paripriv.h

/* Copyright (C) 2004  The PARI group.

This file is part of the PARI/GP package.

PARI/GP is free software; you can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version. It is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY WHATSOEVER.

Check the License for details. You should have received a copy of it, along
with the package; see the file 'COPYING'. If not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */

BEGINEXTERN

/* for qsort */
typedef int (*QSCOMP)(const void *, const void *);

#define uel(a,i)            (((ulong*)(a))[i])
#define ucoeff(a,i,j)       (((ulong**)(a))[j][i])
#define umael(a,i,j)        (((ulong**)(a))[i][j])
#define umael2(a,i,j)       (((ulong**)(a))[i][j])
#define umael3(a,i,j,k)     (((ulong***)(a))[i][j][k])
#define umael4(a,i,j,k,l)   (((ulong****)(a))[i][j][k][l])
#define umael5(a,i,j,k,l,m) (((ulong*****)(a))[i][j][k][l][m])

#define numberof(x) (sizeof(x) / sizeof((x)[0]))

/* to manipulate 'blocs' */
#define BL_HEAD 8
#define bl_base(x) (void*)((x) - BL_HEAD)
#define bl_height(x) (((GEN)x)[-8])
#define bl_left(x)   (((GEN*)x)[-7])
#define bl_right(x)  (((GEN*)x)[-6])
#define bl_size(x)   (((GEN)x)[-5])
#define bl_refc(x)   (((GEN)x)[-4])
#define bl_next(x)   (((GEN*)x)[-3])
#define bl_prev(x)   (((GEN*)x)[-2])
#define bl_num(x)    (((GEN)x)[-1])

void clone_lock(GEN C);
void clone_unlock(GEN C);
void clone_unlock_deep(GEN C);

/* swap */
#define lswap(x,y) {long _z=x; x=y; y=_z;}
#define pswap(x,y) {GEN *_z=x; x=y; y=_z;}
#define swap(x,y)  {GEN  _z=x; x=y; y=_z;}
#define dswap(x,y) { double _t=x; x=y; y=_t; }
#define pdswap(x,y) { double* _t=x; x=y; y=_t; }
#define swapspec(x,y, nx,ny) {swap(x,y); lswap(nx,ny);}

/* loops */
GEN incloop(GEN a);
GEN resetloop(GEN a, GEN b);
GEN setloop(GEN a);

/* parser */

/* GP control structures */
#define EXPR_WRAP(code, call) \
{ GEN z; GEN __E = code; \
  push_lex(gen_0, __E); z = call; pop_lex(1); return z; }
#define EXPRVOID_WRAP(code, call) \
{ GEN __E = code; \
  push_lex(gen_0, __E); call; pop_lex(1); }
#define EXPR_ARG __E, &gp_eval
#define EXPR_ARGPREC __E, &gp_evalprec
#define EXPR_ARGUPTO __E, &gp_evalupto
#define EXPR_ARGBOOL __E, &gp_evalbool
#define EXPR_ARGVOID __E, &gp_evalvoid

GEN  iferrpari(GEN a, GEN b, GEN c);
void forfactored(GEN a, GEN b, GEN code);
void forpari(GEN a, GEN b, GEN node);
void foreachpari(GEN a, GEN node);
void forsquarefree(GEN a, GEN b, GEN code);
void untilpari(GEN a, GEN b);
void whilepari(GEN a, GEN b);
GEN  ifpari(GEN g, GEN a, GEN b);
GEN  andpari(GEN a, GEN b);
GEN  orpari(GEN a, GEN b);
void ifpari_void(GEN g, GEN a, GEN b);
GEN  ifpari_multi(GEN g, GEN a);
GEN  geval_gp(GEN x, GEN t);

GEN  gadde(GEN *x, GEN y);
GEN  gadd1e(GEN *x);
GEN  gdive(GEN *x, GEN y);
GEN  gdivente(GEN *x, GEN y);
GEN  gdivrounde(GEN *x, GEN y);
GEN  gmode(GEN *x, GEN y);
GEN  gmule(GEN *x, GEN y);
GEN  gshiftle(GEN *x, long n);
GEN  gshiftre(GEN *x, long n);
GEN  gsube(GEN *x, GEN y);
GEN  gsub1e(GEN *x);
GEN  gshift_right(GEN x, long n);

