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 v2.16.1 lcov report (development 28904-c3aa21e911) Lines: 1443 1586 91.0 %
Date: 2023-12-04 07:51:13 Functions: 647 718 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             : /*********************************************************************/
      17             : /*                       MALLOC/FREE WRAPPERS                        */
      18             : /*********************************************************************/
      19             : #define BLOCK_SIGALRM_START          \
      20             : {                                    \
      21             :   int block=PARI_SIGINT_block;       \
      22             :   PARI_SIGINT_block = 2;             \
      23             :   MT_SIGINT_BLOCK(block);
      24             : 
      25             : #define BLOCK_SIGINT_START           \
      26             : {                                    \
      27             :   int block=PARI_SIGINT_block;       \
      28             :   PARI_SIGINT_block = 1;             \
      29             :   MT_SIGINT_BLOCK(block);
      30             : 
      31             : #define BLOCK_SIGINT_END             \
      32             :   PARI_SIGINT_block = block;         \
      33             :   MT_SIGINT_UNBLOCK(block);          \
      34             :   if (!block && PARI_SIGINT_pending) \
      35             :   {                                  \
      36             :     int sig = PARI_SIGINT_pending;   \
      37             :     PARI_SIGINT_pending = 0;         \
      38             :     raise(sig);                      \
      39             :   }                                  \
      40             : }
      41             : 
      42             : /*******************************************************************/
      43             : /*                                                                 */
      44             : /*                          CONSTRUCTORS                           */
      45             : /*                                                                 */
      46             : /*******************************************************************/
      47             : #define retmkfrac(x,y)\
      48             :   do { GEN _v = cgetg(3, t_FRAC);\
      49             :        gel(_v,1) = (x);\
      50             :        gel(_v,2) = (y); return _v; } while(0)
      51             : #define retmkrfrac(x,y)\
      52             :   do { GEN _v = cgetg(3, t_RFRAC);\
      53             :        gel(_v,1) = (x);\
      54             :        gel(_v,2) = (y); return _v; } while(0)
      55             : #define retmkintmod(x,y)\
      56             :   do { GEN _v = cgetg(3, t_INTMOD);\
      57             :        gel(_v,1) = (y);\
      58             :        gel(_v,2) = (x); return _v; } while(0)
      59             : #define retmkcomplex(x,y)\
      60             :   do { GEN _v = cgetg(3, t_COMPLEX);\
      61             :        gel(_v,1) = (x);\
      62             :        gel(_v,2) = (y); return _v; } while(0)
      63             : #define retmkpolmod(x,y)\
      64             :   do { GEN _v = cgetg(3, t_POLMOD);\
      65             :        gel(_v,1) = (y);\
      66             :        gel(_v,2) = (x); return _v; } while(0)
      67             : #define retmkvec(x)\
      68             :   do { GEN _v = cgetg(2, t_VEC);\
      69             :        gel(_v,1) = (x); return _v; } while(0)
      70             : #define retmkvec2(x,y)\
      71             :   do { GEN _v = cgetg(3, t_VEC);\
      72             :        gel(_v,1) = (x);\
      73             :        gel(_v,2) = (y); return _v; } while(0)
      74             : #define retmkvec3(x,y,z)\
      75             :   do { GEN _v = cgetg(4, t_VEC);\
      76             :        gel(_v,1) = (x);\
      77             :        gel(_v,2) = (y);\
      78             :        gel(_v,3) = (z); return _v; } while(0)
      79             : #define retmkqfb(x,y,z,d)\
      80             :   do { GEN _v = cgetg(5, t_QFB);\
      81             :        gel(_v,1) = (x);\
      82             :        gel(_v,2) = (y);\
      83             :        gel(_v,3) = (z);\
      84             :        gel(_v,4) = (d); return _v; } while(0)
      85             : #define retmkquad(x,y,z)\
      86             :   do { GEN _v = cgetg(4, t_QUAD);\
      87             :        gel(_v,1) = (x);\
      88             :        gel(_v,2) = (y);\
      89             :        gel(_v,3) = (z); return _v; } while(0)
      90             : #define retmkvec4(x,y,z,t)\
      91             :   do { GEN _v = cgetg(5, t_VEC);\
      92             :        gel(_v,1) = (x);\
      93             :        gel(_v,2) = (y);\
      94             :        gel(_v,3) = (z);\
      95             :        gel(_v,4) = (t); return _v; } while(0)
      96             : #define retmkvec5(x,y,z,t,u)\
      97             :   do { GEN _v = cgetg(6, t_VEC);\
      98             :        gel(_v,1) = (x);\
      99             :        gel(_v,2) = (y);\
     100             :        gel(_v,3) = (z);\
     101             :        gel(_v,4) = (t);\
     102             :        gel(_v,5) = (u); return _v; } while(0)
     103             : #define retmkcol(x)\
     104             :   do { GEN _v = cgetg(2, t_COL);\
     105             :        gel(_v,1) = (x); return _v; } while(0)
     106             : #define retmkcol2(x,y)\
     107             :   do { GEN _v = cgetg(3, t_COL);\
     108             :        gel(_v,1) = (x);\
     109             :        gel(_v,2) = (y); return _v; } while(0)
     110             : #define retmkcol3(x,y,z)\
     111             :   do { GEN _v = cgetg(4, t_COL);\
     112             :        gel(_v,1) = (x);\
     113             :        gel(_v,2) = (y);\
     114             :        gel(_v,3) = (z); return _v; } while(0)
     115             : #define retmkcol4(x,y,z,t)\
     116             :   do { GEN _v = cgetg(5, t_COL);\
     117             :        gel(_v,1) = (x);\
     118             :        gel(_v,2) = (y);\
     119             :        gel(_v,3) = (z);\
     120             :        gel(_v,4) = (t); return _v; } while(0)
     121             : #define retmkcol5(x,y,z,t,u)\
     122             :   do { GEN _v = cgetg(6, t_COL);\
     123             :        gel(_v,1) = (x);\
     124             :        gel(_v,2) = (y);\
     125             :        gel(_v,3) = (z);\
     126             :        gel(_v,4) = (t);\
     127             :        gel(_v,5) = (u); return _v; } while(0)
     128             : #define retmkcol6(x,y,z,t,u,v)\
     129             :   do { GEN _v = cgetg(7, t_COL);\
     130             :        gel(_v,1) = (x);\
     131             :        gel(_v,2) = (y);\
     132             :        gel(_v,3) = (z);\
     133             :        gel(_v,4) = (t);\
     134             :        gel(_v,5) = (u);\
     135             :        gel(_v,6) = (v); return _v; } while(0)
     136             : #define retmkmat(x)\
     137             :   do { GEN _v = cgetg(2, t_MAT);\
     138             :        gel(_v,1) = (x); return _v; } while(0)
     139             : #define retmkmat2(x,y)\
     140             :   do { GEN _v = cgetg(3, t_MAT);\
     141             :        gel(_v,1) = (x);\
     142             :        gel(_v,2) = (y); return _v; } while(0)
     143             : #define retmkmat3(x,y,z)\
     144             :   do { GEN _v = cgetg(4, t_MAT);\
     145             :        gel(_v,1) = (x);\
     146             :        gel(_v,2) = (y);\
     147             :        gel(_v,3) = (z); return _v; } while(0)
     148             : #define retmkmat4(x,y,z,t)\
     149             :   do { GEN _v = cgetg(5, t_MAT);\
     150             :        gel(_v,1) = (x);\
     151             :        gel(_v,2) = (y);\
     152             :        gel(_v,3) = (z);\
     153             :        gel(_v,4) = (t); return _v; } while(0)
     154             : #define retmkmat5(x,y,z,t,u)\
     155             :   do { GEN _v = cgetg(6, t_MAT);\
     156             :        gel(_v,1) = (x);\
     157             :        gel(_v,2) = (y);\
     158             :        gel(_v,3) = (z);\
     159             :        gel(_v,4) = (t);\
     160             :        gel(_v,5) = (u); return _v; } while(0)
     161             : #define retmkmat22(a,b,c,d)\
     162             :   do { GEN _v = cgetg(3, t_MAT);\
     163             :        gel(_v,1) = mkcol2(a,c);\
     164             :        gel(_v,2) = mkcol2(b,d); return _v; } while(0)
     165             : INLINE GEN
     166     6535504 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
     167             : INLINE GEN
     168        1806 : mkintmodu(ulong x, ulong y) {
     169        1806 :   GEN v = cgetg(3,t_INTMOD);
     170        1806 :   gel(v,1) = utoipos(y);
     171        1806 :   gel(v,2) = utoi(x); return v;
     172             : }
     173             : INLINE GEN
     174     2611210 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
     175             : INLINE GEN
     176    31412060 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
     177             : INLINE GEN
     178     1205620 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
     179             : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
     180             : INLINE void
     181       19229 : Qtoss(GEN q, long *n, long *d)
     182             : {
     183       19229 :   if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
     184        5691 :   else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
     185       19229 : }
     186             : INLINE GEN
     187      770301 : sstoQ(long n, long d)
     188             : {
     189             :   ulong r;
     190             :   long g, q;
     191      770301 :   if (!n)
     192             :   {
     193       92554 :     if (!d) pari_err_INV("sstoQ",gen_0);
     194       92554 :     return gen_0;
     195             :   }
     196      677747 :   if (d < 0) { d = -d; n = -n; }
     197      677747 :   if (d == 1) return stoi(n);
     198      664748 :   r = labs(n);
     199      664748 :   if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
     200      630371 :   q = udivuu_rem(r, d, &r);
     201      630371 :   if (!r) return n > 0? utoipos(q): utoineg(q);
     202      575666 :   g = ugcd(d,r); /* gcd(n,d) */
     203      575666 :   if (g != 1) { n /= g; d /= g; }
     204      575666 :   retmkfrac(stoi(n), utoipos(d));
     205             : }
     206             : 
     207             : INLINE GEN
     208   157969934 : uutoQ(ulong n, ulong d)
     209             : {
     210             :   ulong r;
     211             :   long g, q;
     212   157969934 :   if (!n)
     213             :   {
     214        9438 :     if (!d) pari_err_INV("uutoQ",gen_0);
     215        9438 :     return gen_0;
     216             :   }
     217   157960496 :   if (d == 1) return utoipos(n);
     218   157949394 :   if (n == 1) retmkfrac(gen_1, utoipos(d));
     219   157860550 :   q = udivuu_rem(n,d,&r);
     220   157860550 :   if (!r) return utoipos(q);
     221     5141991 :   g = ugcd(d,r); /* gcd(n,d) */
     222     5141991 :   if (g != 1) { n /= g; d /= g; }
     223     5141991 :   retmkfrac(utoipos(n), utoipos(d));
     224             : }
     225             : 
     226             : INLINE GEN
     227     4703399 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
     228             : INLINE GEN
     229      697634 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
     230      697634 :   gel(v,1) = x; gel(v,2) = y; return v; }
     231             : INLINE GEN
     232           7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
     233           7 :   gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
     234             : INLINE GEN
     235    75735740 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
     236             : INLINE GEN
     237      830157 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
     238             : INLINE GEN
     239      554671 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
     240             : INLINE GEN
     241       69132 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
     242       69132 :   gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
     243             : /* vecsmall */
     244             : INLINE GEN
     245   124580511 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
     246             : INLINE GEN
     247   216178151 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
     248   216152668 :   v[1]=x; v[2]=y; return v; }
     249             : INLINE GEN
     250    93709983 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
     251    93699298 :   v[1]=x; v[2]=y; v[3]=z; return v; }
     252             : INLINE GEN
     253    15174131 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
     254    15169230 :   v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
     255             : INLINE GEN
     256      664464 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
     257      664465 :   v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
     258             : 
     259             : INLINE GEN
     260    27908232 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
     261             : /* vec */
     262             : INLINE GEN
     263    63280436 : mkvec(GEN x) { retmkvec(x); }
     264             : INLINE GEN
     265   177412843 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
     266             : INLINE GEN
     267    98797736 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
     268             : INLINE GEN
     269     6279467 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
     270             : INLINE GEN
     271    15651505 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
     272             : INLINE GEN
     273         161 : mkvecs(long x) { retmkvec(stoi(x)); }
     274             : INLINE GEN
     275      212900 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
     276             : INLINE GEN
     277      488650 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
     278             : INLINE GEN
     279          21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
     280             : INLINE GEN
     281       35889 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
     282             : INLINE GEN
     283      118455 : mkvec2copy(GEN x, GEN y) {
     284      118455 :   GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
     285             : /* col */
     286             : INLINE GEN
     287     9340124 : mkcol(GEN x) { retmkcol(x); }
     288             : INLINE GEN
     289   126306159 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
     290             : INLINE GEN
     291       86466 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
     292             : INLINE GEN
     293      102935 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
     294             : INLINE GEN
     295          94 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
     296             : INLINE GEN
     297       12679 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
     298             : INLINE GEN
     299       40411 : mkcols(long x) { retmkcol(stoi(x)); }
     300             : INLINE GEN
     301     2998352 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
     302             : INLINE GEN
     303         308 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
     304             : INLINE GEN
     305           0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
     306             : INLINE GEN
     307       28804 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
     308             : /* mat */
     309             : INLINE GEN
     310     4417594 : mkmat(GEN x) { retmkmat(x); }
     311             : INLINE GEN
     312    30899674 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
     313             : INLINE GEN
     314       16777 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
     315             : INLINE GEN
     316           0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
     317             : INLINE GEN
     318           0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
     319             : INLINE GEN
     320      112610 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
     321             : INLINE GEN
     322           0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
     323             : INLINE GEN
     324      200747 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
     325             : INLINE GEN
     326      103349 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
     327             : INLINE long
     328      316296 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
     329             : INLINE GEN
     330      130830 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
     331             : INLINE GEN
     332    37238384 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
     333             : 
     334             : /* pol */
     335             : INLINE GEN
     336     2571685 : pol_x(long v) {
     337     2571685 :   GEN p = cgetg(4, t_POL);
     338     2571718 :   p[1] = evalsigne(1)|evalvarn(v);
     339     2571718 :   gel(p,2) = gen_0;
     340     2571718 :   gel(p,3) = gen_1; return p;
     341             : }
     342             : /* x^n, assume n >= 0 */
     343             : INLINE GEN
     344     2168574 : pol_xn(long n, long v) {
     345     2168574 :   long i, a = n+2;
     346     2168574 :   GEN p = cgetg(a+1, t_POL);
     347     2168579 :   p[1] = evalsigne(1)|evalvarn(v);
     348     5100895 :   for (i = 2; i < a; i++) gel(p,i) = gen_0;
     349     2168579 :   gel(p,a) = gen_1; return p;
     350             : }
     351             : /* x^n, no assumption on n */
     352             : INLINE GEN
     353         294 : pol_xnall(long n, long v)
     354             : {
     355         294 :   if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
     356         287 :   return pol_xn(n, v);
     357             : }
     358             : /* x^n, assume n >= 0 */
     359             : INLINE GEN
     360         371 : polxn_Flx(long n, long sv) {
     361         371 :   long i, a = n+2;
     362         371 :   GEN p = cgetg(a+1, t_VECSMALL);
     363         371 :   p[1] = sv;
     364        1806 :   for (i = 2; i < a; i++) p[i] = 0;
     365         371 :   p[a] = 1; return p;
     366             : }
     367             : INLINE GEN
     368     4448938 : pol_1(long v) {
     369     4448938 :   GEN p = cgetg(3, t_POL);
     370     4448919 :   p[1] = evalsigne(1)|evalvarn(v);
     371     4448919 :   gel(p,2) = gen_1; return p;
     372             : }
     373             : INLINE GEN
     374    34796982 : pol_0(long v)
     375             : {
     376    34796982 :   GEN x = cgetg(2,t_POL);
     377    34796969 :   x[1] = evalvarn(v); return x;
     378             : }
     379             : #define retconst_vec(n,x)\
     380             :   do { long _i, _n = (n);\
     381             :        GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
     382             :        for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
     383             :        return _v; } while(0)
     384             : INLINE GEN
     385   224666391 : const_vec(long n, GEN x) { retconst_vec(n, x); }
     386             : #define retconst_col(n,x)\
     387             :   do { long _i, _n = (n);\
     388             :        GEN _v = cgetg(_n+1, t_COL), _x = (x);\
     389             :        for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
