalize(GEN z, GEN T, GEN p)
    2447        3969 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
    2448             : INLINE GEN
    2449      291893 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
    2450             : INLINE GEN
    2451           0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
    2452             : INLINE GEN
    2453       86456 : FqX_factor(GEN f, GEN T, GEN p)
    2454       86456 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
    2455             : INLINE GEN
    2456           7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
    2457           7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
    2458             : INLINE GEN
    2459           7 : FqX_ddf(GEN f, GEN T, GEN p)
    2460           7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
    2461             : INLINE GEN
    2462       63112 : FqX_degfact(GEN f, GEN T, GEN p)
    2463       63112 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
    2464             : INLINE GEN
    2465        7147 : FqX_roots(GEN f, GEN T, GEN p)
    2466        7147 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
    2467             : INLINE GEN
    2468         175 : FqX_to_mod(GEN f, GEN T, GEN p)
    2469         175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
    2470             : 
    2471             : /*FqXQ*/
    2472             : INLINE GEN
    2473           0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
    2474           0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
    2475             : INLINE GEN
    2476           0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
    2477           0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
    2478             : INLINE GEN
    2479           0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
    2480           0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
    2481             : INLINE GEN
    2482           0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
    2483           0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
    2484             : INLINE GEN
    2485           0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
    2486           0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
    2487             : INLINE GEN
    2488       22320 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
    2489       22320 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
    2490             : INLINE GEN
    2491           0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
    2492           0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
    2493             : INLINE GEN
    2494           0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
    2495           0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
    2496             : 
    2497             : /*FqXn*/
    2498             : INLINE GEN
    2499        6610 : FqXn_expint(GEN x, long n, GEN T, GEN p)
    2500        6610 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
    2501             : INLINE GEN
    2502           0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
    2503           0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
    2504             : INLINE GEN
    2505        6916 : FqXn_inv(GEN x, long n, GEN T, GEN p)
    2506        6916 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
    2507             : INLINE GEN
    2508      254926 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
    2509      254926 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
    2510             : INLINE GEN
    2511           0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
    2512           0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
    2513             : 
    2514             : /*FpXQ*/
    2515             : INLINE GEN
    2516           0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
    2517           0 : { (void)T; return FpX_add(x,y,p); }
    2518             : INLINE GEN
    2519           0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
    2520           0 : { (void)T; return FpX_sub(x,y,p); }
    2521             : 
    2522             : /*Flxq*/
    2523             : INLINE GEN
    2524           0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
    2525           0 : { (void)T; return Flx_add(x,y,p); }
    2526             : INLINE GEN
    2527           0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
    2528           0 : { (void)T; return Flx_sub(x,y,p); }
    2529             : 
    2530             : /* F2x */
    2531             : 
    2532             : INLINE ulong
    2533   539028979 : F2x_coeff(GEN x,long v)
    2534             : {
    2535   539028979 :    ulong u=(ulong)x[2+divsBIL(v)];
    2536   539027789 :    return (u>>remsBIL(v))&1UL;
    2537             : }
    2538             : 
    2539             : INLINE void
    2540    12330224 : F2x_clear(GEN x,long v)
    2541             : {
    2542    12330224 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2543    12330166 :    *u&=~(1UL<<remsBIL(v));
    2544    12330175 : }
    2545             : 
    2546             : INLINE void
    2547   119797422 : F2x_set(GEN x,long v)
    2548             : {
    2549   119797422 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2550   119781319 :    *u|=1UL<<remsBIL(v);
    2551   119774916 : }
    2552             : 
    2553             : INLINE void
    2554     1564591 : F2x_flip(GEN x,long v)