GEN  asympnum0(GEN u, GEN alpha, long prec);
GEN  asympnumraw0(GEN u, long LIM, GEN alpha, long prec);
GEN  derivnum0(GEN a, GEN code, GEN ind, long prec);
GEN  derivfun0(GEN args, GEN def, GEN code, long k, long prec);
GEN  direuler0(GEN a, GEN b, GEN code, GEN c);
GEN  direuler_bad(void *E, GEN (*eval)(void *, GEN, long), GEN a, GEN b, GEN c, GEN Sbad);
void forcomposite(GEN a, GEN b, GEN code);
void fordiv(GEN a, GEN code);
void fordivfactored(GEN a, GEN code);
void forell0(long a, long b, GEN code, long flag);
void forperm0(GEN k, GEN code);
void forprime(GEN a, GEN b, GEN code);
void forprimestep(GEN a, GEN b, GEN q, GEN code);
void forstep(GEN a, GEN b, GEN s, GEN code);
void forsubgroup0(GEN cyc, GEN bound, GEN code);
void forsubset0(GEN nk, GEN code);
void forvec(GEN x, GEN code, long flag);
void forpart0(GEN k, GEN code , GEN nbound, GEN abound);
GEN  intcirc0(GEN a, GEN R, GEN code, GEN tab, long prec);
GEN  intfuncinit0(GEN a, GEN b, GEN code, long m, long prec);
GEN  intnum0(GEN a, GEN b, GEN code, GEN tab, long prec);
GEN  intnumgauss0(GEN a, GEN b, GEN code, GEN tab, long prec);
GEN  intnumromb0_bitprec(GEN a, GEN b, GEN code, long flag, long bit);
GEN  laurentseries0(GEN f, long M, long v, long prec);
GEN  limitnum0(GEN u, GEN alpha, long prec);
GEN  matrice(GEN nlig, GEN ncol, GEN code);
void pariplot0(GEN a, GEN b, GEN code, GEN ysmlu, GEN ybigu, long prec);
GEN  prodeuler0(GEN a, GEN b, GEN code, long prec);
GEN  prodinf0(GEN a, GEN code, long flag, long prec);
GEN  produit(GEN a, GEN b, GEN code, GEN x);
GEN  somme(GEN a, GEN b, GEN code, GEN x);
GEN  sumalt0(GEN a, GEN code,long flag, long prec);
GEN  sumdivexpr(GEN num, GEN code);
GEN  sumdivmultexpr0(GEN num, GEN code);
GEN  suminf0_bitprec(GEN a, GEN code, long bit);
GEN  sumnum0(GEN a, GEN code, GEN tab, long prec);
GEN  sumnumap0(GEN a, GEN code, GEN tab, long prec);
GEN  sumnumlagrange0(GEN a, GEN code, GEN tab, long prec);
GEN  sumnummonien0(GEN a, GEN code, GEN tab, long prec);
GEN  sumpos0(GEN a, GEN code, long flag,long prec);
GEN  vecexpr0(GEN nmax, GEN code, GEN pred);
GEN  vecexpr1(GEN nmax, GEN code, GEN pred);
GEN  vecteursmall(GEN nmax, GEN code);
GEN  vecteur(GEN nmax, GEN n);
GEN  vvecteur(GEN nmax, GEN n);
GEN  zbrent0(GEN a, GEN b, GEN code, long prec);
GEN  solvestep0(GEN a, GEN b, GEN step, GEN code, long flag, long prec);

GEN  ploth0(GEN a, GEN b, GEN code, long flag, long n, long prec);
GEN  plothexport0(GEN fmt, GEN a, GEN b, GEN code, long flags, long n, long prec);
GEN  psploth0(GEN a,GEN b,GEN code,long flag,long n,long prec);
GEN  plotrecth0(long ne,GEN a,GEN b,GEN code,ulong flags,long n,long prec);

GEN  listcreate_gp(long n);

/* mt */
void mt_sigint(void);
void mt_err_recover(long er);
void mt_export_add(const char *str, GEN val);
void mt_export_del(const char *str);
void mt_init_stack(size_t s);
int  mt_is_thread(void);

GEN  eisker_worker(GEN Ei, GEN M, GEN D, GEN co, GEN CD);
GEN  pareval_worker(GEN code);
GEN  parselect_worker(GEN d, GEN code);
void parfor0(GEN a, GEN b, GEN code, GEN code2);
GEN  parfor_worker(GEN i, GEN C);
void parforeach0(GEN x, GEN code, GEN code2);
void parforprime0(GEN a, GEN b, GEN code, GEN code2);
void parforprimestep0(GEN a, GEN b, GEN q, GEN code, GEN code2);
void parforvec0(GEN a, GEN code, GEN code2, long flag);
GEN  parvector_worker(GEN i, GEN C);
GEN  polmodular_worker(GEN pt, ulong L, GEN hilb, GEN factu,
       GEN vne, GEN vinfo, long compute_derivs, GEN j_powers, GEN fdb);
GEN  nmV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
GEN  nmV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
GEN  nxMV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
GEN  nxMV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
GEN  F2xq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
GEN  Flxq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
GEN  Fp_log_sieve_worker(long a, long prmax, GEN C, GEN c, GEN Ci, GEN ci, GEN pr, GEN sz);
GEN  QM_charpoly_ZX_worker(GEN P, GEN M, GEN dM);
GEN  QXQ_div_worker(GEN P, GEN A, GEN B, GEN C);
GEN  QXQ_inv_worker(GEN P, GEN A, GEN B);
GEN  ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB);
GEN  ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB);
GEN  ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v);
GEN  ZX_direct_compositum_worker(GEN P, GEN A, GEN B);
GEN  ZXQX_direct_compositum_worker(GEN P, GEN A, GEN B, GEN C);
GEN  ZX_gcd_worker(GEN P, GEN A, GEN B, GEN g);
GEN  ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d);
GEN  ZM_det_worker(GEN P, GEN A);
GEN  ZM_inv_worker(GEN P, GEN A);
GEN  ZM_ker_worker(GEN P, GEN A);
GEN  ZM_mul_worker(GEN P, GEN A, GEN B);
GEN  ZabM_inv_worker(GEN P, GEN A, GEN Q);
GEN  aprcl_step4_worker(ulong q, GEN pC, GEN N, GEN v);
GEN  aprcl_step6_worker(GEN r, long t, GEN N, GEN N1, GEN et);
GEN  ecpp_sqrt_worker(GEN g, GEN N, GEN p);
GEN  ecpp_ispsp_worker(GEN N);
GEN  ecpp_step2_worker(GEN S, GEN HD, GEN primelist, long dbg);
GEN  primecertisvalid_ecpp_worker(GEN certi);
GEN  lfuninit_worker(long r, GEN K, GEN L, GEN peh2d, GEN vroots, GEN dr, GEN di, GEN an, GEN bn);
GEN  lfuninit_theta2_worker(long r, GEN L, GEN qk, GEN a, GEN di, GEN an, GEN bn);
GEN  gen_parapply(GEN worker, GEN D);
GEN  parapply_slice_worker(GEN worker, GEN D);
GEN  gen_parapply_slice(GEN worker, GEN D, long mmin);
GEN  gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pt_mod,
             GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN));
void gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
           forprime_t *S, GEN *pt_H, GEN *pt_mod, GEN crt(GEN, GEN, GEN*),
           GEN center(GEN, GEN, GEN));
void gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
           forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
           GEN center(GEN, GEN, GEN));
GEN  direllnf_worker(GEN P, ulong X, GEN E);
GEN  dirartin_worker(GEN P, ulong X, GEN nf, GEN G, GEN V, GEN aut);
GEN  direllsympow_worker(GEN P, ulong X, GEN E, ulong m);
GEN  dirgenus2_worker(GEN P, ulong X, GEN Q);
GEN  pardireuler(GEN worker, GEN a, GEN b, GEN c, GEN Sbad);
GEN  FpM_ratlift_worker(GEN A, GEN mod, GEN B);
GEN  ellQ_factorback_worker(GEN P, GEN E, GEN A, GEN L, ulong l);
GEN  chinese_unit_worker(GEN P, GEN A, GEN U, GEN B, GEN D, GEN C);