     390             :        return _v; } while(0)
     391             : INLINE GEN
     392    37149957 : const_col(long n, GEN x) { retconst_col(n, x); }
     393             : INLINE GEN
     394    17548519 : const_vecsmall(long n, long c)
     395             : {
     396             :   long i;
     397    17548519 :   GEN V = cgetg(n+1,t_VECSMALL);
     398   639056043 :   for(i=1;i<=n;i++) V[i] = c;
     399    17548469 :   return V;
     400             : }
     401             : 
     402             : /***   ZERO   ***/
     403             : /* O(p^e) */
     404             : INLINE GEN
     405      846614 : zeropadic(GEN p, long e)
     406             : {
     407      846614 :   GEN y = cgetg(5,t_PADIC);
     408      846616 :   gel(y,4) = gen_0;
     409      846616 :   gel(y,3) = gen_1;
     410      846616 :   gel(y,2) = icopy(p);
     411      846544 :   y[1] = evalvalp(e) | _evalprecp(0);
     412      846531 :   return y;
     413             : }
     414             : INLINE GEN
     415       10101 : zeropadic_shallow(GEN p, long e)
     416             : {
     417       10101 :   GEN y = cgetg(5,t_PADIC);
     418       10101 :   gel(y,4) = gen_0;
     419       10101 :   gel(y,3) = gen_1;
     420       10101 :   gel(y,2) = p;
     421       10101 :   y[1] = evalvalp(e) | _evalprecp(0);
     422       10101 :   return y;
     423             : }
     424             : /* O(pol_x(v)^e) */
     425             : INLINE GEN
     426      136360 : zeroser(long v, long e)
     427             : {
     428      136360 :   GEN x = cgetg(2, t_SER);
     429      136360 :   x[1] = evalvalser(e) | evalvarn(v); return x;
     430             : }
     431             : INLINE int
     432    10042708 : ser_isexactzero(GEN x)
     433             : {
     434    10042708 :   if (!signe(x)) switch(lg(x))
     435             :   {
     436      131194 :     case 2: return 1;
     437        3899 :     case 3: return isexactzero(gel(x,2));
     438             :   }
     439     9907615 :   return 0;
     440             : }
     441             : /* 0 * pol_x(v) */
     442             : INLINE GEN
     443    14734266 : zeropol(long v) { return pol_0(v); }
     444             : /* vector(n) */
     445             : INLINE GEN
     446   111476217 : zerocol(long n)
     447             : {
     448   111476217 :   GEN y = cgetg(n+1,t_COL);
     449   748553724 :   long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
     450   111476264 :   return y;
     451             : }
     452             : /* vectorv(n) */
     453             : INLINE GEN
     454    24870734 : zerovec(long n)
     455             : {
     456    24870734 :   GEN y = cgetg(n+1,t_VEC);
     457   337819521 :   long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
     458    24870716 :   return y;
     459             : }
     460             : /* matrix(m, n) */
     461             : INLINE GEN
     462       90594 : zeromat(long m, long n)
     463             : {
     464       90594 :   GEN y = cgetg(n+1,t_MAT);
     465       90592 :   GEN v = zerocol(m);
     466      312440 :   long i; for (i=1; i<=n; i++) gel(y,i) = v;
     467       90591 :   return y;
     468             : }
     469             : /* = zero_zx, sv is a evalvarn()*/
     470             : INLINE GEN
     471     1331152 : zero_Flx(long sv) { return pol0_Flx(sv); }
     472             : INLINE GEN
     473    58586533 : zero_Flv(long n)
     474             : {
     475    58586533 :   GEN y = cgetg(n+1,t_VECSMALL);
     476   949190008 :   long i; for (i=1; i<=n; i++) y[i] = 0;
     477    58586808 :   return y;
     478             : }
     479             : /* matrix(m, n) */
     480             : INLINE GEN
     481     2544052 : zero_Flm(long m, long n)
     482             : {
     483     2544052 :   GEN y = cgetg(n+1,t_MAT);
     484     2544027 :   GEN v = zero_Flv(m);
     485    16139142 :   long i; for (i=1; i<=n; i++) gel(y,i) = v;
     486     2544049 :   return y;
     487             : }
     488             : /* matrix(m, n) */
     489             : INLINE GEN
     490      229378 : zero_Flm_copy(long m, long n)
     491             : {
     492      229378 :   GEN y = cgetg(n+1,t_MAT);
     493     2371535 :   long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
     494      229387 :   return y;
     495             : }
     496             : 
     497             : INLINE GEN
     498     3409605 : zero_F2v(long m)
     499             : {
     500     3409605 :   long l = nbits2nlong(m);
     501     3409589 :   GEN v  = zero_Flv(l+1);
     502     3409554 :   v[1] = m;
     503     3409554 :   return v;
     504             : }
     505             : 
     506             : INLINE GEN
     507           0 : zero_F2m(long m, long n)
     508             : {
     509             :   long i;
     510           0 :   GEN M = cgetg(n+1, t_MAT);
     511           0 :   GEN v = zero_F2v(m);
     512           0 :   for (i = 1; i <= n; i++)
     513           0 :     gel(M,i) = v;
     514           0 :   return M;
     515             : }
     516             : 
     517             : 
     518             : INLINE GEN
     519      835354 : zero_F2m_copy(long m, long n)
     520             : {
     521             :   long i;
     522      835354 :   GEN M = cgetg(n+1, t_MAT);
     523     1974563 :   for (i = 1; i <= n; i++)
     524     1139215 :     gel(M,i)= zero_F2v(m);
     525      835348 :   return M;
     526             : }
     527             : 
     528             : /* matrix(m, n) */
     529             : INLINE GEN
     530    12876857 : zeromatcopy(long m, long n)
     531             : {
     532    12876857 :   GEN y = cgetg(n+1,t_MAT);
     533    65227803 :   long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
     534    12876902 :   return y;
     535             : }
     536             : 
     537             : INLINE GEN
     538       24072 : zerovec_block(long len)
     539             : {
     540             :   long i;
     541       24072 :   GEN blk = cgetg_block(len + 1, t_VEC);
     542      794376 :   for (i = 1; i <= len; ++i)
     543      770304 :     gel(blk, i) = gen_0;
     544       24072 :   return blk;
     545             : }
     546             : 
     547             : /* i-th vector in the standard basis */
     548             : INLINE GEN
     549     5077497 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
     550             : INLINE GEN
     551     1697442 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
     552             : INLINE GEN
     553          42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
     554             : INLINE GEN
     555       50225 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
     556             : INLINE GEN
     557     1213154 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
     558             : 
     559             : INLINE GEN
     560    19169682 : shallowcopy(GEN x)
     561    19169682 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
     562             : 
     563             : /* routines for naive growarrays */
     564             : INLINE GEN
     565    11242012 : vectrunc_init(long l)
     566             : {
     567    11242012 :   GEN z = new_chunk(l);
     568    11241816 :   z[0] = evaltyp(t_VEC) | _evallg(1); return z;
     569             : }
     570             : INLINE GEN
     571      348929 : coltrunc_init(long l)
     572             : {
     573      348929 :   GEN z = new_chunk(l);
     574      348929 :   z[0] = evaltyp(t_COL) | _evallg(1); return z;
     575             : }
     576             : INLINE void
     577   295630627 : lg_increase(GEN x) { x[0]++; }
     578             : INLINE void
     579    14070543 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
     580             : INLINE void
     581       10864 : vectrunc_append_batch(GEN x, GEN y)
     582             : {
     583       10864 :   long i, l = lg(x), ly = lg(y);
     584       10864 :   GEN z = x + l-1;
     585       36358 :   for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
     586       10864 :   setlg(x, l+ly-1);
     587       10864 : }
     588             : INLINE GEN
     589   137835774 : vecsmalltrunc_init(long l)
     590             : {
     591   137835774 :   GEN z = new_chunk(l);
     592   137736783 :   z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
     593             : }
     594             : INLINE void
     595    62523513 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
     596             : 
     597             : /*******************************************************************/
     598             : /*                                                                 */
     599             : /*                    STRING HASH FUNCTIONS                        */
     600             : /*                                                                 */
     601             : /*******************************************************************/
     602             : INLINE ulong
     603     2570881 : hash_str(const char *str)
     604             : {
     605     2570881 :   ulong hash = 5381UL, c;
     606    26550014 :   while ( (c = (ulong)*str++) )
     607    23979133 :     hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
     608     2570881 :   return hash;
     609             : }
     610             : INLINE ulong
     611    17569644 : hash_str_len(const char *str, long len)
     612             : {
     613    17569644 :   ulong hash = 5381UL;
     614             :   long i;
     615   161818004 :   for (i = 0; i < len; i++)
     616             :   {
     617   144248360 :     ulong c = (ulong)*str++;
     618   144248360 :     hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
     619             :   }
     620    17569644 :   return hash;
     621             : }
     622             : 
     623             : /*******************************************************************/
     624             : /*                                                                 */
     625             : /*                        VEC / COL / VECSMALL                     */
     626             : /*                                                                 */
     627             : /*******************************************************************/
     628             : /* shallow*/
     629             : INLINE GEN
     630       11542 : vec_shorten(GEN v, long n)
     631             : {
     632       11542 :   GEN V = cgetg(n+1, t_VEC);
     633             :   long i;
     634       12998 :   for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
     635       11542 :   return V;
     636             : }
     637             : /* shallow*/
     638             : INLINE GEN
     639       18927 : vec_lengthen(GEN v, long n)
     640             : {
     641       18927 :   GEN V = cgetg(n+1, t_VEC);
     642       18927 :   long i, l = lg(v);
     643     1935611 :   for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
     644       18927 :   return V;
     645             : }
     646             : /* shallow*/
     647             : INLINE GEN
     648     3423884 : vec_append(GEN V, GEN s)
     649             : {
     650     3423884 :   long i, l2 = lg(V);
     651     3423884 :   GEN res = cgetg(l2+1, typ(V));
     652    10719903 :   for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
     653     3423868 :   gel(res,l2) = s; return res;
     654             : }
     655             : /* shallow*/
     656             : INLINE GEN
     657      300481 : vec_prepend(GEN v, GEN s)
     658             : {
     659      300481 :   long i, l = lg(v);
     660      300481 :   GEN w = cgetg(l+1, typ(v));
     661      300481 :   gel(w,1) = s;
     662      769122 :   for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
     663      300481 :   return w;
     664             : }
     665             : /* shallow*/
     666             : INLINE GEN
     667           0 : vec_setconst(GEN v, GEN x)
     668             : {
     669           0 :   long i, l = lg(v);
     670           0 :   for (i = 1; i < l; i++) gel(v,i) = x;
     671           0 :   return v;
     672             : }
     673             : INLINE GEN
     674       71410 : vecsmall_shorten(GEN v, long n)
     675             : {
     676       71410 :   GEN V = cgetg(n+1,t_VECSMALL);
     677             :   long i;
     678      878378 :   for(i = 1; i <= n; i++) V[i] = v[i];
     679       71412 :   return V;
     680             : }
     681             : INLINE GEN
     682         490 : vecsmall_lengthen(GEN v, long n)
     683             : {
     684         490 :   long i, l = lg(v);
     685         490 :   GEN V = cgetg(n+1,t_VECSMALL);
     686       25053 :   for(i = 1; i < l; i++) V[i] = v[i];
     687         490 :   return V;
     688             : }
     689             : 
     690             : INLINE GEN
     691     4010697 : vec_to_vecsmall(GEN x)
     692    18847663 : { pari_APPLY_long(itos(gel(x,i))) }
     693             : INLINE GEN
     694      499217 : vecsmall_to_vec(GEN x)
     695     5558901 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
     696             : INLINE GEN
     697        2464 : vecsmall_to_vec_inplace(GEN z)
     698             : {
     699        2464 :   long i, l = lg(z);
     700       77014 :   for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
     701        2464 :   settyp(z, t_VEC); return z;
     702             : }
     703             : INLINE GEN
     704     7621472 : vecsmall_to_col(GEN x)
     705    57194120 : { pari_APPLY_type(t_COL, stoi(x[i])) }
     706             : 
     707             : INLINE int
     708     7073305 : vecsmall_lexcmp(GEN x, GEN y)
     709             : {
     710             :   long lx,ly,l,i;
     711     7073305 :   lx = lg(x);
     712     7073305 :   ly = lg(y); l = minss(lx,ly);
     713    30509223 :   for (i=1; i<l; i++)
     714    28882371 :     if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
     715     1626852 :   if (lx == ly) return 0;
     716       30578 :   return (lx < ly)? -1 : 1;
     717             : }
     718             : 
     719             : INLINE int
     720   108088071 : vecsmall_prefixcmp(GEN x, GEN y)
     721             : {
     722   108088071 :   long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
     723   542691324 :   for (i=1; i<l; i++)
     724   519806035 :     if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
     725    22885289 :   return 0;
     726             : }
     727             : 
     728             : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
     729             : INLINE GEN
     730      184924 : vecsmall_prepend(GEN V, long s)
     731             : {
     732      184924 :   long i, l2 = lg(V);
     733      184924 :   GEN res = cgetg(l2+1, typ(V));
     734      184924 :   res[1] = s;
     735      619431 :   for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
     736      184924 :   return res;
     737             : }
     738             : 
     739             : INLINE GEN
     740     4054754 : vecsmall_append(GEN V, long s)
     741             : {
     742     4054754 :   long i, l2 = lg(V);
     743     4054754 :   GEN res = cgetg(l2+1, t_VECSMALL);
     744     5973394 :   for (i = 1; i < l2; ++i) res[i] = V[i];
     745     4054749 :   res[l2] = s; return res;
     746             : }
     747             : 
     748             : INLINE GEN
     749     1472953 : vecsmall_concat(GEN u, GEN v)
     750             : {
     751     1472953 :   long i, l1 = lg(u)-1, l2 = lg(v)-1;
     752     1472953 :   GEN res = cgetg(l1+l2+1, t_VECSMALL);
     753    11687918 :   for (i = 1; i <= l1; ++i) res[i]    = u[i];
     754    14974743 :   for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
     755     1472953 :   return res;
     756             : }
     757             : 
     758             : /* return the number of indices where u and v are equal */
     759             : INLINE long
     760           0 : vecsmall_coincidence(GEN u, GEN v)
     761             : {
     762           0 :   long i, s = 0, l = minss(lg(u),lg(v));
     763           0 :   for(i=1; i<l; i++)
     764           0 :     if(u[i] == v[i]) s++;
     765           0 :   return s;
     766             : }
     767             : 
     768             : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
     769             : INLINE long
     770          84 : vecsmall_isin(GEN v, long x)
     771             : {
     772          84 :   long i, l = lg(v);
     773         124 :   for (i = 1; i < l; i++)
     774          80 :     if (v[i] == x) return i;
     775          44 :   return 0;
     776             : }
     777             : 
     778             : INLINE long
     779          84 : vecsmall_pack(GEN V, long base, long mod)
     780             : {
     781          84 :   long i, s = 0;
     782         273 :   for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
     783          84 :   return s;
     784             : }
     785             : 
     786             : INLINE long
     787          14 : vecsmall_indexmax(GEN x)
     788             : {
     789          14 :   long i, i0 = 1, t = x[1], lx = lg(x);
     790          56 :   for (i=2; i<lx; i++)
     791          42 :     if (x[i] > t) t = x[i0=i];
     792          14 :   return i0;
     793             : }
     794             : 
     795             : INLINE long
     796      920789 : vecsmall_max(GEN x)
     797             : {
     798      920789 :   long i, t = x[1], lx = lg(x);
     799     2533827 :   for (i=2; i<lx; i++)
     800     1613038 :     if (x[i] > t) t = x[i];
     801      920789 :   return t;
     802             : }
     803             : 
     804             : INLINE long
     805          14 : vecsmall_indexmin(GEN x)
     806             : {
     807          14 :   long i, i0 = 1, t = x[1], lx =lg(x);
     808          56 :   for (i=2; i<lx; i++)
     809          42 :     if (x[i] < t) t = x[i0=i];
     810          14 :   return i0;
     811             : }
     812             : 
     813             : INLINE long
     814        1442 : vecsmall_min(GEN x)
     815             : {
     816        1442 :   long i, t = x[1], lx =lg(x);
     817       10094 :   for (i=2; i<lx; i++)
     818        8652 :     if (x[i] < t) t = x[i];
     819        1442 :   return t;
     820             : }
     821             : 
     822             : INLINE int
     823    24305364 : ZV_isscalar(GEN x)
     824             : {
     825    24305364 :   long l = lg(x);
     826    55714934 :   while (--l > 1)
     827    55362956 :     if (signe(gel(x, l))) return 0;
     828      351978 :   return 1;
     829             : }
     830             : INLINE int
     831    41622774 : QV_isscalar(GEN x)
     832             : {
     833    41622774 :   long lx = lg(x),i;
     834    48590092 :   for (i=2; i<lx; i++)
     835    46300469 :     if (!isintzero(gel(x, i))) return 0;
     836     2289623 :   return 1;
     837             : }
     838             : INLINE int
     839        8305 : RgV_isscalar(GEN x)
     840             : {
     841        8305 :   long lx = lg(x),i;
     842       10175 :   for (i=2; i<lx; i++)
     843       10133 :     if (!gequal0(gel(x, i))) return 0;
     844          42 :   return 1;
     845             : }
     846             : INLINE int
     847           0 : RgX_isscalar(GEN x)
     848             : {
     849             :   long i;
     850           0 :   for (i=lg(x)-1; i>2; i--)
     851           0 :     if (!gequal0(gel(x, i))) return 0;
     852           0 :   return 1;
     853             : }
     854             : INLINE long