    2555             : {
    2556     1564591 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2557     1564591 :    *u^=1UL<<remsBIL(v);
    2558     1564591 : }
    2559             : 
    2560             : /* F2v */
    2561             : 
    2562             : INLINE ulong
    2563   532263321 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
    2564             : 
    2565             : INLINE void
    2566    12330236 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
    2567             : 
    2568             : INLINE void
    2569    94176703 : F2v_set(GEN x,long v)   { F2x_set(x,v-1); }
    2570             : 
    2571             : INLINE void
    2572     1564591 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
    2573             : 
    2574             : /* F2m */
    2575             : 
    2576             : INLINE ulong
    2577     6852248 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
    2578             : 
    2579             : INLINE void
    2580           0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
    2581             : 
    2582             : INLINE void
    2583         672 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
    2584             : 
    2585             : INLINE void
    2586     1564592 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
    2587             : 
    2588             : /* F3m */
    2589             : 
    2590             : INLINE ulong
    2591     1919366 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
    2592             : 
    2593             : INLINE void
    2594           0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
    2595             : 
    2596             : /* ARITHMETIC */
    2597             : INLINE GEN
    2598       34125 : matpascal(long n) { return matqpascal(n, NULL); }
    2599             : INLINE long
    2600      523444 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
    2601             : INLINE long
    2602          98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
    2603             : INLINE GEN
    2604     4946709 : sqrti(GEN x) { return sqrtremi(x,NULL); }
    2605             : INLINE GEN
    2606   128398173 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
    2607             : INLINE int
    2608      551628 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
    2609             : INLINE int
    2610       24976 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
    2611             : INLINE GEN
    2612           0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
    2613             : INLINE GEN
    2614           0 : gminsg(long s, GEN y) { return gmings(y,s); }
    2615             : INLINE GEN
    2616    47096183 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
    2617             : INLINE GEN
    2618   132229460 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
    2619             : INLINE GEN
    2620     1389562 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
    2621             : INLINE GEN
    2622      709451 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
    2623             : 
    2624             : INLINE GEN
    2625    13508495 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
    2626             : INLINE GEN
    2627      868432 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
    2628             : 
    2629             : /* x t_COMPLEX */
    2630             : INLINE GEN
    2631    77049284 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
    2632             : /* q t_QUAD */
    2633             : INLINE GEN
    2634       69860 : quadnorm(GEN q)
    2635             : {
    2636       69860 :   GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
    2637       69860 :   GEN z, u = gel(q,3), v = gel(q,2);
    2638       69860 :   if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
    2639             :   {
    2640       69671 :     z = signe(b)? mulii(v, addii(u,v)): sqri(v);
    2641       69671 :     return addii(z, mulii(c, sqri(u)));
    2642             :   }
    2643             :   else
    2644             :   {
    2645         189 :     z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
    2646         189 :     return gadd(z, gmul(c, gsqr(u)));
    2647             :   }
    2648             : }
    2649             : /* x a t_QUAD, return the attached discriminant */
    2650             : INLINE GEN
    2651        1071 : quad_disc(GEN x)
    2652             : {
    2653        1071 :   GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
    2654        1071 :   if (is_pm1(b)) return subsi(1, c4);
    2655         154 :   togglesign_safe(&c4); return c4;
    2656             : }
    2657             : INLINE GEN
    2658       85015 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
    2659             : INLINE GEN
    2660    18274662 : qfb_disc(GEN x) { return gel(x,4); }
    2661             : 
    2662             : INLINE GEN
    2663     2977346 : sqrfrac(GEN x)
    2664             : {
    2665     2977346 :   GEN z = cgetg(3,t_FRAC);
    2666     2977346 :   gel(z,1) = sqri(gel(x,1));
    2667     2977346 :   gel(z,2) = sqri(gel(x,2)); return z;
    2668             : }
    2669             : 
    2670             : INLINE void
    2671    14344255 : normalize_frac(GEN z) {
    2672    14344255 :   if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
    2673    14344255 : }
    2674             : 