/* Relative number fields */
enum { rnf_NFABS = 1, rnf_MAPS };

/* Finite fields */
enum { t_FF_FpXQ = 0, t_FF_Flxq = 1, t_FF_F2xq = 2 };
GEN FF_ellinit(GEN E, GEN fg);
GEN FF_elldata(GEN E, GEN fg);

/* L functions */
enum { t_LFUN_GENERIC, t_LFUN_ZETA, t_LFUN_NF, t_LFUN_ELL, t_LFUN_KRONECKER,
       t_LFUN_CHIZ, t_LFUN_CHIGEN, t_LFUN_ETA,
       t_LFUN_DIV, t_LFUN_MUL, t_LFUN_CONJ,
       t_LFUN_SYMPOW_ELL, t_LFUN_QF, t_LFUN_ARTIN, t_LFUN_MFCLOS,
       t_LFUN_GENUS2, t_LFUN_TWIST, t_LFUN_CLOSURE0, t_LFUN_SHIFT};
enum { t_LDESC_INIT, t_LDESC_THETA, t_LDESC_PRODUCT };

/* Elliptic curves */
/* common to Q and Rg */
enum { R_PERIODS = 1, R_ETA, R_ROOTS, R_AB };

enum { Qp_ROOT = 1, Qp_TATE };
enum { Q_GROUPGEN = 5, Q_GLOBALRED, Q_ROOTNO, Q_MINIMALMODEL };
enum { NF_MINIMALMODEL = 1, NF_GLOBALRED, NF_MINIMALPRIMES, NF_ROOTNO, NF_NF };

/* common to Fp and Fq */
enum { FF_CARD = 1, FF_GROUP, FF_GROUPGEN, FF_O };

/* for Buchall_param */
enum { fupb_NONE = 0, fupb_RELAT, fupb_LARGE, fupb_PRECI };

/* Polycyclic presentation for the classgroup of discriminant D */
typedef struct {
  long D; /* Negative discriminant */
  long h; /* Size of classgroup */
  long enum_cnt; /* Either h or h/2 (if L0 is set) */
  /* If nonzero, L0=L[0] and n[0]=2 and classpoly is a perfect square
   * (and we enumerate each double root just once), default is 0 */
  long L0;
  /* Product of primes L that are prohibited as norms of generators or
   * auxilliary prime forms (by default, primes that make enumeration hard) */
  long Lfilter;
  /* Norms of implicit generators (primeforms a=(L*x^2+b*x*y+c*y^2)
   * with norm L and b >=0) */
  long *L;
  long *m; /* products of relative orders: m[i] is the order of <g_1,...,g_i> */
  long *n; /* Relative orders */
  long *o; /* Absolute orders */
  /* Power relations (a[i]^n[i] = a[0]^e[0]*...*a[i-1]^e[i-1], where e
   * is an exponent vector of length i stored at offset binom(i,2) of r) */
  long *r;
  long *orient_p; /* Optional list of norms of orienting primes p ... */
  long *orient_q; /* or product of primes p*q (q=1 when only p is needed) */
  long *orient_reps; /* Representation of orienting norm p*q in terms of Ls */
  long inv; /* Attached invariant */
  long k; /* Number of generators */
  GEN _data; /* Storage space for the above arrays */
} classgp_pcp_struct;
typedef classgp_pcp_struct classgp_pcp_t[1];

/* Represents the data in the equation(s)
 *   4p = t^2 - v^2 D = t^2 - v^2 u^2 D_K = w^2 D_K.
 * t is the absolute trace, so always > 0.
 * T is a twisting parameter, which satisfies (T|p) == -1. */
typedef struct {
  long D, t, u, v;
  ulong p, pi, s2, T;
} norm_eqn_struct;
typedef norm_eqn_struct norm_eqn_t[1];

#define zv_to_longptr(v) (&((v)[1]))
#define zv_to_ulongptr(v) ((ulong *)&((v)[1]))

/* Modular invariants */
#define INV_J       0
#define INV_F       1
#define INV_F2      2
#define INV_F3      3
#define INV_F4      4
#define INV_G2      5
#define INV_W2W3    6
#define INV_F8      8
#define INV_W3W3    9
#define INV_W2W5    10
#define INV_W2W7    14
#define INV_W3W5    15
#define INV_W3W7    21
#define INV_W2W3E2  23
#define INV_W2W5E2  24
#define INV_W2W13   26
#define INV_W2W7E2  27
#define INV_W3W3E2  28
#define INV_W5W7    35
#define INV_W3W13   39