     855    25520600 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
     856             : INLINE GEN
     857         140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
     858             : 
     859             : INLINE int
     860       66770 : RgX_is_rational(GEN x)
     861             : {
     862             :   long i;
     863      305100 :   for (i = lg(x)-1; i > 1; i--)
     864      289775 :     if (!is_rational_t(typ(gel(x,i)))) return 0;
     865       15325 :   return 1;
     866             : }
     867             : INLINE int
     868    13175411 : RgX_is_ZX(GEN x)
     869             : {
     870             :   long i;
     871    54955120 :   for (i = lg(x)-1; i > 1; i--)
     872    41841944 :     if (typ(gel(x,i)) != t_INT) return 0;
     873    13113176 :   return 1;
     874             : }
     875             : INLINE int
     876      361458 : RgX_is_QX(GEN x)
     877             : {
     878      361458 :   long k = lg(x)-1;
     879     1372163 :   for ( ; k>1; k--)
     880     1011048 :     if (!is_rational_t(typ(gel(x,k)))) return 0;
     881      361115 :   return 1;
     882             : }
     883             : INLINE int
     884     2924713 : RgX_is_monomial(GEN x)
     885             : {
     886             :   long i;
     887     2924713 :   if (!signe(x)) return 0;
     888     6890152 :   for (i=lg(x)-2; i>1; i--)
     889     4531456 :     if (!isexactzero(gel(x,i))) return 0;
     890     2358696 :   return 1;
     891             : }
     892             : INLINE int
     893    31170838 : RgV_is_ZV(GEN x)
     894             : {
     895             :   long i;
     896   124192917 :   for (i = lg(x)-1; i > 0; i--)
     897    93051577 :     if (typ(gel(x,i)) != t_INT) return 0;
     898    31141340 :   return 1;
     899             : }
     900             : INLINE int
     901      110647 : RgV_is_QV(GEN x)
     902             : {
     903             :   long i;
     904      529326 :   for (i = lg(x)-1; i > 0; i--)
     905      421633 :     if (!is_rational_t(typ(gel(x,i)))) return 0;
     906      107693 :   return 1;
     907             : }
     908             : INLINE long
     909      109073 : RgV_isin_i(GEN v, GEN x, long n)
     910             : {
     911             :   long i;
     912     1031386 :   for (i = 1; i <= n; i++)
     913     1025597 :     if (gequal(gel(v,i), x)) return i;
     914        5789 :   return 0;
     915             : }
     916             : INLINE long
     917      109073 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
     918             : 
     919             : /********************************************************************/
     920             : /**                                                                **/
     921             : /**            Dynamic arrays implementation                       **/
     922             : /**                                                                **/
     923             : /********************************************************************/
     924             : INLINE void **
     925   683201301 : pari_stack_base(pari_stack *s) { return s->data; }
     926             : 
     927             : INLINE void
     928     5915871 : pari_stack_init(pari_stack *s, size_t size, void **data)
     929             : {
     930     5915871 :   s->data = data;
     931     5915871 :   *data = NULL;
     932     5915871 :   s->n = 0;
     933     5915871 :   s->alloc = 0;
     934     5915871 :   s->size = size;
     935     5915871 : }
     936             : 
     937             : INLINE void
     938   677764690 : pari_stack_alloc(pari_stack *s, long nb)
     939             : {
     940   677764690 :   void **sdat = pari_stack_base(s);
     941   677728125 :   long alloc = s->alloc;
     942   677728125 :   if (s->n+nb <= alloc) return;
     943     2207031 :   if (!alloc)
     944     2106081 :     alloc = nb;
     945             :   else
     946             :   {
     947      203729 :     while (s->n+nb > alloc) alloc <<= 1;
     948             :   }
     949     2207031 :   pari_realloc_ip(sdat,alloc*s->size);
     950     2209642 :   s->alloc = alloc;
     951             : }
     952             : 
     953             : INLINE long
     954   585138233 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
     955             : 
     956             : INLINE void
     957     5447923 : pari_stack_delete(pari_stack *s)
     958             : {
     959     5447923 :   void **sdat = pari_stack_base(s);
     960     5435683 :   if (*sdat) pari_free(*sdat);
     961     5472101 : }
     962             : 
     963             : INLINE void
     964        5599 : pari_stack_pushp(pari_stack *s, void *u)
     965             : {
     966        5599 :   long n = pari_stack_new(s);
     967        5599 :   void **sdat =(void**) *pari_stack_base(s);
     968        5599 :   sdat[n] = u;
     969        5599 : }
     970             : 
     971             : /*******************************************************************/
     972             : /*                                                                 */
     973             : /*                            EXTRACT                              */
     974             : /*                                                                 */
     975             : /*******************************************************************/
     976             : INLINE GEN
     977   587503774 : vecslice(GEN A, long y1, long y2)
     978             : {
     979   587503774 :   long i,lB = y2 - y1 + 2;
     980   587503774 :   GEN B = cgetg(lB, typ(A));
     981  2614862490 :   for (i=1; i<lB; i++) B[i] = A[y1-1+i];
     982   587483368 :   return B;
     983             : }
     984             : INLINE GEN
     985     2335694 : vecslicepermute(GEN A, GEN p, long y1, long y2)
     986             : {
     987     2335694 :   long i,lB = y2 - y1 + 2;
     988     2335694 :   GEN B = cgetg(lB, typ(A));
     989    27515258 :   for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
     990     2335680 :   return B;
     991             : }
     992             : /* rowslice(rowpermute(A,p), x1, x2) */
     993             : INLINE GEN
     994      152818 : rowslicepermute(GEN x, GEN p, long j1, long j2)
     995      654319 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
     996             : 
     997             : INLINE GEN
     998    75207362 : rowslice(GEN x, long j1, long j2)
     999   604365703 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
    1000             : 
    1001             : INLINE GEN
    1002    15937967 : matslice(GEN A, long x1, long x2, long y1, long y2)
    1003    15937967 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
    1004             : 
    1005             : /* shallow, remove coeff of index j */
    1006             : INLINE GEN
    1007         210 : rowsplice(GEN x, long j)
    1008        1036 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
    1009             : 
    1010             : /* shallow, remove coeff of index j */
    1011             : INLINE GEN
    1012      354303 : vecsplice(GEN a, long j)
    1013             : {
    1014      354303 :   long i, k, l = lg(a);
    1015             :   GEN b;
    1016      354303 :   if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
    1017      354303 :   b = cgetg(l-1, typ(a));
    1018     1499709 :   for (i = k = 1; i < l; i++)
    1019     1145404 :     if (i != j) gel(b, k++) = gel(a,i);
    1020      354305 :   return b;
    1021             : }
    1022             : /* shallow */
    1023             : INLINE GEN
    1024        1036 : RgM_minor(GEN a, long i, long j)
    1025             : {
    1026        1036 :   GEN b = vecsplice(a, j);
    1027        1036 :   long k, l = lg(b);
    1028        4242 :   for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
    1029        1036 :   return b;
    1030             : }
    1031             : 
    1032             : /* A[x0,] */
    1033             : INLINE GEN
    1034      742153 : row(GEN x, long j)
    1035     6625140 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
    1036             : INLINE GEN
    1037     7790089 : Flm_row(GEN x, long j)
    1038   202842007 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
    1039             : /* A[x0,] */
    1040             : INLINE GEN
    1041      204988 : rowcopy(GEN x, long j)
    1042     2105509 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
    1043             : /* A[x0, x1..x2] */
    1044             : INLINE GEN
    1045         987 : row_i(GEN A, long x0, long x1, long x2)
    1046             : {
    1047         987 :   long i, lB = x2 - x1 + 2;
    1048         987 :   GEN B  = cgetg(lB, t_VEC);
    1049        2989 :   for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
    1050         987 :   return B;
    1051             : }
    1052             : 
    1053             : INLINE GEN
    1054      481642 : vecreverse(GEN A)
    1055             : {
    1056             :   long i, l;
    1057      481642 :   GEN B = cgetg_copy(A, &l);
    1058     1761613 :   for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
    1059      481642 :   return B;
    1060             : }
    1061             : 
    1062             : INLINE GEN
    1063        3003 : vecsmall_reverse(GEN A)
    1064             : {
    1065             :   long i, l;
    1066        3003 :   GEN B = cgetg_copy(A, &l);
    1067       12523 :   for (i=1; i<l; i++) B[i] = A[l-i];
    1068        3003 :   return B;
    1069             : }
    1070             : 
    1071             : INLINE void
    1072        2549 : vecreverse_inplace(GEN y)
    1073             : {
    1074        2549 :   long l = lg(y), lim = l>>1, i;
    1075        8179 :   for (i = 1; i <= lim; i++)
    1076             :   {
    1077        5630 :     GEN z = gel(y,i);
    1078        5630 :     gel(y,i)    = gel(y,l-i);
    1079        5630 :     gel(y,l-i) = z;
    1080             :   }
    1081        2549 : }
    1082             : 
    1083             : INLINE GEN
    1084    73407321 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
    1085             : 
    1086             : INLINE GEN
    1087    18008290 : vecpermute(GEN A, GEN x)
    1088   103758450 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
    1089             : 
    1090             : INLINE GEN
    1091     4386563 : veclast(GEN A) { return gel(A, lg(A)-1); }
    1092             : 
    1093             : INLINE GEN
    1094    13418841 : rowpermute(GEN x, GEN p)
    1095    94067151 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
    1096             :                                               : vecpermute(gel(x, i), p))
    1097             : }
    1098             : /*******************************************************************/
    1099             : /*                                                                 */
    1100             : /*                          PERMUTATIONS                           */
    1101             : /*                                                                 */
    1102             : /*******************************************************************/
    1103             : INLINE GEN
    1104     2631113 : identity_zv(long n)
    1105             : {
    1106     2631113 :   GEN v = cgetg(n+1, t_VECSMALL);
    1107             :   long i;
    1108    29312100 :   for (i = 1; i <= n; i++) v[i] = i;
    1109     2631072 :   return v;
    1110             : }
    1111             : INLINE GEN
    1112        4249 : identity_ZV(long n)
    1113             : {
    1114        4249 :   GEN v = cgetg(n+1, t_VEC);
    1115             :   long i;
    1116       51569 :   for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
    1117        4249 :   return v;
    1118             : }
    1119             : /* identity permutation */
    1120             : INLINE GEN
    1121     2606776 : identity_perm(long n) { return identity_zv(n); }
    1122             : 
    1123             : /* assume d <= n */
    1124             : INLINE GEN
    1125       98483 : cyclic_perm(long n, long d)
    1126             : {
    1127       98483 :   GEN perm = cgetg(n+1, t_VECSMALL);
    1128             :   long i;
    1129      504098 :   for (i = 1; i <= n-d; i++) perm[i] = i+d;
    1130      225029 :   for (     ; i <= n;   i++) perm[i] = i-n+d;
    1131       98483 :   return perm;
    1132             : }
    1133             : 
    1134             : /* Multiply (compose) two permutations */
    1135             : INLINE GEN
    1136    75395497 : perm_mul(GEN s, GEN x)
    1137   940952391 : { pari_APPLY_long(s[x[i]]) }
    1138             : 
    1139             : INLINE GEN
    1140         728 : perm_sqr(GEN x)
    1141       18284 : { pari_APPLY_long(x[x[i]]) }
    1142             : 
    1143             : /* Compute the inverse (reciprocal) of a permutation. */
    1144             : INLINE GEN
    1145     2672559 : perm_inv(GEN x)
    1146             : {
    1147             :   long i, lx;
    1148     2672559 :   GEN y = cgetg_copy(x, &lx);
    1149    34401426 :   for (i=1; i<lx; i++) y[ x[i] ] = i;
    1150     2672533 :   return y;
    1151             : }
    1152             : /* Return s*t*s^-1 */
    1153             : INLINE GEN
    1154      418299 : perm_conj(GEN s, GEN t)
    1155             : {
    1156             :   long i, l;
    1157      418299 :   GEN v = cgetg_copy(s, &l);
    1158     6857893 :   for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
    1159      418299 :   return v;
    1160             : }
    1161             : 
    1162             : INLINE void
    1163   437379577 : pari_free(void *pointer)
    1164             : {
    1165   437379577 :   BLOCK_SIGINT_START;
    1166   437452482 :   free(pointer);
    1167   437452482 :   BLOCK_SIGINT_END;
    1168   437442714 : }
    1169             : INLINE void*
    1170   665866125 : pari_malloc(size_t size)
    1171             : {
    1172   665866125 :   if (size)
    1173             :   {
    1174             :     char *tmp;
    1175   665867854 :     BLOCK_SIGINT_START;
    1176   665938398 :     tmp = (char*)malloc(size);
    1177   665938398 :     BLOCK_SIGINT_END;
    1178   665924324 :     if (!tmp) pari_err(e_MEM);
    1179   665927103 :     return tmp;
    1180             :   }
    1181           0 :   return NULL;
    1182             : }
    1183             : INLINE void*
    1184        1806 : pari_realloc(void *pointer, size_t size)
    1185             : {
    1186             :   char *tmp;
    1187             : 
    1188        1806 :   BLOCK_SIGINT_START;
    1189        1806 :   if (!pointer) tmp = (char *) malloc(size);
    1190        1806 :   else tmp = (char *) realloc(pointer,size);
    1191        1806 :   BLOCK_SIGINT_END;
    1192        1806 :   if (!tmp) pari_err(e_MEM);
    1193        1806 :   return tmp;
    1194             : }
    1195             : INLINE void
    1196     2210462 : pari_realloc_ip(void **pointer, size_t size)
    1197             : {
    1198             :   char *tmp;
    1199     2210462 :   BLOCK_SIGINT_START;
    1200     2210272 :   if (!*pointer) tmp = (char *) malloc(size);
    1201      104812 :   else tmp = (char *) realloc(*pointer,size);
    1202     2210272 :   if (!tmp) pari_err(e_MEM);
    1203     2210272 :   *pointer = tmp;
    1204     2210272 :   BLOCK_SIGINT_END;
    1205     2209633 : }
    1206             : 
    1207             : INLINE void*
    1208       44745 : pari_calloc(size_t size)
    1209             : {
    1210       44745 :   void *t = pari_malloc(size);
    1211       44745 :   memset(t, 0, size); return t;
    1212             : }
    1213             : INLINE GEN
    1214        8045 : cgetalloc(size_t l, long t)
    1215             : { /* evallg may raise e_OVERFLOW, which would leak x */
    1216        8045 :   ulong x0 = evaltyp(t) | evallg(l);
    1217        8045 :   GEN x = (GEN)pari_malloc(l * sizeof(long));
    1218        8045 :   x[0] = x0; return x;
    1219             : }
    1220             : 
    1221             : /*******************************************************************/
    1222             : /*                                                                 */
    1223             : /*                       GARBAGE COLLECTION                        */
    1224             : /*                                                                 */
    1225             : /*******************************************************************/
    1226             : /* copy integer x as if we had set_avma(av) */
    1227             : INLINE GEN
    1228  6968139329 : icopy_avma(GEN x, pari_sp av)
    1229             : {
    1230  6968139329 :   long i = lgefint(x), lx = i;
    1231  6968139329 :   GEN y = ((GEN)av) - i;
    1232 50305284455 :   while (--i > 0) y[i] = x[i];
    1233  6968139329 :   y[0] = evaltyp(t_INT)|evallg(lx);
    1234  6972183637 :   return y;
    1235             : }
    1236             : /* copy leaf x as if we had set_avma(av) */
    1237             : INLINE GEN
    1238   525243301 : leafcopy_avma(GEN x, pari_sp av)
    1239             : {
    1240   525243301 :   long i = lg(x);
    1241   525243301 :   GEN y = ((GEN)av) - i;
    1242  2986035925 :   while (--i > 0) y[i] = x[i];
    1243   525243301 :   y[0] = x[0] & (~CLONEBIT);
    1244   525243301 :   return y;
    1245             : }
    1246             : INLINE GEN
    1247  1019537283 : gerepileuptoleaf(pari_sp av, GEN x)
    1248             : {
    1249             :   long lx;
    1250             :   GEN q;
    1251             : 
    1252  1019537283 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1253  1018608538 :   lx = lg(x);
    1254  1018608538 :   q = ((GEN)av) - lx;
    1255  1018608538 :   set_avma((pari_sp)q);
    1256 10199359331 :   while (--lx >= 0) q[lx] = x[lx];
    1257  1018576268 :   return q;
    1258             : }
    1259             : INLINE GEN
    1260  3234295252 : gerepileuptoint(pari_sp av, GEN x)
    1261             : {
    1262  3234295252 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1263  2851320411 :   set_avma((pari_sp)icopy_avma(x, av));
    1264  2854551114 :   return (GEN)avma;
    1265             : }
    1266             : INLINE GEN
    1267  1520500998 : gerepileupto(pari_sp av, GEN x)
    1268             : {
    1269  1520500998 :   if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
    1270  1341554161 :   switch(typ(x))
    1271             :   { /* non-default = !is_recursive_t(tq) */
    1272   374089575 :     case t_INT: return gerepileuptoint(av, x);
    1273   305224498 :     case t_REAL:
    1274             :     case t_STR:
    1275   305224498 :     case t_VECSMALL: return gerepileuptoleaf(av,x);
    1276   662240088 :     default:
    1277             :       /* NB: x+i --> ((long)x) + i*sizeof(long) */
    1278   662240088 :       return gerepile(av, (pari_sp) (x+lg(x)), x);
    1279             :   }
    1280             : }
    1281             : 
    1282             : /* gerepileupto(av, gcopy(x)) */
    1283             : INLINE GEN
    1284   184833786 : gerepilecopy(pari_sp av, GEN x)
    1285             : {
    1286   184833786 :   if (is_recursive_t(typ(x)))
    1287             :   {
    1288   176579012 :     GENbin *p = copy_bin(x);
    1289   176601438 :     set_avma(av); return bin_copy(p);
    1290             :   }
    1291             :   else
    1292             :   {
    1293     8254316 :     set_avma(av);
    1294     8254361 :     if (x < (GEN)av) {
    1295     6391153 :       if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