    2675             : INLINE GEN
    2676      663633 : powii(GEN x, GEN n)
    2677             : {
    2678      663633 :   long ln = lgefint(n);
    2679      663633 :   if (ln == 3) {
    2680             :     GEN z;
    2681      641111 :     if (signe(n) > 0) return powiu(x, n[2]);
    2682       69694 :     z = cgetg(3, t_FRAC);
    2683       69702 :     gel(z,1) = gen_1;
    2684       69702 :     gel(z,2) = powiu(x, n[2]);
    2685       69704 :     return z;
    2686             :   }
    2687       22522 :   if (ln == 2) return gen_1; /* rare */
    2688             :   /* should never happen */
    2689           0 :   return powgi(x, n); /* overflow unless x = 0, 1, -1 */
    2690             : }
    2691             : INLINE GEN
    2692        1575 : powIs(long n) {
    2693        1575 :   switch(n & 3)
    2694             :   {
    2695          63 :     case 1: return mkcomplex(gen_0,gen_1);
    2696         385 :     case 2: return gen_m1;
    2697         721 :     case 3: return mkcomplex(gen_0,gen_m1);
    2698             :   }
    2699         406 :   return gen_1;
    2700             : }
    2701             : 
    2702             : /*******************************************************************/
    2703             : /*                                                                 */
    2704             : /*                             ASSIGNMENTS                         */
    2705             : /*                                                                 */
    2706             : /*******************************************************************/
    2707           0 : INLINE void mpexpz(GEN x, GEN z)
    2708           0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
    2709           0 : INLINE void mplogz(GEN x, GEN z)
    2710           0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
    2711           0 : INLINE void mpcosz(GEN x, GEN z)
    2712           0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
    2713           0 : INLINE void mpsinz(GEN x, GEN z)
    2714           0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
    2715           0 : INLINE void gnegz(GEN x, GEN z)
    2716           0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
    2717           0 : INLINE void gabsz(GEN x, long prec, GEN z)
    2718           0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
    2719           0 : INLINE void gaddz(GEN x, GEN y, GEN z)
    2720           0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
    2721           0 : INLINE void gsubz(GEN x, GEN y, GEN z)
    2722           0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
    2723           0 : INLINE void gmulz(GEN x, GEN y, GEN z)
    2724           0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
    2725           0 : INLINE void gdivz(GEN x, GEN y, GEN z)
    2726           0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
    2727           0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
    2728           0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
    2729           0 : INLINE void gmodz(GEN x, GEN y, GEN z)
    2730           0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
    2731           0 : INLINE void gmul2nz(GEN x, long s, GEN z)
    2732           0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
    2733           0 : INLINE void gshiftz(GEN x, long s, GEN z)
    2734           0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
    2735             : 
    2736             : /*******************************************************************/
    2737             : /*                                                                 */
    2738             : /*                       ELLIPTIC CURVES                           */
    2739             : /*                                                                 */
    2740             : /*******************************************************************/
    2741     4215484 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
    2742     3208994 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
    2743     4041737 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
    2744     3978595 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
    2745     4764758 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
    2746     3390756 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
    2747     1058130 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
    2748     1664176 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
    2749     1490531 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
    2750     6094740 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
    2751     7292781 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
    2752     9251766 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
    2753     1044209 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
    2754     9926449 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
    2755     1571397 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
    2756      683553 : INLINE GEN ellff_get_a4a6(GEN x)  { return gmael(x, 15, 2); }
    2757        1484 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
    2758         315 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
    2759        1134 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
    2760       37562 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