/* Get coefficient of x^d in f, assuming f is nonzero. */
INLINE ulong Flx_coeff(GEN f, long d) { return f[d + 2]; }
/* Return the root of f, assuming deg(f) = 1. */
INLINE ulong Flx_deg1_root(GEN f, ulong p) {
  if (degpol(f) != 1) pari_err_BUG("Flx_deg1_root");
  return Fl_div(Fl_neg(Flx_coeff(f, 0), p), Flx_coeff(f, 1), p);
}

/* Allocation / gerepile */
long   getdebugvar(void);
void   setdebugvar(long n);
void   debug_stack(void);
void   fill_stack(void);
void   minim_alloc(long n, double ***q, GEN *x, double **y,  double **z, double **v);
int    pop_entree_block(entree *ep, long loc);
int    pop_val_if_newer(entree *ep, long loc);

/* general printing */
void print_errcontext(PariOUT *out, const char *msg, const char *s, const char *entry);
void print_prefixed_text(PariOUT *out, const char *s, const char *prefix, const char *str);
INLINE void
print_text(const char *s) { print_prefixed_text(pariOut, s,NULL,NULL); }
INLINE void
out_print_text(PariOUT *out, const char *s) { print_prefixed_text(out, s,NULL,NULL); }
INLINE long
is_keyword_char(char c) { return (isalnum((int)c) || c=='_'); }

/* Interfaces (GP, etc.) */
hashtable *hash_from_link(GEN e, GEN names, int use_stack);
void gen_relink(GEN x, hashtable *table);
entree* do_alias(entree *ep);
char* get_sep(const char *t);
long get_int(const char *s, long dflt);
ulong get_uint(const char *s);
void gp_initrc(pari_stack *p_A);

void pari_sigint(const char *s);
void* get_stack(double fraction, long min);
void  free_graph(void);
void  initout(int initerr);
void  resetout(int initerr);
void  init_linewrap(long w);
void  print_functions_hash(const char *s);
GEN   readbin(const char *name, FILE *f, int *vector);
int   term_height(void);
int   term_width(void);
/* gp_colors */
void decode_color(long n, long *c);

/* defaults */
extern long precreal;

void lim_lines_output(char *s, long n, long max);
int tex2mail_output(GEN z, long n);
void gen_output(GEN x);
void fputGEN_pariout(GEN x, pariout_t *T, FILE *out);

void parsestate_reset(void);
void parsestate_save(struct pari_parsestate *state);
void parsestate_restore(struct pari_parsestate *state);

void compilestate_reset(void);
void compilestate_save(struct pari_compilestate *comp);
void compilestate_restore(struct pari_compilestate *comp);

void filestate_save(struct pari_filestate *file);
void filestate_restore(struct pari_filestate *file);
void tmp_restore(pariFILE *F);

long evalstate_get_trace(void);
void evalstate_set_trace(long lvl);
void evalstate_clone(void);
void evalstate_reset(void);
void evalstate_restore(struct pari_evalstate *state);
GEN  evalstate_restore_err(struct pari_evalstate *state);
void evalstate_save(struct pari_evalstate *state);
void varstate_save(struct pari_varstate *s);
void varstate_restore(struct pari_varstate *s);

void mtstate_save(struct pari_mtstate *s);
void mtstate_reset(void);
void mtstate_restore(struct pari_mtstate *s);

void debug_context(void);

typedef struct {
  const char *s;
  size_t ls;
  char **dir;
} forpath_t;
void forpath_init(forpath_t *T, gp_path *path, const char *s);
char *forpath_next(forpath_t *T);

/* GP output && output format */
void gpwritebin(const char *s, GEN x);
extern char *current_logfile;

/* colors */
extern long    gp_colors[];
extern int     disable_color;

/* entrees */
#define EpVALENCE(ep) ((ep)->valence & 0xFF)
#define EpSTATIC(ep) ((ep)->valence & 0x100)
#define EpSETSTATIC(ep) ((ep)->valence |= 0x100)
enum { EpNEW = 100, EpALIAS, EpVAR, EpINSTALL };
#define initial_value(ep) ((ep)+1)

/* functions lists */
extern const long functions_tblsz;  /* hashcodes table size */
extern entree **functions_hash;   /* functions hashtable */
extern entree **defaults_hash;    /* defaults hashtable */

/* buffers */
typedef struct Buffer {
  char *buf;
  ulong len;
  jmp_buf env;
} Buffer;
Buffer *new_buffer(void);
void delete_buffer(Buffer *b);
void fix_buffer(Buffer *b, long newlbuf);

typedef struct {
  const char *s; /* source */
  char *t, *end; /* target, last char read */
  int in_string, in_comment, more_input, wait_for_brace;
  Buffer *buf;
} filtre_t;
void init_filtre(filtre_t *F, Buffer *buf);
Buffer *filtered_buffer(filtre_t *F);
void kill_buffers_upto_including(Buffer *B);
void pop_buffer(void);
void kill_buffers_upto(Buffer *B);
int gp_read_line(filtre_t *F, const char *PROMPT);
void parse_key_val(char *src, char **ps, char **pt);
extern int (*cb_pari_get_line_interactive)(const char*, const char*, filtre_t *F);
extern char *(*cb_pari_fgets_interactive)(char *s, int n, FILE *f);
int get_line_from_file(const char *prompt, filtre_t *F, FILE *file);
void pari_skip_space(char **s);
void pari_skip_alpha(char **s);
char *pari_translate_string(const char *src, char *s, char *entry);

gp_data *default_gp_data(void);

typedef char *(*fgets_t)(char *, int, void*);

typedef struct input_method {
/* optional */
  fgets_t myfgets;  /* like libc fgets() but last argument is (void*) */
/* mandatory */
  char * (*getline)(char**, int f, struct input_method*, filtre_t *F);
  int free; /* boolean: must we free the output of getline() ? */
/* optional */
  const char *prompt, *prompt_cont;
  void *file;  /* can be used as last argument for fgets() */
} input_method;

int input_loop(filtre_t *F, input_method *IM);
char *file_input(char **s0, int junk, input_method *IM, filtre_t *F);
char *file_getline(Buffer *b, char **s0, input_method *IM);