    1296     6391153 :       x = leafcopy_avma(x, av);
    1297     6391181 :       set_avma((pari_sp)x);
    1298             :     } else
    1299     1863208 :       x = leafcopy(x);
    1300     8254394 :     return x;
    1301             :   }
    1302             : }
    1303             : 
    1304             : INLINE void
    1305    47716965 : guncloneNULL(GEN x) { if (x) gunclone(x); }
    1306             : INLINE void
    1307     1409728 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
    1308             : 
    1309             : /* Takes an array of pointers to GENs, of length n. Copies all
    1310             :  * objects to contiguous locations and cleans up the stack between
    1311             :  * av and avma. */
    1312             : INLINE void
    1313      971815 : gerepilemany(pari_sp av, GEN* gptr[], int n)
    1314             : {
    1315             :   int i;
    1316     3878562 :   for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
    1317      971422 :   set_avma(av);
    1318     3879295 :   for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1319      972062 : }
    1320             : 
    1321             : INLINE void
    1322    18254235 : gerepileall(pari_sp av, int n, ...)
    1323             : {
    1324             :   int i;
    1325    18254235 :   va_list a; va_start(a, n);
    1326    18254235 :   if (n < 10)
    1327             :   {
    1328             :     GEN *gptr[10];
    1329    54982388 :     for (i=0; i<n; i++)
    1330    36727639 :     { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
    1331    18254749 :     set_avma(av);
    1332    54982793 :     for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1333             : 
    1334             :   }
    1335             :   else
    1336             :   {
    1337           0 :     GEN **gptr = (GEN**)  pari_malloc(n*sizeof(GEN*));
    1338           0 :     for (i=0; i<n; i++)
    1339           0 :     { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
    1340           0 :     set_avma(av);
    1341           0 :     for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
    1342           0 :     pari_free(gptr);
    1343             :   }
    1344    18255343 :   va_end(a);
    1345    18255343 : }
    1346             : 
    1347             : /* assume 1 <= n < 10 */
    1348             : INLINE GEN
    1349    77865176 : gc_all(pari_sp av, int n, ...)
    1350             : {
    1351             :   int i;
    1352             :   GEN *v[10];
    1353    77865176 :   va_list a; va_start(a, n);
    1354   261828733 :   for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
    1355    77865495 :   set_avma(av);
    1356   261829408 :   for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
    1357    77865705 :   return *v[0];
    1358             : }
    1359             : 
    1360             : INLINE void
    1361     2159216 : gerepilecoeffs(pari_sp av, GEN x, int n)
    1362             : {
    1363             :   int i;
    1364    26096842 :   for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
    1365     2159639 :   set_avma(av);
    1366    26098112 :   for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
    1367     2159379 : }
    1368             : 
    1369             : /* p from copy_bin. Copy p->x back to stack, then destroy p */
    1370             : INLINE GEN
    1371   424170933 : bin_copy(GENbin *p)
    1372             : {
    1373             :   GEN x, y, base;
    1374             :   long dx, len;
    1375             : 
    1376   424170933 :   x   = p->x; if (!x) { pari_free(p); return gen_0; }
    1377   399039316 :   len = p->len;
    1378   399039316 :   base= p->base; dx = x - base;
    1379   399039316 :   y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
    1380   399031089 :   y += dx;
    1381   399031089 :   p->rebase(y, ((ulong)y-(ulong)x));
    1382   399035642 :   pari_free(p); return y;
    1383             : }
    1384             : 
    1385             : INLINE GEN
    1386   823185564 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
    1387             : 
    1388             : INLINE void
    1389   118477146 : cgiv(GEN x)
    1390             : {
    1391   118477146 :   pari_sp av = (pari_sp)(x+lg(x));
    1392   118477146 :   if (isonstack((GEN)av)) set_avma(av);
    1393   118480228 : }
    1394             : 
    1395             : INLINE void
    1396     1789494 : killblock(GEN x) { gunclone(x); }
    1397             : 
    1398             : INLINE int
    1399   288693946 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
    1400             : 
    1401             : /*******************************************************************/
    1402             : /*                                                                 */
    1403             : /*                    CONVERSION / ASSIGNMENT                      */
    1404             : /*                                                                 */
    1405             : /*******************************************************************/
    1406             : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
    1407             : INLINE GEN
    1408    16986172 : cxcompotor(GEN z, long prec)
    1409             : {
    1410    16986172 :   switch(typ(z))
    1411             :   {
    1412    11125911 :     case t_INT:  return itor(z, prec);
    1413      289877 :     case t_FRAC: return fractor(z, prec);
    1414     5570672 :     case t_REAL: return rtor(z, prec);
    1415           0 :     default: pari_err_TYPE("cxcompotor",z);
    1416             :              return NULL; /* LCOV_EXCL_LINE */
    1417             :   }
    1418             : }
    1419             : INLINE GEN
    1420     8477404 : cxtofp(GEN x, long prec)
    1421     8477404 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
    1422             : 
    1423             : INLINE GEN
    1424      275770 : cxtoreal(GEN q)
    1425      275770 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
    1426             : 
    1427             : INLINE double
    1428    56505482 : gtodouble(GEN x)
    1429             : {
    1430    56505482 :   if (typ(x)!=t_REAL) {
    1431     6382436 :     pari_sp av = avma;
    1432     6382436 :     x = gtofp(x, DEFAULTPREC);
    1433     6381925 :     if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
    1434     6381925 :     set_avma(av);
    1435             :   }
    1436    56504901 :   return rtodbl(x);
    1437             : }
    1438             : 
    1439             : INLINE int
    1440     2624406 : gisdouble(GEN x, double *g)
    1441             : {
    1442     2624406 :   if (typ(x)!=t_REAL) {
    1443       56689 :     pari_sp av = avma;
    1444       56689 :     x = gtofp(x, DEFAULTPREC);
    1445       56688 :     if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
    1446       56688 :     set_avma(av);
    1447             :   }
    1448     2624396 :   if (expo(x) >= 0x3ff) return 0;
    1449     2624396 :   *g = rtodbl(x); return 1;
    1450             : }
    1451             : 
    1452             : INLINE long
    1453    85688503 : gtos(GEN x) {
    1454    85688503 :   if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
    1455    85688489 :   return itos(x);
    1456             : }
    1457             : 
    1458             : INLINE ulong
    1459      106327 : gtou(GEN x) {
    1460      106327 :   if (typ(x) != t_INT || signe(x)<0)
    1461           7 :     pari_err_TYPE("gtou [integer >=0 expected]",x);
    1462      106320 :   return itou(x);
    1463             : }
    1464             : 
    1465             : INLINE GEN
    1466    41530352 : absfrac(GEN x)
    1467             : {
    1468    41530352 :   GEN y = cgetg(3, t_FRAC);
    1469    41530378 :   gel(y,1) = absi(gel(x,1));
    1470    41530402 :   gel(y,2) = icopy(gel(x,2)); return y;
    1471             : }
    1472             : INLINE GEN
    1473       46150 : absfrac_shallow(GEN x)
    1474       46150 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
    1475             : INLINE GEN
    1476     7158276 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
    1477             : INLINE GEN
    1478      166750 : Q_abs_shallow(GEN x)
    1479      166750 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
    1480             : INLINE GEN
    1481       12971 : R_abs_shallow(GEN x)
    1482       12971 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
    1483             : INLINE GEN
    1484           0 : R_abs(GEN x)
    1485           0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
    1486             : 
    1487             : /* Force z to be of type real/complex with floating point components */
    1488             : INLINE GEN
    1489   208117850 : gtofp(GEN z, long prec)
    1490             : {
    1491   208117850 :   switch(typ(z))
    1492             :   {
    1493   175573053 :     case t_INT:  return itor(z, prec);
    1494     4093372 :     case t_FRAC: return fractor(z, prec);
    1495    20238266 :     case t_REAL: return rtor(z, prec);
    1496     8219626 :     case t_COMPLEX: {
    1497     8219626 :       GEN a = gel(z,1), b = gel(z,2);
    1498     8219626 :       if (isintzero(b)) return cxcompotor(a, prec);
    1499     8219646 :       if (isintzero(a)) {
    1500        8903 :         GEN y = cgetg(3, t_COMPLEX);
    1501        8903 :         b = cxcompotor(b, prec);
    1502        8903 :         gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
    1503        8903 :         gel(y,2) = b; return y;
    1504             :       }
    1505     8210701 :       return cxtofp(z, prec);
    1506             :     }
    1507           0 :     case t_QUAD: return quadtofp(z, prec);
    1508           0 :     default: pari_err_TYPE("gtofp",z);
    1509             :              return NULL; /* LCOV_EXCL_LINE */
    1510             :   }
    1511             : }
    1512             : /* Force z to be of type real / int */
    1513             : INLINE GEN
    1514       22428 : gtomp(GEN z, long prec)
    1515             : {
    1516       22428 :   switch(typ(z))
    1517             :   {
    1518          42 :     case t_INT:  return z;
    1519       22386 :     case t_FRAC: return fractor(z, prec);
    1520           0 :     case t_REAL: return rtor(z, prec);
    1521           0 :     case t_QUAD: z = quadtofp(z, prec);
    1522           0 :                  if (typ(z) == t_REAL) return z;
    1523           0 :     default: pari_err_TYPE("gtomp",z);
    1524             :              return NULL; /* LCOV_EXCL_LINE */
    1525             :   }
    1526             : }
    1527             : 
    1528             : INLINE GEN
    1529     4617714 : RgX_gtofp(GEN x, long prec)
    1530             : {
    1531             :   long l;
    1532     4617714 :   GEN y = cgetg_copy(x, &l);
    1533    26123572 :   while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
    1534     4616306 :   y[1] = x[1]; return y;
    1535             : }
    1536             : INLINE GEN
    1537    29487836 : RgC_gtofp(GEN x, long prec)
    1538   184084076 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
    1539             : 
    1540             : INLINE GEN
    1541          56 : RgV_gtofp(GEN x, long prec)
    1542        4781 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
    1543             : 
    1544             : INLINE GEN
    1545     7119399 : RgM_gtofp(GEN x, long prec)
    1546    35979419 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
    1547             : 
    1548             : INLINE GEN
    1549         574 : RgC_gtomp(GEN x, long prec)
    1550       23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
    1551             : 
    1552             : INLINE GEN
    1553          21 : RgM_gtomp(GEN x, long prec)
    1554         595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
    1555             : 
    1556             : INLINE GEN
    1557       59828 : RgX_fpnorml2(GEN x, long prec)
    1558             : {
    1559       59828 :   pari_sp av = avma;
    1560       59828 :   return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
    1561             : }
    1562             : INLINE GEN
    1563      616605 : RgC_fpnorml2(GEN x, long prec)
    1564             : {
    1565      616605 :   pari_sp av = avma;
    1566      616605 :   return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
    1567             : }
    1568             : INLINE GEN
    1569       21569 : RgM_fpnorml2(GEN x, long prec)
    1570             : {
    1571       21569 :   pari_sp av = avma;
    1572       21569 :   return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
    1573             : }
    1574             : 
    1575             : /* y a t_REAL */
    1576             : INLINE void
    1577      220528 : affgr(GEN x, GEN y)
    1578             : {
    1579             :   pari_sp av;
    1580      220528 :   switch(typ(x)) {
    1581        5992 :     case t_INT:  affir(x,y); break;
    1582      214536 :     case t_REAL: affrr(x,y); break;
    1583           0 :     case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
    1584           0 :     case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
    1585           0 :     default: pari_err_TYPE2("=",x,y);
    1586             :   }
    1587      220528 : }
    1588             : 
    1589             : INLINE GEN
    1590      245323 : affc_fixlg(GEN x, GEN res)
    1591             : {
    1592      245323 :   if (typ(x) == t_COMPLEX)
    1593             :   {
    1594      212863 :     affrr_fixlg(gel(x,1), gel(res,1));
    1595      212863 :     affrr_fixlg(gel(x,2), gel(res,2));
    1596             :   }
    1597             :   else
    1598             :   {
    1599       32460 :     set_avma((pari_sp)(res+3));
    1600       32460 :     res = cgetr(realprec(gel(res,1)));
    1601       32460 :     affrr_fixlg(x, res);
    1602             :   }
    1603      245323 :   return res;
    1604             : }
    1605             : 
    1606             : INLINE GEN
    1607           0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
    1608             : 
    1609             : /*******************************************************************/
    1610             : /*                                                                 */
    1611             : /*                          LENGTH CONVERSIONS                     */
    1612             : /*                                                                 */
    1613             : /*******************************************************************/
    1614             : INLINE long
    1615       39722 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
    1616             : INLINE long
    1617       31480 : ndec2prec(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
    1618             : INLINE long
    1619        8242 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
    1620             : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
    1621             :  * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
    1622             :  *   addl, shrl instead of subl, sarl, addl */
    1623             : INLINE long
    1624    12082210 : nbits2nlong(long x) {
    1625    12082210 :   return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1626             : }
    1627             : 
    1628             : INLINE long
    1629  1120904668 : nbits2extraprec(long x) {
    1630  1120904668 :   return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
    1631             : }
    1632             : 
    1633             : INLINE long
    1634   137773855 : nbits2prec(long x) {
    1635   137773855 :   return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
    1636             : }
    1637             : INLINE long
    1638  1863734549 : nbits2lg(long x) {
    1639  1863734549 :   return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1640             : }
    1641             : INLINE long
    1642    11973166 : prec2lg(long x) {
    1643    11973166 :   return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
    1644             : }
    1645             : INLINE long
    1646   796163462 : lg2prec(long x){ return (x-2) * BITS_IN_LONG; }
    1647             : 
    1648             : /* ceil(x / sizeof(long)) */
    1649             : INLINE long
    1650    82400107 : nchar2nlong(long x) {
    1651    82400107 :   return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
    1652             : }
    1653             : INLINE long
    1654   226338107 : prec2nbits(long x) { return x; }
    1655             : INLINE double
    1656     2871305 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
    1657             : INLINE double
    1658      590469 : prec2nbits_mul(long x, double y) { return x * y; }
    1659             : INLINE long
    1660   124132025 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
    1661             : INLINE long
    1662  2594101996 : bit_accuracy(long x) { return (x-2) * BITS_IN_LONG; }
    1663             : INLINE long
    1664        9515 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
    1665             : INLINE long
    1666         214 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
    1667             : INLINE long
    1668        4636 : precdbl(long x) {return x << 1;}
    1669             : INLINE long
    1670  7013471785 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
    1671             : INLINE long
    1672  6927120687 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
    1673             : 
    1674             : /*********************************************************************/
    1675             : /**                                                                 **/
    1676             : /**                      OPERATIONS MODULO m                        **/
    1677             : /**                                                                 **/
    1678             : /*********************************************************************/
    1679             : /* Assume m > 0, more efficient if 0 <= a, b < m */
    1680             : 
    1681             : INLINE GEN
    1682    46530576 : Fp_red(GEN a, GEN m) { return modii(a, m); }
    1683             : INLINE GEN
    1684   168508893 : Fp_add(GEN a, GEN b, GEN m)
    1685             : {
    1686   168508893 :   pari_sp av=avma;
    1687   168508893 :   GEN p = addii(a,b);
    1688   167076234 :   long s = signe(p);
    1689   167076234 :   if (!s) return p; /* = gen_0 */
    1690   155935067 :   if (s > 0) /* general case */
    1691             :   {
    1692   155948455 :     GEN t = subii(p, m);
    1693   155597177 :     s = signe(t);
    1694   155597177 :     if (!s) return gc_const(av, gen_0);
    1695   148021620 :     if (s < 0) return gc_const((pari_sp)p, p);
    1696    71877264 :     if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
    1697     3311788 :     p = remii(t, m);
    1698             :   }
    1699             :   else
    1700      265415 :     p = modii(p, m);
    1701     3577296 :   return gerepileuptoint(av, p);
    1702             : }
    1703             : INLINE GEN
    1704    20382100 : Fp_double(GEN x, GEN N)
    1705             : {
    1706    20382100 :   GEN z = shifti(x, 1);
    1707    19660819 :   return cmpii(z, N) >= 0? subii(z, N): z;
    1708             : }
    1709             : INLINE GEN
    1710   134812393 : Fp_sub(GEN a, GEN b, GEN m)
    1711             : {
    1712   134812393 :   pari_sp av=avma;
    1713   134812393 :   GEN p = subii(a,b);
    1714   132957377 :   long s = signe(p);