    2761       17246 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
    2762      735255 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
    2763          70 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
    2764             : 
    2765     4140215 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
    2766    38713722 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
    2767      931122 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
    2768             : 
    2769             : /*******************************************************************/
    2770             : /*                                                                 */
    2771             : /*                    ALGEBRAIC NUMBER THEORY                      */
    2772             : /*                                                                 */
    2773             : /*******************************************************************/
    2774    16980424 : INLINE GEN modpr_get_pr(GEN x)  { return gel(x,3); }
    2775      725135 : INLINE GEN modpr_get_p(GEN x)  { return pr_get_p(modpr_get_pr(x)); }
    2776     7118905 : INLINE GEN modpr_get_T(GEN x)  { return lg(x) == 4? NULL: gel(x,4); }
    2777             : 
    2778    69509107 : INLINE GEN pr_get_p(GEN pr)  { return gel(pr,1); }
    2779     9044121 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
    2780             : /* .[2] instead of itos works: e and f are small positive integers */
    2781     8675370 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
    2782    24047809 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
    2783    45533329 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
    2784             : INLINE int
    2785     5837122 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
    2786             : INLINE GEN
    2787     1213271 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
    2788             : INLINE ulong
    2789      339009 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
    2790             : 
    2791             : /* assume nf a genuine nf */
    2792             : INLINE long
    2793      829511 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
    2794             : INLINE GEN
    2795    67496061 : nf_get_pol(GEN nf) { return gel(nf,1); }
    2796             : INLINE long
    2797    47302098 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
    2798             : INLINE long
    2799     4085376 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
    2800             : INLINE long
    2801        4007 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
    2802             : INLINE GEN
    2803      450552 : nf_get_disc(GEN nf) { return gel(nf,3); }
    2804             : INLINE GEN
    2805     2459976 : nf_get_index(GEN nf) { return gel(nf,4); }
    2806             : INLINE GEN
    2807     3938567 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
    2808             : INLINE GEN
    2809      547115 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
    2810             : INLINE GEN
    2811     1316310 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
    2812             : INLINE GEN
    2813       22194 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
    2814             : INLINE GEN
    2815        6034 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
    2816             : INLINE GEN
    2817       55265 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
    2818             : INLINE GEN
    2819     1234103 : nf_get_roots(GEN nf) { return gel(nf,6); }
    2820             : INLINE GEN
    2821        1792 : nf_get_zk(GEN nf)
    2822             : {
    2823        1792 :   GEN y = gel(nf,7), D = gel(y, 1);
    2824        1792 :   if (typ(D) == t_POL) D = gel(D, 2);
    2825        1792 :   if (!equali1(D)) y = gdiv(y, D);
    2826        1792 :   return y;
    2827             : }
    2828             : INLINE GEN
    2829     3133280 : nf_get_zkprimpart(GEN nf)
    2830             : {
    2831     3133280 :   GEN y = gel(nf,7);
    2832             :   /* test for old format of nf.zk: non normalized */
    2833     3133280 :   if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
    2834     3133279 :   return y;
    2835             : }
    2836             : INLINE GEN
    2837     3179965 : nf_get_zkden(GEN nf)
    2838             : {
    2839     3179965 :   GEN y = gel(nf,7), D = gel(y,1);
    2840     3179965 :   if (typ(D) == t_POL) D = gel(D,2);
    2841             :   /* test for old format of nf.zk: non normalized */
    2842     3179965 :   if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
    2843     3179952 :   return D;
    2844             : }
    2845             : INLINE GEN
    2846     7742680 : nf_get_invzk(GEN nf) { return gel(nf,8); }
    2847             : INLINE void
    2848      283422 : nf_get_sign(GEN nf, long *r1, long *r2)
    2849             : {
    2850      283422 :   GEN x = gel(nf,2);
    2851      283422 :   *r1 = itou(gel(x,1));
    2852      283422 :   *r2 = itou(gel(x,2));
    2853      283422 : }
    2854             : 
    2855             : INLINE GEN
    2856     1495985 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
    2857             : INLINE GEN
    2858      387530 : abgrp_get_no(GEN x) { return gel(x,1); }
    2859             : INLINE GEN
    2860     5872162 : abgrp_get_cyc(GEN x) { return gel(x,2); }
    2861             : INLINE GEN