/* readline */
typedef struct {
  /* pointers to readline variables/functions */
  char **line_buffer;
  int *point;
  int *end;
  char **(*completion_matches)(const char *, char *(*)(const char*, int));
  char *(*filename_completion_function)(const char *, int);
  char *(*username_completion_function)(const char *, int);
  int (*insert)(int, int);
  int *completion_append_character;

  /* PARI-specific */
  int back;  /* rewind the cursor by this number of chars */
} pari_rl_interface;

/* Code which wants to use readline needs to do the following:

#include <readline.h>
#include <paripriv.h>
pari_rl_interface pari_rl;
pari_use_readline(pari_rl);

This will initialize the pari_rl structure. A pointer to this structure
must be given as first argument to all PARI readline functions. */

/* IMPLEMENTATION NOTE: this really must be a macro (not a function),
 * since we refer to readline symbols. */
#define pari_use_readline(pari_rl) do {\
    (pari_rl).line_buffer = &rl_line_buffer; \
    (pari_rl).point = &rl_point; \
    (pari_rl).end = &rl_end; \
    (pari_rl).completion_matches = &rl_completion_matches; \
    (pari_rl).filename_completion_function = &rl_filename_completion_function; \
    (pari_rl).username_completion_function = &rl_username_completion_function; \
    (pari_rl).insert = &rl_insert; \
    (pari_rl).completion_append_character = &rl_completion_append_character; \
    (pari_rl).back = 0; } while(0)

/* FIXME: EXPORT AND DOCUMENT THE FOLLOWING */

/* PROBABLY NOT IN THE RIGHT FILE, SORT BY THEME */

/* multiprecision */
GEN   adduispec_offset(ulong s, GEN x, long offset, long nx);
int   lgcdii(ulong* d, ulong* d1, ulong* u, ulong* u1, ulong* v, ulong* v1, ulong vmax);
ulong rgcduu(ulong d, ulong d1, ulong vmax, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
ulong xgcduu(ulong d, ulong d1, int f, ulong* v, ulong* v1, long *s);
ulong xxgcduu(ulong d, ulong d1, int f, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
GEN   divgunu(GEN x, ulong i);
GEN   divrunu(GEN x, ulong i);
GEN   muliispec(GEN x, GEN y, long nx, long ny);
GEN   red_montgomery(GEN T, GEN N, ulong inv);
GEN   sqrispec(GEN x, long nx);
ulong *convi(GEN x, long *l);

int approx_0(GEN x, GEN y);

/* powers */
GEN    rpowuu(ulong a, ulong n, long prec);

/* floats */
double dabs(double s, double t);
double darg(double s, double t);
void   dcxlog(double s, double t, double *a, double *b);
double dnorm(double s, double t);
double dbllog2(GEN z);
double dbllambertW0(double a);
double dbllambertW_1(double a);

/* hnf */
GEN hnfadd(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
GEN hnfadd_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
GEN hnfspec_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN hnfspec(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN mathnfspec(GEN x, GEN *ptperm, GEN *ptdep, GEN *ptB, GEN *ptC);
GEN ZM_hnfmodall_i(GEN x, GEN dm, long flag);

GEN LLL_check_progress(GEN Bnorm, long n0, GEN m, int final, long *ti_LLL);

/* integer factorization / discrete log */
ulong is_kth_power(GEN x, ulong p, GEN *pt);
GEN   mpqs(GEN N);

/* Polynomials */
/* a) Arithmetic/conversions */
GEN  lift_if_rational(GEN x);
GEN  monomial(GEN a, long degpol, long v);
GEN  monomialcopy(GEN a, long degpol, long v);
GEN  ser2pol_i(GEN x, long lx);
GEN  ser2rfrac_i(GEN x);
GEN  swap_vars(GEN b0, long v);
GEN  RgX_recipspec_shallow(GEN x, long l, long n);

/* b) Modular */
GEN  bezout_lift_fact(GEN T, GEN Tmod, GEN p, long e);
GEN  polsym_gen(GEN P, GEN y0, long n, GEN T, GEN N);
GEN  ZXQ_charpoly_sqf(GEN A, GEN B, long *lambda, long v);
GEN  ZX_disc_all(GEN,ulong);
GEN  ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound);
GEN  ZX_ZXY_resultant_all(GEN A, GEN B, long *lambda, GEN *LPRS);

GEN FlxqM_mul_Kronecker(GEN A, GEN B, GEN T, ulong p);
GEN FqM_mul_Kronecker(GEN x, GEN y, GEN T, GEN p);

/* c) factorization */
GEN chk_factors_get(GEN lt, GEN famod, GEN c, GEN T, GEN N);
long cmbf_maxK(long nb);
GEN ZX_DDF(GEN x);
GEN initgaloisborne(GEN T, GEN dn, long prec, GEN *pL, GEN *pprep, GEN *pdis);