    1715   132957377 :   if (!s) return p; /* = gen_0 */
    1716   123572546 :   if (s > 0)
    1717             :   {
    1718    62181131 :     if (cmpii(p, m) < 0) return p; /* general case ! */
    1719     1322211 :     p = remii(p, m);
    1720             :   }
    1721             :   else
    1722             :   {
    1723    61391415 :     GEN t = addii(p, m);
    1724    63056002 :     if (!s) return gc_const(av, gen_0);
    1725    63114439 :     if (s > 0) return gerepileuptoint(av, t); /* general case ! */
    1726    63114439 :     p = modii(t, m);
    1727             :   }
    1728    64733474 :   return gerepileuptoint(av, p);
    1729             : }
    1730             : INLINE GEN
    1731    26330713 : Fp_neg(GEN b, GEN m)
    1732             : {
    1733    26330713 :   pari_sp av = avma;
    1734    26330713 :   long s = signe(b);
    1735             :   GEN p;
    1736    26330713 :   if (!s) return gen_0;
    1737    22578785 :   if (s > 0)
    1738             :   {
    1739    21458189 :     p = subii(m, b);
    1740    21456152 :     if (signe(p) >= 0) return p; /* general case ! */
    1741      384298 :     p = modii(p, m);
    1742             :   } else
    1743     1121379 :     p = remii(negi(b), m);
    1744     1505922 :   return gerepileuptoint(av, p);
    1745             : }
    1746             : 
    1747             : INLINE GEN
    1748      252533 : Fp_halve(GEN a, GEN p)
    1749             : {
    1750      252533 :   if (mpodd(a)) a = addii(a,p);
    1751      252533 :   return shifti(a,-1);
    1752             : }
    1753             : 
    1754             : /* assume 0 <= u < p and ps2 = p>>1 */
    1755             : INLINE GEN
    1756    70379299 : Fp_center(GEN u, GEN p, GEN ps2)
    1757    70379299 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
    1758             : /* same without copy */
    1759             : INLINE GEN
    1760    13218741 : Fp_center_i(GEN u, GEN p, GEN ps2)
    1761    13218741 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
    1762             : 
    1763             : /* x + y*z mod p */
    1764             : INLINE GEN
    1765    11051124 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
    1766             : {
    1767             :   pari_sp av;
    1768    11051124 :   if (!signe(y) || !signe(z)) return Fp_red(x, p);
    1769    10721096 :   if (!signe(x)) return Fp_mul(z,y, p);
    1770     9729007 :   av = avma;
    1771     9729007 :   return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
    1772             : }
    1773             : 
    1774             : INLINE GEN
    1775   173556576 : Fp_mul(GEN a, GEN b, GEN m)
    1776             : {
    1777   173556576 :   pari_sp av=avma;
    1778             :   GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1779   173556576 :   (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
    1780   173558225 :   p = mulii(a,b);
    1781   173553725 :   set_avma(av); return modii(p,m);
    1782             : }
    1783             : INLINE GEN
    1784    61784367 : Fp_sqr(GEN a, GEN m)
    1785             : {
    1786    61784367 :   pari_sp av=avma;
    1787             :   GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1788    61784367 :   (void)new_chunk((lg(a)+lg(m))<<1);
    1789    62087441 :   p = sqri(a);
    1790    59777971 :   set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
    1791             : }
    1792             : INLINE GEN
    1793    62868249 : Fp_mulu(GEN a, ulong b, GEN m)
    1794             : {
    1795    62868249 :   long l = lgefint(m);
    1796    62868249 :   if (l == 3)
    1797             :   {
    1798    40529566 :     ulong mm = m[2];
    1799    40529566 :     return utoi( Fl_mul(umodiu(a, mm), b, mm) );
    1800             :   } else {
    1801    22338683 :     pari_sp av = avma;
    1802             :     GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1803    22338683 :     (void)new_chunk(lg(a)+1+(l<<1));
    1804    22347519 :     p = muliu(a,b);
    1805    21926523 :     set_avma(av); return modii(p,m);
    1806             :   }
    1807             : }
    1808             : INLINE GEN
    1809       17780 : Fp_muls(GEN a, long b, GEN m)
    1810             : {
    1811       17780 :   long l = lgefint(m);
    1812       17780 :   if (l == 3)
    1813             :   {
    1814        3578 :     ulong mm = m[2];
    1815        3578 :     if (b < 0)
    1816             :     {
    1817        3578 :       ulong t = Fl_mul(umodiu(a, mm), -b, mm);
    1818        3578 :       return t? utoipos(mm - t): gen_0;
    1819             :     }
    1820             :     else
    1821           0 :       return utoi( Fl_mul(umodiu(a, mm), b, mm) );
    1822             :   } else {
    1823       14202 :     pari_sp av = avma;
    1824             :     GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1825       14202 :     (void)new_chunk(lg(a)+1+(l<<1));
    1826       14202 :     p = mulis(a,b);
    1827       14202 :     set_avma(av); return modii(p,m);
    1828             :   }
    1829             : }
    1830             : 
    1831             : INLINE GEN
    1832    24990906 : Fp_inv(GEN a, GEN m)
    1833             : {
    1834             :   GEN res;
    1835    24990906 :   if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
    1836    24990440 :   return res;
    1837             : }
    1838             : INLINE GEN
    1839     1182486 : Fp_invsafe(GEN a, GEN m)
    1840             : {
    1841             :   GEN res;
    1842     1182486 :   if (! invmod(a,m,&res)) return NULL;
    1843     1182393 :   return res;
    1844             : }
    1845             : INLINE GEN
    1846     1462198 : Fp_div(GEN a, GEN b, GEN m)
    1847             : {
    1848     1462198 :   pari_sp av = avma;
    1849             :   GEN p;
    1850     1462198 :   if (lgefint(b) == 3)
    1851             :   {
    1852      507777 :     a = Fp_divu(a, b[2], m);
    1853      507777 :     if (signe(b) < 0) a = Fp_neg(a, m);
    1854      507777 :     return a;
    1855             :   }
    1856             :   /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
    1857      954421 :   (void)new_chunk(lg(a)+(lg(m)<<1));
    1858      954421 :   p = mulii(a, Fp_inv(b,m));
    1859      954421 :   set_avma(av); return modii(p,m);
    1860             : }
    1861             : INLINE GEN
    1862     1754996 : Fp_divu(GEN x, ulong a, GEN p)
    1863             : {
    1864     1754996 :   pari_sp av = avma;
    1865             :   ulong b;
    1866     1754996 :   if (lgefint(p) == 3)
    1867             :   {
    1868     1356781 :     ulong pp = p[2], xp = umodiu(x, pp);
    1869     1356781 :     return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
    1870             :   }
    1871      398215 :   x = Fp_red(x, p);
    1872      398217 :   b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
    1873      398217 :   return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
    1874             : }
    1875             : 
    1876             : INLINE GEN
    1877     1085598 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
    1878             : 
    1879             : INLINE GEN
    1880     2517216 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1881             : 
    1882             : INLINE long
    1883     2472568 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
    1884             : 
    1885             : INLINE long
    1886     1934518 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
    1887             : 
    1888             : INLINE GEN
    1889         399 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1890             : 
    1891             : INLINE long
    1892      376978 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1893             : 
    1894             : INLINE long
    1895      201663 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1896             : 
    1897             : INLINE GEN
    1898    25423485 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1899             : 
    1900             : INLINE long
    1901    66728146 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
    1902             : 
    1903             : INLINE long
    1904    83682856 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1905             : 
    1906             : INLINE GEN
    1907        7977 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1908             : 
    1909             : INLINE long
    1910      261845 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1911             : 
    1912             : INLINE long
    1913      315054 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1914             : 
    1915             : INLINE GEN
    1916     3471589 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1917             : 
    1918             : INLINE long
    1919     6977016 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1920             : 
    1921             : INLINE long
    1922     5803184 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1923             : 
    1924             : INLINE GEN
    1925      146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
    1926             : 
    1927             : INLINE long
    1928       51837 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
    1929             : 
    1930             : INLINE long
    1931        3686 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
    1932             : 
    1933             : /*******************************************************************/
    1934             : /*                                                                 */
    1935             : /*                        ADDMULII / SUBMULII                      */
    1936             : /*                                                                 */
    1937             : /*******************************************************************/
    1938             : /* x - y*z */
    1939             : INLINE GEN
    1940    32792527 : submulii(GEN x, GEN y, GEN z)
    1941             : {
    1942    32792527 :   long lx = lgefint(x), ly, lz;
    1943             :   pari_sp av;
    1944             :   GEN t;
    1945    32792527 :   if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
    1946    30206963 :   ly = lgefint(y);
    1947    30206963 :   if (ly == 2) return icopy(x);
    1948    29026619 :   lz = lgefint(z);
    1949    29026619 :   av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
    1950    29026619 :   t = mulii(z, y);
    1951    29026619 :   set_avma(av); return subii(x,t);
    1952             : }
    1953             : /* y*z - x */
    1954             : INLINE GEN
    1955     3542240 : mulsubii(GEN y, GEN z, GEN x)
    1956             : {
    1957     3542240 :   long lx = lgefint(x), ly, lz;
    1958             :   pari_sp av;
    1959             :   GEN t;
    1960     3542240 :   if (lx == 2) return mulii(z,y);
    1961     2268102 :   ly = lgefint(y);
    1962     2268102 :   if (ly == 2) return negi(x);
    1963     2058968 :   lz = lgefint(z);
    1964     2058968 :   av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
    1965     2058993 :   t = mulii(z, y);
    1966     2058939 :   set_avma(av); return subii(t,x);
    1967             : }
    1968             : 
    1969             : /* x - u*y */
    1970             : INLINE GEN
    1971        7693 : submuliu(GEN x, GEN y, ulong u)
    1972             : {
    1973             :   pari_sp av;
    1974        7693 :   long ly = lgefint(y);
    1975        7693 :   if (ly == 2) return icopy(x);
    1976        7693 :   av = avma;
    1977        7693 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1978        7693 :   y = mului(u,y);
    1979        7693 :   set_avma(av); return subii(x, y);
    1980             : }
    1981             : /* x + u*y */
    1982             : INLINE GEN
    1983      406285 : addmuliu(GEN x, GEN y, ulong u)
    1984             : {
    1985             :   pari_sp av;
    1986      406285 :   long ly = lgefint(y);
    1987      406285 :   if (ly == 2) return icopy(x);
    1988      406285 :   av = avma;
    1989      406285 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    1990      406285 :   y = mului(u,y);
    1991      406285 :   set_avma(av); return addii(x, y);
    1992             : }
    1993             : /* x - u*y */
    1994             : INLINE GEN
    1995    59282201 : submuliu_inplace(GEN x, GEN y, ulong u)
    1996             : {
    1997             :   pari_sp av;
    1998    59282201 :   long ly = lgefint(y);
    1999    59282201 :   if (ly == 2) return x;
    2000    37999446 :   av = avma;
    2001    37999446 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    2002    38003975 :   y = mului(u,y);
    2003    38002445 :   set_avma(av); return subii(x, y);
    2004             : }
    2005             : /* x + u*y */
    2006             : INLINE GEN
    2007    58558834 : addmuliu_inplace(GEN x, GEN y, ulong u)
    2008             : {
    2009             :   pari_sp av;
    2010    58558834 :   long ly = lgefint(y);
    2011    58558834 :   if (ly == 2) return x;
    2012    37858224 :   av = avma;
    2013    37858224 :   (void)new_chunk(3+ly+lgefint(x)); /* HACK */
    2014    37862851 :   y = mului(u,y);
    2015    37861285 :   set_avma(av); return addii(x, y);
    2016             : }
    2017             : /* ux + vy */
    2018             : INLINE GEN
    2019    36638903 : lincombii(GEN u, GEN v, GEN x, GEN y)
    2020             : {
    2021    36638903 :   long lx = lgefint(x), ly;
    2022             :   GEN p1, p2;
    2023             :   pari_sp av;
    2024    36638903 :   if (lx == 2) return mulii(v,y);
    2025    23086794 :   ly = lgefint(y);
    2026    23086794 :   if (ly == 2) return mulii(u,x);
    2027    20633355 :   av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
    2028    20636942 :   p1 = mulii(u,x);
    2029    20634895 :   p2 = mulii(v,y);
    2030    20634883 :   set_avma(av); return addii(p1,p2);
    2031             : }
    2032             : 
    2033             : /*******************************************************************/
    2034             : /*                                                                 */
    2035             : /*                          GEN SUBTYPES                           */
    2036             : /*                                                                 */
    2037             : /*******************************************************************/
    2038             : 
    2039             : INLINE int
    2040  4551632133 : is_const_t(long t) { return (t < t_POLMOD); }
    2041             : INLINE int
    2042        6932 : is_extscalar_t(long t) { return (t <= t_POL); }
    2043             : INLINE int
    2044     7900926 : is_intreal_t(long t) { return (t <= t_REAL); }
    2045             : INLINE int
    2046   585581157 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
    2047             : INLINE int
    2048    92855623 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
    2049             : INLINE int
    2050           0 : is_qfb_t(long t) { return (t == t_QFB); }
    2051             : INLINE int
    2052     4024174 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
    2053             : INLINE int
    2054    62038356 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
    2055             : INLINE int
    2056  7514442611 : is_recursive_t(long t) { return lontyp[t]; }
    2057             : INLINE int
    2058   297716833 : is_scalar_t(long t) { return (t < t_POL); }
    2059             : INLINE int
    2060     1709000 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
    2061             : 
    2062             : INLINE int
    2063    58914816 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
    2064             : 
    2065             : /*******************************************************************/
    2066             : /*                                                                 */
    2067             : /*                         TRANSCENDENTAL                          */
    2068             : /*                                                                 */
    2069             : /*******************************************************************/
    2070             : INLINE GEN
    2071    65159851 : sqrtr(GEN x) {
    2072    65159851 :   long s = signe(x);
    2073    65159851 :   if (s == 0) return real_0_bit(expo(x) >> 1);
    2074    65126707 :   if (s >= 0) return sqrtr_abs(x);
    2075      259437 :   retmkcomplex(gen_0, sqrtr_abs(x));
    2076             : }
    2077             : INLINE GEN
    2078           0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
    2079             : INLINE GEN
    2080           0 : cbrtr(GEN x) {
    2081           0 :   long s = signe(x);
    2082             :   GEN r;
    2083           0 :   if (s == 0) return real_0_bit(expo(x) / 3);
    2084           0 :   r = cbrtr_abs(x);
    2085           0 :   if (s < 0) togglesign(r);
    2086           0 :   return r;
    2087             : }
    2088             : INLINE GEN
    2089     2479084 : sqrtnr(GEN x, long n) {
    2090     2479084 :   long s = signe(x);
    2091             :   GEN r;
    2092     2479084 :   if (s == 0) return real_0_bit(expo(x) / n);
    2093     2479084 :   r = sqrtnr_abs(x, n);
    2094     2479126 :   if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
    2095     2479126 :   return r;
    2096             : }
    2097             : INLINE long
    2098      742451 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
    2099             : INLINE ulong
    2100     1786833 : ulogint(ulong B, ulong y)
    2101             : {
    2102             :   ulong r;
    2103             :   long e;
    2104     1786833 :   if (y == 2) return expu(B);
    2105     1737909 :   r = y;
    2106     5296293 :   for (e=1;; e++)
    2107             :   { /* here, r = y^e, r2 = y^(e-1) */
    2108     5296293 :     if (r >= B) return r == B? e: e-1;
    2109     3559840 :     r = umuluu_or_0(y, r);
    2110     3559935 :     if (!r) return e;
    2111             :   }
    2112             : }
    2113             : 
    2114             : /*******************************************************************/
    2115             : /*                                                                 */
    2116             : /*                         MISCELLANEOUS                           */
    2117             : /*                                                                 */
    2118             : /*******************************************************************/
    2119     7900843 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
    2120  2625359541 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
    2121    14844932 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
    2122     4563978 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
    2123  1077968143 : INLINE int equali1(GEN n)
    2124  1077968143 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
    2125   137922217 : INLINE int equalim1(GEN n)
    2126   137922217 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
    2127             : /* works only for POSITIVE integers */
    2128  2181775793 : INLINE int is_pm1(GEN n)
    2129  2181775793 : { return lgefint(n) == 3 && n[2] == 1; }
    2130   503179816 : INLINE int is_bigint(GEN n)
    2131   503179816 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
    2132             : 
    2133  1995062156 : INLINE int odd(long x) { return x & 1; }
    2134    66451746 : INLINE int both_odd(long x, long y) { return x & y & 1; }