    2862     1024261 : abgrp_get_gen(GEN x) { return gel(x,3); }
    2863             : INLINE GEN
    2864     5189592 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
    2865             : INLINE GEN
    2866     2868691 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
    2867             : INLINE GEN
    2868        8162 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
    2869             : INLINE GEN
    2870     1893306 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
    2871             : INLINE GEN
    2872      967066 : bnf_get_gen(GEN bnf)  { return abgrp_get_gen(bnf_get_clgp(bnf)); }
    2873             : INLINE GEN
    2874         625 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
    2875             : INLINE GEN
    2876     1479194 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
    2877             : INLINE GEN
    2878      661641 : bnf_get_sunits(GEN bnf)
    2879      661641 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
    2880             : INLINE GEN
    2881      289708 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
    2882             : INLINE long
    2883      264405 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
    2884             : INLINE GEN
    2885      287529 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
    2886             : INLINE GEN
    2887       26212 : nfV_to_scalar_or_alg(GEN nf, GEN x)
    2888       63261 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
    2889             : INLINE GEN
    2890       25777 : bnf_get_fu(GEN bnf) {
    2891       25777 :   GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
    2892       25778 :   if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
    2893       25778 :   return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
    2894             : }
    2895             : 
    2896             : INLINE GEN
    2897     1630618 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
    2898             : INLINE GEN
    2899      935265 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
    2900             : INLINE GEN
    2901      137676 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
    2902             : INLINE GEN
    2903      565053 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
    2904             : INLINE GEN
    2905     1717621 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
    2906             : INLINE GEN
    2907      311337 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
    2908             : INLINE GEN
    2909     1388956 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
    2910             : INLINE GEN
    2911          70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
    2912             : INLINE GEN
    2913        7847 : bnr_get_gen(GEN bnr) {
    2914        7847 :   GEN G = bnr_get_clgp(bnr);
    2915        7847 :   if (lg(G) !=  4)
    2916           0 :     pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
    2917        7847 :   return gel(G,3);
    2918             : }
    2919             : 
    2920             : /* localstar, used in gchar */
    2921             : INLINE GEN
    2922       49179 : locs_get_cyc(GEN locs) { return gel(locs,1); }
    2923             : INLINE GEN
    2924      190792 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
    2925             : INLINE GEN
    2926        1155 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
    2927             : INLINE GEN
    2928        7959 : locs_get_mod(GEN locs) { return gel(locs,4); }
    2929             : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
    2930             :  * return a t_MAT whose columns are the logs
    2931             :  * of generators of U_i(pr)/U_{i+1}(pr). */
    2932             : INLINE GEN
    2933        1155 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
    2934             : INLINE GEN
    2935      205996 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
    2936             : 
    2937             : /* G a grossenchar group */
    2938             : INLINE GEN
    2939       30553 : gchar_get_basis(GEN gc)  { return  gel(gc, 1); }
    2940             : INLINE GEN
    2941      205933 : gchar_get_bnf(GEN gc)    { return  gel(gc, 2); }
    2942             : INLINE GEN
    2943      237479 : gchar_get_nf(GEN gc)    { return  gel(gc, 3); }
    2944             : INLINE GEN
    2945      274565 : gchar_get_zm(GEN gc)     { return  gel(gc, 4); }
    2946             : INLINE GEN
    2947        7959 : gchar_get_mod(GEN gc)    { return  locs_get_mod(gchar_get_zm(gc)); }
    2948             : INLINE GEN
    2949        3969 : gchar_get_modP(GEN gc)    { return gmael(gchar_get_mod(gc),1,1); }
    2950             : INLINE GEN
    2951       35069 : gchar_get_S(GEN gc)      { return  gel(gc, 5); }
    2952             : INLINE GEN
    2953      187845 : gchar_get_DLdata(GEN gc)   { return  gel(gc, 6); }
    2954             : INLINE GEN
    2955        1821 : gchar_get_sfu(GEN gc) { return  gel(gc, 7); }
    2956             : INLINE GEN
    2957       15433 : gchar_get_cyc(GEN gc)    { return  gel(gc, 9); }
    2958             : INLINE GEN
    2959           0 : gchar_get_hnf(GEN gc)    { return  gmael(gc, 10, 1); }
    2960             : INLINE GEN
    2961           0 : gchar_get_U(GEN gc)      { return  gmael(gc, 10, 2); }
    2962             : INLINE GEN
    2963       10458 : gchar_get_Ui(GEN gc)     { return  gmael(gc, 10, 3); }