/* number fields */
GEN nflist_C3_worker(GEN gv, GEN T);
GEN nflist_C4vec_worker(GEN gm, GEN X, GEN Xinf, GEN gs);
GEN nflist_V4_worker(GEN D1, GEN X, GEN Xinf, GEN gs);
GEN nflist_D4_worker(GEN D, GEN X, GEN Xinf, GEN listarch);
GEN nflist_A4S4_worker(GEN P3, GEN X, GEN Xinf, GEN cards);
GEN nflist_C5_worker(GEN N, GEN bnfC5);
GEN nflist_CL_worker(GEN Fcond, GEN bnf, GEN ellprec);
GEN nflist_DL_worker(GEN P2, GEN X1pow, GEN X0pow, GEN X, GEN Xinf, GEN ells);
GEN nflist_Mgen_worker(GEN field, GEN X, GEN Xinf, GEN ella);
GEN nflist_C6_worker(GEN P3, GEN X, GEN Xinf, GEN M, GEN T);
GEN nflist_D612_worker(GEN P3, GEN X, GEN Xinf, GEN limd2s2);
GEN nflist_A46S46P_worker(GEN P3, GEN Xinf, GEN sqX, GEN cards);
GEN nflist_S46M_worker(GEN P3, GEN X, GEN Xinf, GEN gs);
GEN nflist_A462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch, GEN GAL);
GEN nflist_S3C3_worker(GEN D2, GEN X, GEN Xinf);
GEN nflist_S462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch13, GEN GAL);
GEN nflist_S36_worker(GEN pol, GEN X, GEN Xinf);
GEN nflist_C32C4_worker(GEN P4, GEN X, GEN Xinf, GEN GAL);
GEN nflist_C32D4_worker(GEN P, GEN X, GEN Xinf, GEN gs);
GEN nflist_C9_worker(GEN P, GEN X, GEN Xinf);
GEN nflist_C3C3_worker(GEN gi, GEN V3, GEN V3D, GEN X);
GEN nflist_S3R_worker(GEN ga, GEN ALLCTS);
GEN nflist_S3I_worker(GEN ga, GEN ALLCTS);
GEN nflist_D9_worker(GEN P2, GEN X, GEN Xinf);
GEN nflist_S32_worker(GEN all1, GEN X, GEN Xinf, GEN V3, GEN gs);

/* pari_init / pari_close */
void pari_close_compiler(void);
void pari_close_evaluator(void);
void pari_close_files(void);
void pari_close_floats(void);
void pari_close_homedir(void);
void pari_close_parser(void);
void pari_close_paths(void);
void pari_close_primes(void);
void pari_init_buffers(void);
void pari_init_compiler(void);
void pari_init_defaults(void);
void pari_init_ellcondfile(void);
void pari_init_evaluator(void);
void pari_init_files(void);
void pari_init_floats(void);
void pari_init_homedir(void);
void pari_init_graphics(void);
void pari_init_parser(void);
void pari_init_rand(void);
void pari_init_paths(void);
void pari_init_primetab(void);
void pari_init_seadata(void);
GEN pari_get_seadata(void);
void pari_set_primetab(GEN global_primetab);
void pari_set_seadata(GEN seadata);
void pari_set_varstate(long *vp, struct pari_varstate *vs);
void pari_thread_close_files(void);

void export_add(const char *str, GEN val);
void export_del(const char *str);
GEN  export_get(const char *str);
void exportall(void);
void unexportall(void);

/* BY FILES */

/* parinf.h */

GEN fincke_pohst(GEN a,GEN BOUND,long stockmax,long PREC, FP_chk_fun *CHECK);
void init_zlog(zlog_S *S, GEN bid);
GEN  log_gen_arch(zlog_S *S, long index);
GEN  log_gen_pr(zlog_S *S, long index, GEN nf, long e);
GEN  sprk_log_gen_pr(GEN nf, GEN sprk, long e);
GEN  sprk_log_prk1(GEN nf, GEN a, GEN sprk);
GEN    poltobasis(GEN nf,GEN x);
GEN    coltoalg(GEN nf,GEN x);

GEN    rnfdisc_get_T(GEN nf, GEN P, GEN *lim);
GEN    make_integral(GEN nf, GEN L0, GEN f, GEN listpr);
GEN    rnfallbase(GEN nf, GEN pol, GEN lim, GEN rnfeq, GEN *pD, GEN *pfi,
                  GEN *pdKP);
GEN    subgroupcondlist(GEN cyc, GEN bound, GEN listKer);

/* Qfb.c */

GEN     redimagsl2(GEN q, GEN *U);

/* alglin1.c */

typedef long (*pivot_fun)(GEN,GEN,long,GEN);
GEN ZM_pivots(GEN x0, long *rr);
GEN RgM_pivots(GEN x0, GEN data, long *rr, pivot_fun pivot);
void RgMs_structelim_col(GEN M, long nbcol, long nbrow, GEN A, GEN *p_col, GEN *p_lin);

/* arith1.c */

int     is_gener_Fp(GEN x, GEN p, GEN p_1, GEN L);
int     is_gener_Fl(ulong x, ulong p, ulong p_1, GEN L);

/* arith2.c */

int     divisors_init(GEN n, GEN *pP, GEN *pE);
long    set_optimize(long what, GEN g);

/* base1.c */

GEN zk_galoisapplymod(GEN nf, GEN z, GEN S, GEN p);

/* base2.c */

GEN     dim1proj(GEN prh);
GEN     gen_if_principal(GEN bnf, GEN x);

/* base3.c */

void    check_nfelt(GEN x, GEN *den);
GEN     zk_ei_mul(GEN nf, GEN x, long i);
GEN     log_prk(GEN nf, GEN a, GEN sprk, GEN mod);
GEN     log_prk_units(GEN nf, GEN D, GEN sprk);
GEN     log_prk_units_init(GEN bnf);
GEN     veclog_prk(GEN nf, GEN v, GEN sprk);
GEN     log_prk_init(GEN nf, GEN pr, long k, GEN mod);

/* base4.c */

GEN     factorbackprime(GEN nf, GEN L, GEN e);

/* bb_group.c */

GEN     producttree_scheme(long n);

/* bern.c */
long bernbitprec(long N);

/* bibli2.c */

GEN sort_factor_pol(GEN y, int (*cmp)(GEN,GEN));