    2135             : 
    2136             : INLINE int
    2137  6511196660 : isonstack(GEN x)
    2138  6511196660 : { return ((pari_sp)x >= pari_mainstack->bot
    2139  6511196660 :        && (pari_sp)x <  pari_mainstack->top); }
    2140             : 
    2141             : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
    2142             : INLINE double
    2143    66126853 : dbllog2r(GEN x)
    2144    66126853 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
    2145             : 
    2146             : INLINE GEN
    2147     1343701 : mul_content(GEN cx, GEN cy)
    2148             : {
    2149     1343701 :   if (!cx) return cy;
    2150      529339 :   if (!cy) return cx;
    2151      338138 :   return gmul(cx,cy);
    2152             : }
    2153             : INLINE GEN
    2154           0 : inv_content(GEN c) { return c? ginv(c): NULL; }
    2155             : INLINE GEN
    2156       37781 : div_content(GEN cx, GEN cy)
    2157             : {
    2158       37781 :   if (!cy) return cx;
    2159       36689 :   if (!cx) return ginv(cy);
    2160        7419 :   return gdiv(cx,cy);
    2161             : }
    2162             : INLINE GEN
    2163     5916905 : mul_denom(GEN dx, GEN dy)
    2164             : {
    2165     5916905 :   if (!dx) return dy;
    2166     1703318 :   if (!dy) return dx;
    2167      694210 :   return mulii(dx,dy);
    2168             : }
    2169             : 
    2170             : /* POLYNOMIALS */
    2171             : INLINE GEN
    2172     1371590 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
    2173             : INLINE GEN
    2174   160498038 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
    2175             : INLINE ulong
    2176      761523 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
    2177             : INLINE ulong
    2178      137780 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
    2179             : INLINE long
    2180  4749910547 : degpol(GEN x) { return lg(x)-3; }
    2181             : INLINE long
    2182  2426180432 : lgpol(GEN x) { return lg(x)-2; }
    2183             : INLINE long
    2184   325451952 : lgcols(GEN x) { return lg(gel(x,1)); }
    2185             : INLINE long
    2186   141574255 : nbrows(GEN x) { return lg(gel(x,1))-1; }
    2187             : INLINE GEN
    2188           0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
    2189             : 
    2190             : INLINE GEN
    2191     1677545 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
    2192             : INLINE GEN
    2193      626337 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
    2194             : 
    2195             : INLINE GEN
    2196    97870549 : RgX_copy(GEN x)
    2197             : {
    2198             :   long lx, i;
    2199    97870549 :   GEN y = cgetg_copy(x, &lx); y[1] = x[1];
    2200   356151923 :   for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
    2201    97870587 :   return y;
    2202             : }
    2203             : /* have to use ulong to avoid silly warnings from gcc "assuming signed
    2204             :  * overflow does not occur" */
    2205             : INLINE GEN
    2206     2517576 : RgX_coeff(GEN x, long n)
    2207             : {
    2208     2517576 :   ulong l = lg(x);
    2209     2517576 :   return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
    2210             : }
    2211             : INLINE GEN
    2212      347497 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
    2213             : INLINE GEN
    2214     6916324 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
    2215             : INLINE GEN
    2216        1904 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
    2217             : INLINE GEN
    2218      107442 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
    2219             : INLINE GEN
    2220     5122313 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
    2221             : INLINE GEN
    2222     1987006 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
    2223             : INLINE GEN
    2224    21099141 : Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
    2225    21099141 : { return Flx_divrem_pre(x,y,p,pi, NULL); }
    2226             : INLINE GEN
    2227     1258831 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
    2228             : INLINE GEN
    2229           0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
    2230             : INLINE GEN
    2231    97913469 : pol0_Flx(long sv) { return mkvecsmall(sv); }
    2232             : INLINE GEN
    2233    54801464 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
    2234             : INLINE GEN
    2235    35593031 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
    2236             : INLINE GEN
    2237           0 : zero_zx(long sv) { return zero_Flx(sv); }
    2238             : INLINE GEN
    2239           0 : polx_zx(long sv) { return polx_Flx(sv); }
    2240             : INLINE GEN
    2241           0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
    2242             : INLINE GEN
    2243       14042 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
    2244             : INLINE GEN
    2245        1350 : zero_F2x(long sv) { return zero_Flx(sv); }
    2246             : INLINE GEN
    2247    13125433 : pol0_F2x(long sv) { return pol0_Flx(sv); }
    2248             : INLINE GEN
    2249     3913310 : pol1_F2x(long sv) { return pol1_Flx(sv); }
    2250             : INLINE GEN
    2251     1005552 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
    2252             : INLINE int
    2253     2867655 : F2x_equal1(GEN x) { return Flx_equal1(x); }
    2254             : INLINE int
    2255     4619327 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
    2256             : INLINE GEN
    2257    59910124 : F2x_copy(GEN x) { return leafcopy(x); }
    2258             : INLINE GEN
    2259        4074 : F2v_copy(GEN x) { return leafcopy(x); }
    2260             : INLINE GEN
    2261     2376631 : Flv_copy(GEN x) { return leafcopy(x); }
    2262             : INLINE GEN
    2263   169742472 : Flx_copy(GEN x) { return leafcopy(x); }
    2264             : INLINE GEN
    2265     3956506 : vecsmall_copy(GEN x) { return leafcopy(x); }
    2266             : INLINE int
    2267     9961112 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
    2268             : INLINE int
    2269       14136 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
    2270             : INLINE int
    2271     6040732 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
    2272             : 
    2273             : INLINE GEN
    2274   143431902 : ZX_renormalize(GEN x, long lx)    { return ZXX_renormalize(x,lx); }
    2275             : INLINE GEN
    2276   142223768 : FpX_renormalize(GEN x, long lx)   { return ZXX_renormalize(x,lx); }
    2277             : INLINE GEN
    2278      853094 : FpXX_renormalize(GEN x, long lx)  { return ZXX_renormalize(x,lx); }
    2279             : INLINE GEN
    2280     4702078 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
    2281             : INLINE GEN
    2282   119335904 : F2x_renormalize(GEN x, long lx)   { return Flx_renormalize(x,lx); }
    2283             : 
    2284             : INLINE GEN
    2285           0 : F2xX_shift(GEN a, long n, long vs) { return FlxX_shift(a, n, vs); }
    2286             : 
    2287             : INLINE GEN
    2288       38297 : F2v_to_F2x(GEN x, long sv) {
    2289       38297 :   GEN y = leafcopy(x);
    2290       38296 :   y[1] = sv; F2x_renormalize(y, lg(y)); return y;
    2291             : }
    2292             : 
    2293             : INLINE long
    2294         385 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
    2295             : 
    2296             : INLINE long
    2297        4977 : gval(GEN x, long v)
    2298        4977 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
    2299             : 
    2300             : INLINE void
    2301      479910 : RgX_shift_inplace_init(long v)
    2302      479910 : { if (v) (void)cgetg(v, t_VECSMALL); }
    2303             : /* shift polynomial in place. assume v free cells have been left before x */
    2304             : INLINE GEN
    2305      479910 : RgX_shift_inplace(GEN x, long v)
    2306             : {
    2307             :   long i, lx;
    2308             :   GEN z;
    2309      479910 :   if (!v) return x;
    2310      253169 :   lx = lg(x);
    2311      253169 :   if (lx == 2) return x;
    2312      253169 :   z = x + lx;
    2313             :   /* stackdummy's from normalizepol */
    2314      253169 :   while (lg(z) != v) z += lg(z);
    2315      253169 :   z += v;
    2316     4654514 :   for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
    2317      675895 :   for (i = 0;  i < v; i++) gel(--z,0) = gen_0;
    2318      253169 :   z -= 2;
    2319      253169 :   z[1] = x[1];
    2320      253169 :   z[0] = evaltyp(t_POL) | evallg(lx+v);
    2321      253169 :   stackdummy((pari_sp)z, (pari_sp)x); return z;
    2322             : }
    2323             : 
    2324             : 
    2325             : /* LINEAR ALGEBRA */
    2326             : INLINE GEN
    2327      494135 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
    2328             : INLINE GEN
    2329     7607643 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
    2330             : INLINE GEN
    2331     3189456 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
    2332             : INLINE GEN
    2333           0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
    2334             : INLINE GEN
    2335      104139 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
    2336             : INLINE GEN
    2337           0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
    2338             : INLINE GEN
    2339           0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
    2340             : INLINE GEN
    2341    35144329 : zero_zv(long x) { return zero_Flv(x); }
    2342             : INLINE GEN
    2343         266 : zm_transpose(GEN x) { return Flm_transpose(x); }
    2344             : INLINE GEN
    2345           0 : zm_copy(GEN x) { return Flm_copy(x); }
    2346             : INLINE GEN
    2347     2149386 : zv_copy(GEN x) { return Flv_copy(x); }
    2348             : INLINE GEN
    2349           0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
    2350             : 
    2351             : INLINE GEN
    2352    11371185 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
    2353             : INLINE GEN
    2354      326464 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
    2355             : INLINE GEN
    2356     6892520 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
    2357             : INLINE void
    2358     9228684 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
    2359             : INLINE GEN
    2360    19749527 : RgM_shallowcopy(GEN x)
    2361             : {
    2362             :   long l;
    2363    19749527 :   GEN y = cgetg_copy(x, &l);
    2364    88948887 :   while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
    2365    19748980 :   return y;
    2366             : }
    2367             : INLINE GEN
    2368      195191 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
    2369             : 
    2370             : INLINE GEN
    2371           0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
    2372             : 
    2373             : INLINE GEN
    2374     5971484 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
    2375             : 
    2376             : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
    2377             :  * x,y are ZV of the same length */
    2378             : INLINE int
    2379       23240 : ZV_dvd(GEN x, GEN y)
    2380             : {
    2381       23240 :   long i, l = lg(x);
    2382       36715 :   for (i=1; i < l; i++)
    2383       29568 :     if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
    2384        7147 :   return 1;
    2385             : }
    2386             : INLINE GEN
    2387      535773 : ZM_ZV_mod(GEN x, GEN y)
    2388     1530594 : { pari_APPLY_same(ZV_ZV_mod(gel(x,i), y)) }
    2389             : INLINE GEN
    2390     7306495 : ZV_ZV_mod(GEN x, GEN y)
    2391    18876809 : { pari_APPLY_same(modii(gel(x,i), gel(y,i))) }
    2392             : INLINE GEN
    2393           0 : vecmodii(GEN x, GEN y) { return ZV_ZV_mod(x,y); }
    2394             : INLINE GEN
    2395      174881 : vecmoduu(GEN x, GEN y) { pari_APPLY_ulong(((ulong*)x)[i] % ((ulong*)y)[i]) }
    2396             : 
    2397             : /* Fq */
    2398             : INLINE GEN
    2399     3335886 : Fq_red(GEN x, GEN T, GEN p)
    2400     3335886 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
    2401             : INLINE GEN
    2402      110255 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
    2403             : {
    2404             :   (void) p;
    2405      110255 :   return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
    2406             : }
    2407             : INLINE GEN
    2408         756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
    2409             : 
    2410             : INLINE GEN
    2411       14581 : gener_Fq_local(GEN T, GEN p, GEN L)
    2412           0 : { return T? gener_FpXQ_local(T,p, L)
    2413       14581 :           : pgener_Fp_local(p, L); }
    2414             : 
    2415             : INLINE GEN
    2416           0 : random_Fq(GEN T, GEN p)
    2417           0 : { return T ? random_FpX(get_FpX_degree(T), get_FpX_var(T), p): randomi(p); }
    2418             : 
    2419             : /* FpXQX */
    2420             : INLINE GEN
    2421        4546 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
    2422             : INLINE GEN
    2423           0 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
    2424             : INLINE GEN
    2425      164996 : FlxqX_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi) { return FlxqX_divrem_pre(x, y, T, p, pi, NULL); }
    2426             : INLINE GEN
    2427       33243 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
    2428             : 
    2429             : INLINE GEN
    2430       20587 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    2431       20587 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
    2432             : 
    2433             : /* FqX */
    2434             : INLINE GEN
    2435       25354 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
    2436             : INLINE GEN
    2437      127694 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
    2438             : INLINE GEN
    2439       24956 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
    2440             : INLINE GEN
    2441       68607 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
    2442             : INLINE GEN
    2443      558649 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
    2444      558649 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
    2445             : INLINE GEN
    2446      426565 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
    2447      426565 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
    2448             : INLINE GEN
    2449      367437 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
    2450      367437 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
    2451             : INLINE GEN
    2452       21942 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
    2453       21942 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
    2454             : INLINE GEN
    2455       71855 : FqX_sqr(GEN x, GEN T, GEN p)
    2456       71855 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
    2457             : INLINE GEN
    2458        1295 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
    2459        1295 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
    2460             : INLINE GEN
    2461       19411 : FqX_halve(GEN x, GEN T, GEN p)
    2462       19411 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
    2463             : INLINE GEN
    2464       39546 : FqX_div(GEN x, GEN y, GEN T, GEN p)
    2465       39546 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
    2466             : INLINE GEN
    2467        6090 : FqX_get_red(GEN S, GEN T, GEN p)
    2468        6090 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
    2469             : INLINE GEN
    2470       37743 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
    2471       37743 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
    2472             : INLINE GEN
    2473           0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
    2474           0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
    2475             : INLINE GEN
    2476       71939 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
    2477       71939 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
    2478             : INLINE GEN
    2479           0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
    2480           0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
    2481             : INLINE GEN
    2482      262927 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
    2483      262927 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
    2484             : INLINE GEN
    2485      435376 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
    2486      435376 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
    2487             : INLINE GEN
    2488        4375 : FqX_normalize(GEN z, GEN T, GEN p)
    2489        4375 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
    2490             : INLINE GEN
    2491      294238 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
    2492             : INLINE GEN
    2493           0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
    2494             : INLINE GEN
    2495       87116 : FqX_factor(GEN f, GEN T, GEN p)
    2496       87116 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
    2497             : INLINE GEN
    2498           7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
    2499           7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
    2500             : INLINE GEN
    2501           7 : FqX_ddf(GEN f, GEN T, GEN p)
    2502           7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
    2503             : INLINE GEN
    2504       47341 : FqX_degfact(GEN f, GEN T, GEN p)
    2505       47341 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
    2506             : INLINE GEN
    2507        7273 : FqX_roots(GEN f, GEN T, GEN p)
    2508        7273 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
    2509             : INLINE GEN
    2510         175 : FqX_to_mod(GEN f, GEN T, GEN p)
    2511         175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
    2512             : 
    2513             : /*FqXQ*/
    2514             : INLINE GEN
    2515           0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
    2516           0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
    2517             : INLINE GEN
    2518           0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
    2519           0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
    2520             : INLINE GEN
    2521           0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
    2522           0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
    2523             : INLINE GEN
    2524           0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
    2525           0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
    2526             : INLINE GEN