    2964             : INLINE GEN
    2965        3233 : gchar_get_m0(GEN gc)     { return gel(gc, 11); }
    2966             : INLINE GEN
    2967        4423 : gchar_get_u0(GEN gc)     { return gel(gc, 12); }
    2968             : INLINE long
    2969       16884 : gchar_get_r1(GEN gc)     { return nf_get_r1(gchar_get_nf(gc)); }
    2970             : INLINE long
    2971         525 : gchar_get_r2(GEN gc)     { return nf_get_r2(gchar_get_nf(gc)); }
    2972             : INLINE GEN
    2973       47746 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
    2974             : INLINE long
    2975       35265 : gchar_get_nc(GEN gc)     { return lg(gchar_get_loccyc(gc))-1; }
    2976             : INLINE long
    2977       35069 : gchar_get_ns(GEN gc)     { return lg(gchar_get_S(gc))-1; }
    2978             : INLINE long
    2979        1610 : gchar_get_nm(GEN gc)     { return lg(gchar_get_basis(gc))-1; }
    2980             : INLINE long
    2981        3934 : gchar_get_evalprec(GEN gc)   { return  gmael(gc, 8, 1)[1]; }
    2982             : INLINE long
    2983       17927 : gchar_get_prec(GEN gc)   { return  gmael(gc, 8, 1)[2]; }
    2984             : INLINE long
    2985       12663 : gchar_get_nfprec(GEN gc) { return  gmael(gc, 8, 1)[3]; }
    2986             : INLINE void
    2987        1624 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
    2988             : INLINE void
    2989        1118 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
    2990             : INLINE void
    2991        2939 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
    2992             : INLINE long
    2993         273 : gchar_get_ntors(GEN gc)   { return  gmael(gc, 8, 2)[1]; }
    2994             : INLINE long
    2995         273 : gchar_get_nfree(GEN gc)   { return  gmael(gc, 8, 2)[2]; }
    2996             : INLINE long
    2997        1818 : gchar_get_nalg(GEN gc)   { return  gmael(gc, 8, 2)[3]; }
    2998             : INLINE void
    2999        1412 : gchar_set_basis(GEN gc, GEN m_inv)  { gel(gc, 1) = m_inv; }
    3000             : INLINE void
    3001        2336 : gchar_set_nf(GEN gc, GEN nf)      { gel(gc, 3) = nf; }
    3002             : INLINE void
    3003         532 : gchar_set_ntors(GEN gc, long n)    { gmael(gc, 8, 2)[1] = n; }
    3004             : INLINE void
    3005         532 : gchar_set_nfree(GEN gc, long n)    { gmael(gc, 8, 2)[2] = n; }
    3006             : INLINE void
    3007         532 : gchar_set_nalg(GEN gc, long n)    { gmael(gc, 8, 2)[3] = n; }
    3008             : INLINE void
    3009        1412 : gchar_set_cyc(GEN gc, GEN cyc)      { gel(gc, 9) = cyc; }
    3010             : INLINE void
    3011         532 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
    3012             : INLINE void
    3013           0 : gchar_set_m0(GEN gc, GEN m0)     { gel(gc, 11) = m0; }
    3014             : INLINE void
    3015        1799 : gchar_set_u0(GEN gc, GEN u0)     { gel(gc, 12) = u0; }
    3016             : 
    3017             : INLINE GEN
    3018      387493 : bid_get_mod(GEN bid) { return gel(bid,1); }
    3019             : INLINE GEN
    3020       69552 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
    3021             : INLINE GEN
    3022       33579 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
    3023             : INLINE GEN
    3024     2414470 : bid_get_grp(GEN bid) { return gel(bid,2); }
    3025             : INLINE GEN
    3026     1310401 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
    3027             : INLINE GEN
    3028     1022813 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
    3029             : INLINE GEN
    3030      989005 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
    3031             : INLINE GEN
    3032       50736 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
    3033             : INLINE GEN
    3034     1214715 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
    3035             : INLINE GEN
    3036     1376831 : bid_get_U(GEN bid) { return gel(bid,5); }
    3037             : INLINE GEN
    3038           0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
    3039             : INLINE GEN
    3040     2361296 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
    3041             : INLINE GEN
    3042           0 : bid_get_gen_nocheck(GEN bid)  { return abgrp_get_gen(bid_get_grp(bid)); }
    3043             : INLINE GEN
    3044       52598 : bid_get_gen(GEN bid) {
    3045       52598 :   GEN G = bid_get_grp(bid);
    3046       52598 :   if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
    3047       52598 :   return abgrp_get_gen(G);
    3048             : }
    3049             : 
    3050             : INLINE GEN
    3051    29861412 : znstar_get_N(GEN G) { return gmael(G,1,1); }
    3052             : INLINE GEN
    3053     7087129 : znstar_get_faN(GEN G) { return gel(G,3); }
    3054             : INLINE GEN
    3055          14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
    3056             : INLINE GEN
    3057      212779 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
    3058             : INLINE GEN
    3059         343 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
    3060             : INLINE GEN
    3061     7743757 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
    3062             : INLINE GEN
    3063     3194765 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
    3064             : INLINE GEN