/* buch1.c */

long   bnf_increase_LIMC(long LIMC, long LIMCMAX);

/* buch2.c */

typedef struct GRHprime_t { ulong p; double logp; GEN dec; } GRHprime_t;
typedef struct GRHcheck_t { double cD, cN; GRHprime_t *primes; long clone, nprimes, maxprimes; ulong limp; forprime_t P; } GRHcheck_t;
void    free_GRHcheck(GRHcheck_t *S);
void    init_GRHcheck(GRHcheck_t *S, long N, long R1, double LOGD);
void    GRH_ensure(GRHcheck_t *S, long nb);
ulong   GRH_last_prime(GRHcheck_t *S);
int     GRHok(GRHcheck_t *S, double L, double SA, double SB);
GEN     extract_full_lattice(GEN x);
GEN     init_red_mod_units(GEN bnf, long prec);
GEN     isprincipalarch(GEN bnf, GEN col, GEN kNx, GEN e, GEN dx, long *pe);
GEN     red_mod_units(GEN col, GEN z);

/* buch3.c */

GEN     minkowski_bound(GEN D, long N, long r2, long prec);
int     subgroup_conductor_ok(GEN H, GEN L);
GEN     subgrouplist_cond_sub(GEN bnr, GEN C, GEN bound);

/* crvwtors.c */

void random_curves_with_m_torsion(ulong *a4, ulong *a6, ulong *tx, ulong *ty, long ncurves, long m, ulong p);

/* dirichlet.c */

GEN direuler_factor(GEN s, long n);

/* ellanal.c */

GEN hnaive_max(GEN ell, GEN ht);

/* elliptic.c */

GEN  ellQ_genreduce(GEN E, GEN G, GEN M, long prec);
GEN  ellQ_isdivisible(GEN E, GEN P, ulong l);
GEN  ellintegralbmodel(GEN e, GEN *pv);
void ellprint(GEN e);

/* ellrank.c */

GEN     ell2selmer_basis(GEN ell, GEN *cb, long prec);

/* es.c */

void    killallfiles(void);
pariFILE* newfile(FILE *f, const char *name, int type);
int     popinfile(void);
pariFILE* try_pipe(const char *cmd, int flag);

/* F2m.c */

GEN     F2m_gauss_pivot(GEN x, long *rr);
GEN     F2m_gauss_sp(GEN a, GEN b);
GEN     F2m_invimage_i(GEN A, GEN B);

/* Fle.c */

void    FleV_add_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);
void    FleV_dbl_pre_inplace(GEN P, GEN a4, ulong p, ulong pi);
void    FleV_mulu_pre_inplace(GEN P, ulong n, GEN a4, ulong p, ulong pi);
void    FleV_sub_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);

/* Flv.c */

GEN     Flm_gauss_sp(GEN a, GEN b, ulong *detp, ulong p);
GEN     Flm_invimage_i(GEN A, GEN B, ulong p);
GEN     Flm_inv_sp(GEN a, ulong *detp, ulong p);
GEN     Flm_pivots(GEN x, ulong p, long *rr, long inplace);

/* Flxq_log.c */

GEN Flxq_log_index(GEN a0, GEN b0, GEN m, GEN T0, ulong p);
int Flxq_log_use_index(GEN m, GEN T0, ulong p);

/* FlxqE.c */

GEN     ZpXQ_norm_pcyc(GEN x, GEN T, GEN q, GEN p);
long    zx_is_pcyc(GEN T);

/* FpV.c */

GEN FpMs_leftkernel_elt_col(GEN M, long nbcol, long nbrow, GEN p);
GEN FpX_to_mod_raw(GEN z, GEN p);

/* FpX.c */

GEN     ZlXQXn_expint(GEN h, long e, GEN T, GEN p, ulong pp);

/* FpX_factor.c */

GEN     ddf_to_ddf2(GEN V);
long    ddf_to_nbfact(GEN D);
GEN     vddf_to_simplefact(GEN V, long d);

/* FpXQX_factor.c */

GEN     FpXQX_factor_Berlekamp(GEN x, GEN T, GEN p);

/* forprime.c*/

void    init_modular_big(forprime_t *S);
void    init_modular_small(forprime_t *S);

/* galconj.c */

GEN     galoiscosets(GEN O, GEN perm);
GEN     matrixnorm(GEN M, long prec);

/* gen1.c */

GEN     gred_rfrac_simple(GEN n, GEN d);
GEN     sqr_ser_part(GEN x, long l1, long l2);

/* hash.c */

hashtable *hashstr_import_static(hashentry *e, ulong size);

/* hyperell.c */

GEN     ZlXQX_hyperellpadicfrobenius(GEN H, GEN T, ulong p, long n);
GEN     hyperell_redsl2(GEN Q);

/* ifactor1.c */

ulong snextpr(ulong p, byteptr *d, long *rcn, long *q, int (*ispsp)(ulong));

/* intnum.c */

GEN     contfraceval_inv(GEN CF, GEN tinv, long nlim);

/* mftrace.c */

void pari_close_mf(void);
long polishomogeneous(GEN P);
GEN sertocol(GEN S);
GEN mfrhopol(long n);
GEN mfrhopol_u_eval(GEN Q, ulong t2);
GEN mfrhopol_eval(GEN Q, GEN t2);

/* prime.c */

long    BPSW_psp_nosmalldiv(GEN N);
int     MR_Jaeschke(GEN n);
long    isanypower_nosmalldiv(GEN N, GEN *px);
void    prime_table_next_p(ulong a, byteptr *pd, ulong *pp, ulong *pn);