    2527           0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
    2528           0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
    2529             : INLINE GEN
    2530       22766 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
    2531       22766 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
    2532             : INLINE GEN
    2533           0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
    2534           0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
    2535             : INLINE GEN
    2536           0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
    2537           0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
    2538             : 
    2539             : /*FqXn*/
    2540             : INLINE GEN
    2541        6590 : FqXn_expint(GEN x, long n, GEN T, GEN p)
    2542        6590 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
    2543             : INLINE GEN
    2544           0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
    2545           0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
    2546             : INLINE GEN
    2547        7126 : FqXn_inv(GEN x, long n, GEN T, GEN p)
    2548        7126 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
    2549             : INLINE GEN
    2550      263403 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
    2551      263403 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
    2552             : INLINE GEN
    2553           0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
    2554           0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
    2555             : 
    2556             : /*FpXQ*/
    2557             : INLINE GEN
    2558           0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
    2559           0 : { (void)T; return FpX_add(x,y,p); }
    2560             : INLINE GEN
    2561           0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
    2562           0 : { (void)T; return FpX_sub(x,y,p); }
    2563             : 
    2564             : /*Flxq*/
    2565             : INLINE GEN
    2566           0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
    2567           0 : { (void)T; return Flx_add(x,y,p); }
    2568             : INLINE GEN
    2569           0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
    2570           0 : { (void)T; return Flx_sub(x,y,p); }
    2571             : 
    2572             : /* F2x */
    2573             : 
    2574             : INLINE ulong
    2575   647675854 : F2x_coeff(GEN x,long v)
    2576             : {
    2577   647675854 :    ulong u=(ulong)x[2+divsBIL(v)];
    2578   647674596 :    return (u>>remsBIL(v))&1UL;
    2579             : }
    2580             : 
    2581             : INLINE void
    2582    11574814 : F2x_clear(GEN x,long v)
    2583             : {
    2584    11574814 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2585    11574726 :    *u&=~(1UL<<remsBIL(v));
    2586    11574695 : }
    2587             : 
    2588             : INLINE void
    2589   126149429 : F2x_set(GEN x,long v)
    2590             : {
    2591   126149429 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2592   126133248 :    *u|=1UL<<remsBIL(v);
    2593   126131346 : }
    2594             : 
    2595             : INLINE void
    2596     1562148 : F2x_flip(GEN x,long v)
    2597             : {
    2598     1562148 :    ulong* u=(ulong*)&x[2+divsBIL(v)];
    2599     1562148 :    *u^=1UL<<remsBIL(v);
    2600     1562148 : }
    2601             : 
    2602             : /* F2v */
    2603             : 
    2604             : INLINE ulong
    2605   640789219 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
    2606             : 
    2607             : INLINE void
    2608    11574819 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
    2609             : 
    2610             : INLINE void
    2611    99856840 : F2v_set(GEN x,long v)   { F2x_set(x,v-1); }
    2612             : 
    2613             : INLINE void
    2614     1562148 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
    2615             : 
    2616             : /* F2m */
    2617             : 
    2618             : INLINE ulong
    2619     6439706 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
    2620             : 
    2621             : INLINE void
    2622           0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
    2623             : 
    2624             : INLINE void
    2625         686 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
    2626             : 
    2627             : INLINE void
    2628     1562148 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
    2629             : 
    2630             : /* F3m */
    2631             : 
    2632             : INLINE ulong
    2633     1811185 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
    2634             : 
    2635             : INLINE void
    2636           0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
    2637             : 
    2638             : /* ARITHMETIC */
    2639             : INLINE GEN
    2640       35761 : matpascal(long n) { return matqpascal(n, NULL); }
    2641             : INLINE long
    2642      458491 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
    2643             : INLINE long
    2644          98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
    2645             : INLINE GEN
    2646     6287539 : sqrti(GEN x) { return sqrtremi(x,NULL); }
    2647             : INLINE GEN
    2648   120413485 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
    2649             : INLINE int
    2650      555136 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
    2651             : INLINE int
    2652       26852 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
    2653             : INLINE GEN
    2654           0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
    2655             : INLINE GEN
    2656           0 : gminsg(long s, GEN y) { return gmings(y,s); }
    2657             : INLINE GEN
    2658    36971851 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
    2659             : INLINE GEN
    2660   124118323 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
    2661             : INLINE GEN
    2662     1405794 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
    2663             : INLINE GEN
    2664      490558 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
    2665             : 
    2666             : INLINE GEN
    2667    13508785 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
    2668             : INLINE GEN
    2669      866594 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
    2670             : 
    2671             : /* x t_COMPLEX */
    2672             : INLINE GEN
    2673    84447279 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
    2674             : /* q t_QUAD */
    2675             : INLINE GEN
    2676       69860 : quadnorm(GEN q)
    2677             : {
    2678       69860 :   GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
    2679       69860 :   GEN z, u = gel(q,3), v = gel(q,2);
    2680       69860 :   if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
    2681             :   {
    2682       69671 :     z = signe(b)? mulii(v, addii(u,v)): sqri(v);
    2683       69671 :     return addii(z, mulii(c, sqri(u)));
    2684             :   }
    2685             :   else
    2686             :   {
    2687         189 :     z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
    2688         189 :     return gadd(z, gmul(c, gsqr(u)));
    2689             :   }
    2690             : }
    2691             : /* x a t_QUAD, return the attached discriminant */
    2692             : INLINE GEN
    2693        1078 : quad_disc(GEN x)
    2694             : {
    2695        1078 :   GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
    2696        1078 :   if (is_pm1(b)) return subsi(1, c4);
    2697         154 :   togglesign_safe(&c4); return c4;
    2698             : }
    2699             : INLINE GEN
    2700     4835532 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
    2701             : INLINE GEN
    2702    18470198 : qfb_disc(GEN x) { return gel(x,4); }
    2703             : 
    2704             : INLINE GEN
    2705     3207221 : sqrfrac(GEN x)
    2706             : {
    2707     3207221 :   GEN z = cgetg(3,t_FRAC);
    2708     3207221 :   gel(z,1) = sqri(gel(x,1));
    2709     3207221 :   gel(z,2) = sqri(gel(x,2)); return z;
    2710             : }
    2711             : 
    2712             : INLINE void
    2713    16106610 : normalize_frac(GEN z) {
    2714    16106610 :   if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
    2715    16106610 : }
    2716             : 
    2717             : INLINE GEN
    2718    37958021 : powii(GEN x, GEN n)
    2719             : {
    2720    37958021 :   long ln = lgefint(n);
    2721    37958021 :   if (ln == 3) {
    2722             :     GEN z;
    2723    37935293 :     if (signe(n) > 0) return powiu(x, n[2]);
    2724       73603 :     z = cgetg(3, t_FRAC);
    2725       73612 :     gel(z,1) = gen_1;
    2726       73612 :     gel(z,2) = powiu(x, n[2]);
    2727       73612 :     return z;
    2728             :   }
    2729       22728 :   if (ln == 2) return gen_1; /* rare */
    2730             :   /* should never happen */
    2731           0 :   return powgi(x, n); /* overflow unless x = 0, 1, -1 */
    2732             : }
    2733             : INLINE GEN
    2734        1547 : powIs(long n) {
    2735        1547 :   switch(n & 3)
    2736             :   {
    2737          63 :     case 1: return mkcomplex(gen_0,gen_1);
    2738         385 :     case 2: return gen_m1;
    2739         693 :     case 3: return mkcomplex(gen_0,gen_m1);
    2740             :   }
    2741         406 :   return gen_1;
    2742             : }
    2743             : 
    2744             : /*******************************************************************/
    2745             : /*                                                                 */
    2746             : /*                             ASSIGNMENTS                         */
    2747             : /*                                                                 */
    2748             : /*******************************************************************/
    2749           0 : INLINE void mpexpz(GEN x, GEN z)
    2750           0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
    2751           0 : INLINE void mplogz(GEN x, GEN z)
    2752           0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
    2753           0 : INLINE void mpcosz(GEN x, GEN z)
    2754           0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
    2755           0 : INLINE void mpsinz(GEN x, GEN z)
    2756           0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
    2757           0 : INLINE void gnegz(GEN x, GEN z)
    2758           0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
    2759           0 : INLINE void gabsz(GEN x, long prec, GEN z)
    2760           0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
    2761           0 : INLINE void gaddz(GEN x, GEN y, GEN z)
    2762           0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
    2763           0 : INLINE void gsubz(GEN x, GEN y, GEN z)
    2764           0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
    2765           0 : INLINE void gmulz(GEN x, GEN y, GEN z)
    2766           0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
    2767           0 : INLINE void gdivz(GEN x, GEN y, GEN z)
    2768           0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
    2769           0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
    2770           0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
    2771           0 : INLINE void gmodz(GEN x, GEN y, GEN z)
    2772           0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
    2773           0 : INLINE void gmul2nz(GEN x, long s, GEN z)
    2774           0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
    2775           0 : INLINE void gshiftz(GEN x, long s, GEN z)
    2776           0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
    2777             : 
    2778             : /*******************************************************************/
    2779             : /*                                                                 */
    2780             : /*                       ELLIPTIC CURVES                           */
    2781             : /*                                                                 */
    2782             : /*******************************************************************/
    2783     4227008 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
    2784     3216419 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
    2785     4051732 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
    2786     3985577 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
    2787     4772426 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
    2788     3401194 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
    2789     1063535 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
    2790     1670246 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
    2791     1492303 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
    2792     6115365 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
    2793     7308530 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
    2794     9268416 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
    2795     1047317 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
    2796     8502414 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
    2797     1608753 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
    2798      688162 : INLINE GEN ellff_get_a4a6(GEN x)  { return gmael(x, 15, 2); }
    2799        1484 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
    2800         315 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
    2801        1134 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
    2802       75012 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
    2803       18282 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
    2804      788848 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
    2805         119 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
    2806             : 
    2807     3634528 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
    2808    43796265 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
    2809      965767 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
    2810             : 
    2811             : /*******************************************************************/
    2812             : /*                                                                 */
    2813             : /*                    ALGEBRAIC NUMBER THEORY                      */
    2814             : /*                                                                 */
    2815             : /*******************************************************************/
    2816    20702734 : INLINE GEN modpr_get_pr(GEN x)  { return gel(x,3); }
    2817      730632 : INLINE GEN modpr_get_p(GEN x)  { return pr_get_p(modpr_get_pr(x)); }
    2818     8652997 : INLINE GEN modpr_get_T(GEN x)  { return lg(x) == 4? NULL: gel(x,4); }
    2819             : 
    2820    64069288 : INLINE GEN pr_get_p(GEN pr)  { return gel(pr,1); }
    2821    10498954 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
    2822             : /* .[2] instead of itos works: e and f are small positive integers */
    2823     8621178 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
    2824    23079123 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
    2825    37230050 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
    2826             : INLINE int
    2827     8309603 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
    2828             : INLINE GEN
    2829      945922 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
    2830             : INLINE ulong
    2831      343931 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
    2832             : 
    2833             : /* assume nf a genuine nf */
    2834             : INLINE long
    2835      840479 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
    2836             : INLINE GEN
    2837    77068322 : nf_get_pol(GEN nf) { return gel(nf,1); }
    2838             : INLINE long
    2839    53714004 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
    2840             : INLINE long
    2841     5690823 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
    2842             : INLINE long
    2843        4112 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
    2844             : INLINE GEN
    2845      453056 : nf_get_disc(GEN nf) { return gel(nf,3); }
    2846             : INLINE GEN
    2847     3184609 : nf_get_index(GEN nf) { return gel(nf,4); }
    2848             : INLINE GEN
    2849     5805323 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
    2850             : INLINE GEN
    2851      248250 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
    2852             : INLINE GEN
    2853     1626990 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
    2854             : INLINE GEN
    2855       22066 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
    2856             : INLINE GEN
    2857        4430 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
    2858             : INLINE GEN
    2859       58008 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
    2860             : INLINE GEN
    2861     1231383 : nf_get_roots(GEN nf) { return gel(nf,6); }
    2862             : INLINE GEN
    2863        1841 : nf_get_zk(GEN nf)
    2864             : {
    2865        1841 :   GEN y = gel(nf,7), D = gel(y, 1);
    2866        1841 :   if (typ(D) == t_POL) D = gel(D, 2);
    2867        1841 :   if (!equali1(D)) y = gdiv(y, D);
    2868        1841 :   return y;
    2869             : }
    2870             : INLINE GEN
    2871     3616417 : nf_get_zkprimpart(GEN nf)
    2872             : {
    2873     3616417 :   GEN y = gel(nf,7);
    2874             :   /* test for old format of nf.zk: non normalized */
    2875     3616417 :   if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
    2876     3616419 :   return y;
    2877             : }
    2878             : INLINE GEN
    2879     3663003 : nf_get_zkden(GEN nf)
    2880             : {
    2881     3663003 :   GEN y = gel(nf,7), D = gel(y,1);
    2882     3663003 :   if (typ(D) == t_POL) D = gel(D,2);
    2883             :   /* test for old format of nf.zk: non normalized */
    2884     3663003 :   if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
    2885     3662991 :   return D;
    2886             : }
    2887             : INLINE GEN
    2888     9028380 : nf_get_invzk(GEN nf) { return gel(nf,8); }
    2889             : INLINE void
    2890      285873 : nf_get_sign(GEN nf, long *r1, long *r2)
    2891             : {
    2892      285873 :   GEN x = gel(nf,2);
    2893      285873 :   *r1 = itou(gel(x,1));
    2894      285873 :   *r2 = itou(gel(x,2));
    2895      285872 : }
    2896             : 
    2897             : INLINE GEN
    2898     2514697 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
    2899             : INLINE GEN
    2900      391260 : abgrp_get_no(GEN x) { return gel(x,1); }
    2901             : INLINE GEN
    2902    11488421 : abgrp_get_cyc(GEN x) { return gel(x,2); }
    2903             : INLINE GEN