    3065       46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
    3066             : INLINE GEN
    3067      140224 : znstar_get_U(GEN G) { return gel(G,5); }
    3068             : INLINE GEN
    3069     2797242 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
    3070             : INLINE GEN
    3071       36042 : gal_get_pol(GEN gal) { return gel(gal,1); }
    3072             : INLINE GEN
    3073        5978 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
    3074             : INLINE GEN
    3075          91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
    3076             : INLINE GEN
    3077       23589 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
    3078             : INLINE GEN
    3079       32178 : gal_get_roots(GEN gal) { return gel(gal,3); }
    3080             : INLINE GEN
    3081       27334 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
    3082             : INLINE GEN
    3083       27334 : gal_get_den(GEN gal) { return gel(gal,5); }
    3084             : INLINE GEN
    3085       79336 : gal_get_group(GEN gal) { return gel(gal,6); }
    3086             : INLINE GEN
    3087        8869 : gal_get_gen(GEN gal) { return gel(gal,7); }
    3088             : INLINE GEN
    3089        6867 : gal_get_orders(GEN gal) { return gel(gal,8); }
    3090             : 
    3091             : /* assume rnf a genuine rnf */
    3092             : INLINE long
    3093     1235910 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
    3094             : INLINE long
    3095       16772 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
    3096             : INLINE long
    3097      776489 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
    3098             : INLINE GEN
    3099         707 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
    3100             : INLINE GEN
    3101         756 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
    3102             : INLINE GEN
    3103         868 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
    3104             : INLINE GEN
    3105      442370 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
    3106             : INLINE GEN
    3107        4018 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
    3108             : INLINE GEN
    3109      215008 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
    3110             : INLINE GEN
    3111     1483486 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
    3112             : INLINE GEN
    3113         175 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
    3114             : INLINE GEN
    3115         105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
    3116             : INLINE GEN
    3117        1645 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
    3118             : INLINE long
    3119         231 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
    3120             : INLINE GEN
    3121      189378 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
    3122             : INLINE long
    3123        3332 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
    3124             : INLINE GEN
    3125        3591 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
    3126             : INLINE GEN
    3127      103544 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
    3128             : INLINE GEN
    3129        1197 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
    3130             : 
    3131             : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
    3132             :  * T2 matrix. Reduce I wrt G */
    3133             : INLINE GEN
    3134      673045 : idealpseudored(GEN I, GEN G)
    3135      673045 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
    3136             : 
    3137             : /* Same I, G; m in I with T2(m) small */
    3138             : INLINE GEN
    3139      140094 : idealpseudomin(GEN I, GEN G)
    3140             : {
    3141      140094 :   GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
    3142      140096 :   return ZM_ZC_mul(I, gel(u,1));
    3143             : }
    3144             : /* Same I,G; irrational m in I with T2(m) small */
    3145             : INLINE GEN
    3146           0 : idealpseudomin_nonscalar(GEN I, GEN G)
    3147             : {
    3148           0 :   GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
    3149           0 :   GEN m = ZM_ZC_mul(I, gel(u,1));
    3150           0 :   if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
    3151           0 :   return m;
    3152             : }
    3153             : /* Same I,G; t_VEC of irrational m in I with T2(m) small */
    3154             : INLINE GEN
    3155      594370 : idealpseudominvec(GEN I, GEN G)
    3156             : {
    3157      594370 :   long i, j, k, n = lg(I)-1;
    3158      594370 :   GEN x, L, b = idealpseudored(I, G);
    3159      594369 :   L = cgetg(1 + (n*(n+1))/2, t_VEC);
    3160     2420387 :   for (i = k = 1; i <= n; i++)
    3161             :   {
    3162     1826017 :     x = gel(b,i);
    3163     1826017 :     if (!ZV_isscalar(x)) gel(L,k++) = x;
    3164             :   }
    3165     1826019 :   for (i = 2; i <= n; i++)
    3166     3440190 :     for (j = 1; j < i; j++)
    3167             :     {
    3168     2208541 :       x = ZC_add(gel(b,i),gel(b,j));
    3169     2208541 :       if (!ZV_isscalar(x)) gel(L,k++) = x;
    3170             :     }