/* perm.c */

long    cosets_perm_search(GEN C, GEN p);
GEN     perm_generate(GEN S, GEN H, long o);
long    perm_relorder(GEN p, GEN S);
GEN     vecperm_extendschreier(GEN C, GEN v, long n);

/* polclass.c */

GEN polclass0(long D, long inv, long xvar, GEN *db);

/* polmodular.c */

GEN polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db);
GEN Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi);
GEN polmodular_db_init(long inv);
void polmodular_db_clear(GEN db);
void polmodular_db_add_level(GEN *db, long L, long inv);
void polmodular_db_add_levels(GEN *db, long *levels, long k, long inv);
GEN polmodular_db_for_inv(GEN db, long inv);
GEN polmodular_db_getp(GEN fdb, long L, ulong p);

long modinv_level(long inv);
long modinv_degree(long *p1, long *p2, long inv);
long modinv_ramified(long D, long inv);
long modinv_j_from_2double_eta(GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi);
GEN double_eta_raw(long inv);
ulong modfn_root(ulong j, norm_eqn_t ne, long inv);
long modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb);
GEN qfb_nform(long D, long n);

/* Fle.c */

ulong   Flj_order_ufact(GEN P, ulong n, GEN F, ulong a4, ulong p, ulong pi);

/* polarit3.c */

GEN     Flm_Frobenius_pow(GEN M, long d, GEN T, ulong p);
GEN     FpM_Frobenius_pow(GEN M, long d, GEN T, GEN p);
GEN     FpX_compositum(GEN A, GEN B, GEN p);
GEN     Flx_direct_compositum(GEN A, GEN B, ulong p);
GEN     FlxV_direct_compositum(GEN V, ulong p);
GEN     FlxqX_direct_compositum(GEN P, GEN Q, GEN T, ulong p);
GEN     FpX_direct_compositum(GEN A, GEN B, GEN p);
GEN     FpXV_direct_compositum(GEN V, GEN p);
GEN     nf_direct_compositum(GEN nf, GEN A, GEN B);
ulong   ZX_ZXY_ResBound(GEN A, GEN B, GEN dB);
GEN     ffinit_Artin_Schreier(ulong p, long l);
GEN     ffinit_rand(GEN p, long n);

/* nflistQT.c */

GEN nflistQT(long n, long k, long v);

/* ramanujantau.c */
GEN     ramanujantau_worker(GEN gt, GEN p2_7, GEN p_9, GEN p);
GEN     taugen_n_worker(GEN t, GEN pol, GEN p4);

/* readline.c */

char**  pari_completion(pari_rl_interface *pari_rl, char *text, int START, int END);
char**  pari_completion_matches(pari_rl_interface *pari_rl, const char *s, long pos, long *wordpos);

/* RgX.c */

GEN     RgX_homogenous_evalpow(GEN P, GEN A, GEN B);
GEN     QXQX_homogenous_evalpow(GEN P, GEN A, GEN B, GEN T);

/* subcyclo.c */

GEN     galoiscyclo(long n, long v);
GEN     znstar_bits(long n, GEN H);
long    znstar_conductor(GEN H);
long    znstar_conductor_bits(GEN bits);
GEN     znstar_cosets(long n, long phi_n, GEN H);
GEN     znstar_elts(long n, GEN H);
GEN     znstar_generate(long n, GEN V);
GEN     znstar_hnf(GEN Z, GEN M);
GEN     znstar_hnf_elts(GEN Z, GEN H);
GEN     znstar_hnf_generators(GEN Z, GEN M);
GEN     znstar_reduce_modulus(GEN H, long n);
GEN     znstar_small(GEN zn);

/* trans1.c */

struct abpq { GEN *a, *b, *p, *q; };
struct abpq_res { GEN P, Q, B, T; };
void    abpq_init(struct abpq *A, long n);
void    abpq_sum(struct abpq_res *r, long n1, long n2, struct abpq *A);
GEN     logagmcx(GEN q, long prec);
GEN     zellagmcx(GEN a0, GEN b0, GEN r, GEN t, long prec);

/* trans2.c */

GEN     trans_fix_arg(long *prec, GEN *s0, GEN *sig, GEN *tau, pari_sp *av, GEN *res);

/* trans3.c */

GEN     double_eta_quotient(GEN a, GEN w, GEN D, long p, long q, GEN pq, GEN sqrtD);
GEN     inv_szeta_euler(long n, long prec);

/* volcano.c */

long j_level_in_volcano(GEN phi, ulong j, ulong p, ulong pi, long L, long depth);
ulong ascend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
ulong descend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
long next_surface_nbr(ulong *nJ, GEN phi, long L, long h, ulong J, const ulong *pJ, ulong p, ulong pi);
GEN enum_roots(ulong j, norm_eqn_t ne, GEN fdb, classgp_pcp_t G);

/* pic.c */
GEN ZpXQMinv(GEN A, GEN T, GEN pe, GEN p, long e);
GEN ZpXQ_FrobMat(GEN T, GEN p, long e, GEN pe);
GEN JgetT(GEN J);
GEN Jgetp(GEN J);
GEN JgetLp(GEN J);
GEN DivMul(GEN f, GEN W, GEN T, GEN p);
GEN DivAdd1(GEN WA, GEN WB, ulong d, GEN T, GEN pe, GEN p, ulong excess, long flag);
GEN PicRefreshPairings(GEN J, GEN FRparams, GEN T, GEN Pairings, GEN UsedNames, GEN Want, GEN WantNames);
GEN PicTors_UpdatePairings(GEN J, GEN FRparams, GEN BT, GEN R, GEN Tnew, GEN TnewPairings, int* replace);
GEN VecExtend1_shallow(GEN V, GEN X);
GEN PicTorsGalRep_from_basis(GEN J, GEN J1, GEN l, GEN B);

ENDEXTERN