    2904     1651910 : abgrp_get_gen(GEN x) { return gel(x,3); }
    2905             : INLINE GEN
    2906     9409891 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
    2907             : INLINE GEN
    2908     5090737 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
    2909             : INLINE GEN
    2910        8379 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
    2911             : INLINE GEN
    2912     3503810 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
    2913             : INLINE GEN
    2914     1578381 : bnf_get_gen(GEN bnf)  { return abgrp_get_gen(bnf_get_clgp(bnf)); }
    2915             : INLINE GEN
    2916         641 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
    2917             : INLINE GEN
    2918     2699743 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
    2919             : INLINE GEN
    2920     1277249 : bnf_get_sunits(GEN bnf)
    2921     1277249 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
    2922             : INLINE GEN
    2923      290164 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
    2924             : INLINE long
    2925      264826 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
    2926             : INLINE GEN
    2927      287803 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
    2928             : INLINE GEN
    2929       26279 : nfV_to_scalar_or_alg(GEN nf, GEN x)
    2930       63407 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
    2931             : INLINE GEN
    2932       25838 : bnf_get_fu(GEN bnf) {
    2933       25838 :   GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
    2934       25838 :   if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
    2935       25838 :   return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
    2936             : }
    2937             : 
    2938             : INLINE GEN
    2939     3623745 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
    2940             : INLINE GEN
    2941     1932693 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
    2942             : INLINE GEN
    2943      139822 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
    2944             : INLINE GEN
    2945     1257579 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
    2946             : INLINE GEN
    2947     2722080 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
    2948             : INLINE GEN
    2949      313941 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
    2950             : INLINE GEN
    2951     2390585 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
    2952             : INLINE GEN
    2953          70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
    2954             : INLINE GEN
    2955        7847 : bnr_get_gen(GEN bnr) {
    2956        7847 :   GEN G = bnr_get_clgp(bnr);
    2957        7847 :   if (lg(G) !=  4)
    2958           0 :     pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
    2959        7847 :   return gel(G,3);
    2960             : }
    2961             : 
    2962             : /* localstar, used in gchar */
    2963             : INLINE GEN
    2964       52084 : locs_get_cyc(GEN locs) { return gel(locs,1); }
    2965             : INLINE GEN
    2966      191695 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
    2967             : INLINE GEN
    2968        1260 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
    2969             : INLINE GEN
    2970        8225 : locs_get_mod(GEN locs) { return gel(locs,4); }
    2971             : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
    2972             :  * return a t_MAT whose columns are the logs
    2973             :  * of generators of U_i(pr)/U_{i+1}(pr). */
    2974             : INLINE GEN
    2975        1260 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
    2976             : INLINE GEN
    2977      207235 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
    2978             : 
    2979             : /* G a grossenchar group */
    2980             : INLINE GEN
    2981       32639 : gchar_get_basis(GEN gc)  { return  gel(gc, 1); }
    2982             : INLINE GEN
    2983      203105 : gchar_get_bnf(GEN gc)    { return  gel(gc, 2); }
    2984             : INLINE GEN
    2985      241744 : gchar_get_nf(GEN gc)    { return  gel(gc, 3); }
    2986             : INLINE GEN
    2987      279563 : gchar_get_zm(GEN gc)     { return  gel(gc, 4); }
    2988             : INLINE GEN
    2989        8225 : gchar_get_mod(GEN gc)    { return  locs_get_mod(gchar_get_zm(gc)); }
    2990             : INLINE GEN
    2991        4095 : gchar_get_modP(GEN gc)    { return gmael(gchar_get_mod(gc),1,1); }
    2992             : INLINE GEN
    2993       36994 : gchar_get_S(GEN gc)      { return  gel(gc, 5); }
    2994             : INLINE GEN
    2995      188468 : gchar_get_DLdata(GEN gc)   { return  gel(gc, 6); }
    2996             : INLINE GEN
    2997        1877 : gchar_get_sfu(GEN gc) { return  gel(gc, 7); }
    2998             : INLINE GEN
    2999       16168 : gchar_get_cyc(GEN gc)    { return  gel(gc, 9); }
    3000             : INLINE GEN
    3001           0 : gchar_get_hnf(GEN gc)    { return  gmael(gc, 10, 1); }
    3002             : INLINE GEN
    3003           0 : gchar_get_U(GEN gc)      { return  gmael(gc, 10, 2); }
    3004             : INLINE GEN
    3005       10969 : gchar_get_Ui(GEN gc)     { return  gmael(gc, 10, 3); }
    3006             : INLINE GEN
    3007        3450 : gchar_get_m0(GEN gc)     { return gel(gc, 11); }
    3008             : INLINE GEN
    3009        4539 : gchar_get_u0(GEN gc)     { return gel(gc, 12); }
    3010             : INLINE long
    3011       17416 : gchar_get_r1(GEN gc)     { return nf_get_r1(gchar_get_nf(gc)); }
    3012             : INLINE long
    3013         623 : gchar_get_r2(GEN gc)     { return nf_get_r2(gchar_get_nf(gc)); }
    3014             : INLINE GEN
    3015       50476 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
    3016             : INLINE long
    3017       37260 : gchar_get_nc(GEN gc)     { return lg(gchar_get_loccyc(gc))-1; }
    3018             : INLINE long
    3019       36994 : gchar_get_ns(GEN gc)     { return lg(gchar_get_S(gc))-1; }
    3020             : INLINE long
    3021        1841 : gchar_get_nm(GEN gc)     { return lg(gchar_get_basis(gc))-1; }
    3022             : INLINE long
    3023        4011 : gchar_get_evalprec(GEN gc)   { return  gmael(gc, 8, 1)[1]; }
    3024             : INLINE long
    3025       18732 : gchar_get_prec(GEN gc)   { return  gmael(gc, 8, 1)[2]; }
    3026             : INLINE long
    3027       13419 : gchar_get_nfprec(GEN gc) { return  gmael(gc, 8, 1)[3]; }
    3028             : INLINE void
    3029        1785 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
    3030             : INLINE void
    3031        1202 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
    3032             : INLINE void
    3033        1202 : gchar_copy_precs(GEN gc, GEN gc2)
    3034             : {
    3035        1202 :   gel(gc2, 8) = shallowcopy(gel(gc,8));
    3036        1202 :   gmael(gc2, 8, 1) = shallowcopy(gmael(gc, 8, 1));
    3037        1202 : }
    3038             : INLINE void
    3039        3079 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
    3040             : INLINE long
    3041         322 : gchar_get_ntors(GEN gc)   { return  gmael(gc, 8, 2)[1]; }
    3042             : INLINE long
    3043         322 : gchar_get_nfree(GEN gc)   { return  gmael(gc, 8, 2)[2]; }
    3044             : INLINE long
    3045        2042 : gchar_get_nalg(GEN gc)   { return  gmael(gc, 8, 2)[3]; }
    3046             : INLINE void
    3047        1573 : gchar_set_basis(GEN gc, GEN m_inv)  { gel(gc, 1) = m_inv; }
    3048             : INLINE void
    3049        2296 : gchar_set_nf(GEN gc, GEN nf)      { gel(gc, 3) = nf; }
    3050             : INLINE void
    3051         623 : gchar_set_ntors(GEN gc, long n)    { gmael(gc, 8, 2)[1] = n; }
    3052             : INLINE void
    3053         623 : gchar_set_nfree(GEN gc, long n)    { gmael(gc, 8, 2)[2] = n; }
    3054             : INLINE void
    3055         623 : gchar_set_nalg(GEN gc, long n)    { gmael(gc, 8, 2)[3] = n; }
    3056             : INLINE void
    3057        1573 : gchar_set_cyc(GEN gc, GEN cyc)      { gel(gc, 9) = cyc; }
    3058             : INLINE void
    3059         623 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
    3060             : INLINE void
    3061         950 : gchar_set_m0(GEN gc, GEN m0)     { gel(gc, 11) = m0; }
    3062             : INLINE void
    3063        2093 : gchar_set_u0(GEN gc, GEN u0)     { gel(gc, 12) = u0; }
    3064             : 
    3065             : INLINE GEN
    3066     1382941 : bid_get_mod(GEN bid) { return gel(bid,1); }
    3067             : INLINE GEN
    3068       71246 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
    3069             : INLINE GEN
    3070       34944 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
    3071             : INLINE GEN
    3072     5403306 : bid_get_grp(GEN bid) { return gel(bid,2); }
    3073             : INLINE GEN
    3074     2308994 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
    3075             : INLINE GEN
    3076     2020790 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
    3077             : INLINE GEN
    3078     1986995 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
    3079             : INLINE GEN
    3080       51058 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
    3081             : INLINE GEN
    3082     2212906 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
    3083             : INLINE GEN
    3084     3370257 : bid_get_U(GEN bid) { return gel(bid,5); }
    3085             : INLINE GEN
    3086           0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
    3087             : INLINE GEN
    3088     5349611 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
    3089             : INLINE GEN
    3090           0 : bid_get_gen_nocheck(GEN bid)  { return abgrp_get_gen(bid_get_grp(bid)); }
    3091             : INLINE GEN
    3092       53123 : bid_get_gen(GEN bid) {
    3093       53123 :   GEN G = bid_get_grp(bid);
    3094       53123 :   if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
    3095       53123 :   return abgrp_get_gen(G);
    3096             : }
    3097             : 
    3098             : INLINE GEN
    3099    33687460 : znstar_get_N(GEN G) { return gmael(G,1,1); }
    3100             : INLINE GEN
    3101     7126898 : znstar_get_faN(GEN G) { return gel(G,3); }
    3102             : INLINE GEN
    3103          14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
    3104             : INLINE GEN
    3105      228586 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
    3106             : INLINE GEN
    3107       16150 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
    3108             : INLINE GEN
    3109     7762882 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
    3110             : INLINE GEN
    3111     3210579 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
    3112             : INLINE GEN
    3113       46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
    3114             : INLINE GEN
    3115      156031 : znstar_get_U(GEN G) { return gel(G,5); }
    3116             : INLINE GEN
    3117     2813049 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
    3118             : INLINE GEN
    3119       35868 : gal_get_pol(GEN gal) { return gel(gal,1); }
    3120             : INLINE GEN
    3121        6006 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
    3122             : INLINE GEN
    3123          91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
    3124             : INLINE GEN
    3125       23660 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
    3126             : INLINE GEN
    3127       32312 : gal_get_roots(GEN gal) { return gel(gal,3); }
    3128             : INLINE GEN
    3129       27454 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
    3130             : INLINE GEN
    3131       27447 : gal_get_den(GEN gal) { return gel(gal,5); }
    3132             : INLINE GEN
    3133       79455 : gal_get_group(GEN gal) { return gel(gal,6); }
    3134             : INLINE GEN
    3135        8946 : gal_get_gen(GEN gal) { return gel(gal,7); }
    3136             : INLINE GEN
    3137        6944 : gal_get_orders(GEN gal) { return gel(gal,8); }
    3138             : 
    3139             : /* assume rnf a genuine rnf */
    3140             : INLINE long
    3141     1224649 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
    3142             : INLINE long
    3143       17458 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
    3144             : INLINE long
    3145      768035 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
    3146             : INLINE GEN
    3147         819 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
    3148             : INLINE GEN
    3149         805 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
    3150             : INLINE GEN
    3151         903 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
    3152             : INLINE GEN
    3153      459613 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
    3154             : INLINE GEN
    3155        4725 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
    3156             : INLINE GEN
    3157      227273 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
    3158             : INLINE GEN
    3159     1486611 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
    3160             : INLINE GEN
    3161         245 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
    3162             : INLINE GEN
    3163         105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
    3164             : INLINE GEN
    3165        1869 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
    3166             : INLINE long
    3167         455 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
    3168             : INLINE GEN
    3169      199284 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
    3170             : INLINE long
    3171        3388 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
    3172             : INLINE GEN
    3173        3850 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
    3174             : INLINE GEN
    3175      107826 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
    3176             : INLINE GEN
    3177        1225 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
    3178             : 
    3179             : INLINE GEN
    3180      135757 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
    3181             : 
    3182             : INLINE GEN
    3183        3415 : idealchineseinit(GEN nf, GEN x)
    3184        3415 : { return idealchinese(nf,x,NULL); }
    3185             : 
    3186             : /*******************************************************************/
    3187             : /*                                                                 */
    3188             : /*                              CLOSURES                           */
    3189             : /*                                                                 */
    3190             : /*******************************************************************/
    3191   361795082 : INLINE long closure_arity(GEN C)          { return ((ulong)C[1])&ARITYBITS; }
    3192    40007780 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
    3193   313392756 : INLINE const char *closure_codestr(GEN C)  { return GSTR(gel(C,2))-1; }
    3194           0 : INLINE GEN closure_get_code(GEN C)  { return gel(C,2); }
    3195   313367215 : INLINE GEN closure_get_oper(GEN C)  { return gel(C,3); }
    3196   313339173 : INLINE GEN closure_get_data(GEN C)  { return gel(C,4); }
    3197       12690 : INLINE GEN closure_get_dbg(GEN C)   { return gel(C,5); }
    3198       35203 : INLINE GEN closure_get_text(GEN C)  { return gel(C,6); }
    3199    12734431 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
    3200             : 
    3201             : /*******************************************************************/
    3202             : /*                                                                 */
    3203             : /*                               ERRORS                            */
    3204             : /*                                                                 */
    3205             : /*******************************************************************/
    3206             : INLINE long
    3207       60639 : err_get_num(GEN e) { return e[1]; }
    3208             : INLINE GEN
    3209         266 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
    3210             : 
    3211             : INLINE void
    3212          14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
    3213             : INLINE void
    3214          21 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
    3215             : INLINE void
    3216          84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
    3217             : INLINE void
    3218         676 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
    3219             : INLINE void
    3220           0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
    3221             : INLINE void
    3222          36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
    3223             : INLINE void
    3224          98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
    3225             : INLINE void
    3226         483 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
    3227             : INLINE void
    3228       19983 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
    3229             : INLINE void
    3230          63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
    3231             : INLINE void
    3232        2666 : 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); }
    3233             : INLINE void
    3234         200 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
    3235             : INLINE void
    3236           0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
    3237             : INLINE void
    3238         406 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
    3239             : INLINE void
    3240         156 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
    3241             : INLINE void
    3242         238 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
    3243             : INLINE void
    3244           0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
    3245             : INLINE void
    3246          84 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
    3247             : INLINE void
    3248        1316 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
    3249             : INLINE void
    3250          56 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
    3251             : INLINE void
    3252          84 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
    3253             : INLINE void
    3254       14768 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
    3255             : INLINE void
    3256        3500 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
    3257             : INLINE void
    3258         364 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
    3259             : INLINE void
    3260         245 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
    3261         245 : { pari_err(e_PRIORITY, f,x,op,v); }
    3262             : 

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