    3171      594370 :   setlg(L,k); return L;
    3172             : }
    3173             : 
    3174             : INLINE GEN
    3175       13754 : idealred_elt(GEN nf, GEN I) {
    3176       13754 :   pari_sp av = avma;
    3177       13754 :   GEN u = idealpseudomin(I, nf_get_roundG(nf));
    3178       13754 :   return gerepileupto(av, u);
    3179             : }
    3180             : INLINE GEN
    3181      135579 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
    3182             : 
    3183             : INLINE GEN
    3184        2310 : idealchineseinit(GEN nf, GEN x)
    3185        2310 : { return idealchinese(nf,x,NULL); }
    3186             : 
    3187             : /*******************************************************************/
    3188             : /*                                                                 */
    3189             : /*                              CLOSURES                           */
    3190             : /*                                                                 */
    3191             : /*******************************************************************/
    3192   344155010 : INLINE long closure_arity(GEN C)          { return ((ulong)C[1])&ARITYBITS; }
    3193    36570193 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
    3194   301124493 : INLINE const char *closure_codestr(GEN C)  { return GSTR(gel(C,2))-1; }
    3195           0 : INLINE GEN closure_get_code(GEN C)  { return gel(C,2); }
    3196   301111368 : INLINE GEN closure_get_oper(GEN C)  { return gel(C,3); }
    3197   301090644 : INLINE GEN closure_get_data(GEN C)  { return gel(C,4); }
    3198       11591 : INLINE GEN closure_get_dbg(GEN C)   { return gel(C,5); }
    3199       27125 : INLINE GEN closure_get_text(GEN C)  { return gel(C,6); }
    3200     8023014 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
    3201             : 
    3202             : /*******************************************************************/
    3203             : /*                                                                 */
    3204             : /*                               ERRORS                            */
    3205             : /*                                                                 */
    3206             : /*******************************************************************/
    3207             : INLINE long
    3208       57132 : err_get_num(GEN e) { return e[1]; }
    3209             : INLINE GEN
    3210         273 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
    3211             : 
    3212             : INLINE void
    3213          14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
    3214             : INLINE void
    3215           7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
    3216             : INLINE void
    3217          84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
    3218             : INLINE void
    3219         550 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
    3220             : INLINE void
    3221           0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
    3222             : INLINE void
    3223          36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
    3224             : INLINE void
    3225          98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
    3226             : INLINE void
    3227         469 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
    3228             : INLINE void
    3229       19963 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
    3230             : INLINE void
    3231          63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
    3232             : INLINE void
    3233        2575 : pari_err_DOMAIN(const char *f, const char *v, const char *op, GEN l, GEN x) { pari_err(e_DOMAIN, f,v,op,l,x); }
    3234             : INLINE void
    3235         200 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
    3236             : INLINE void
    3237           0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
    3238             : INLINE void
    3239         378 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
    3240             : INLINE void
    3241         142 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
    3242             : INLINE void
    3243         239 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
    3244             : INLINE void
    3245           0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
    3246             : INLINE void
    3247          77 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
    3248             : INLINE void
    3249         756 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
    3250             : INLINE void
    3251          56 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
    3252             : INLINE void
    3253          84 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
    3254             : INLINE void
    3255       13536 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
    3256             : INLINE void
    3257        3395 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
    3258             : INLINE void
    3259         280 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
    3260             : INLINE void
    3261         231 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
    3262         231 : { pari_err(e_PRIORITY, f,x,op,v); }

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