/*
 * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
 * All rights reserved.
 * 
 * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
 * non-exclusive and royalty-free license to use, copy, modify and
 * redistribute, solely for non-commercial and non-profit purposes, the
 * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
 * conditions of this Agreement. For the avoidance of doubt, you acquire
 * only a limited right to use the SOFTWARE hereunder, and FLL or any
 * third party developer retains all rights, including but not limited to
 * copyrights, in and to the SOFTWARE.
 * 
 * (1) FLL does not grant you a license in any way for commercial
 * purposes. You may use the SOFTWARE only for non-commercial and
 * non-profit purposes only, such as academic, research and internal
 * business use.
 * (2) The SOFTWARE is protected by the Copyright Law of Japan and
 * international copyright treaties. If you make copies of the SOFTWARE,
 * with or without modification, as permitted hereunder, you shall affix
 * to all such copies of the SOFTWARE the above copyright notice.
 * (3) An explicit reference to this SOFTWARE and its copyright owner
 * shall be made on your publication or presentation in any form of the
 * results obtained by use of the SOFTWARE.
 * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
 * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
 * for such modification or the source code of the modified part of the
 * SOFTWARE.
 * 
 * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
 * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
 * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2018/builtin/ec.c,v 1.2 2018/09/28 08:20:27 noro Exp $
*/
#include "ca.h"
#include "parse.h"
#include "inline.h"

/*
 * Elliptic curve related functions
 *
 * Argument specifications
 * Point = vector(x,y,z)  (projective representation)
 * ECInfo = vector(a,b,p)
 *         a,b : integer for GF(p), GF2N for GF(2^n)
 *         p : integer for GF(p), polynomial for GF(2^n)
 *
 */

struct oKeyIndexPair {
  unsigned int key;
  int index;
};

void Psha1();
void Psha1_ec();
void Pecm_add_ff();
void Pecm_chsgn_ff();
void Pecm_sub_ff();
void Pecm_compute_all_key_homo_ff();
void Pnextvect1(),Psort_ktarray(),Pecm_find_match(),Pseparate_vect();
void Pecm_set_addcounter();
void Pecm_count_order();

void ecm_add_ff(VECT,VECT,VECT,VECT *);
void ecm_add_gfp(VECT,VECT,VECT,VECT *);
void ecm_add_gf2n(VECT,VECT,VECT,VECT *);

void ecm_chsgn_ff(VECT,VECT *);
void ecm_sub_ff(VECT,VECT,VECT,VECT *);

void compute_all_key_homo_gfp(VECT *,int,unsigned int *);
void compute_all_key_homo_gf2n(VECT *,int,unsigned int *);

unsigned int separate_vect(double *,int);
void ecm_find_match(unsigned int *,int,unsigned int *,int,LIST *);
int find_match(unsigned int,unsigned int *,int);

void sort_ktarray(VECT,VECT,LIST *);
int comp_kip(struct oKeyIndexPair *,struct oKeyIndexPair *);

int nextvect1(VECT,VECT);

unsigned int ecm_count_order_gfp(unsigned int,unsigned int,unsigned int);
unsigned int ecm_count_order_gf2n(UP2,GF2N,GF2N);

void sha_memory(unsigned char *,unsigned int,unsigned int *);

unsigned int ecm_addcounter;
extern int current_ff,lm_lazy;

struct ftab ec_tab[] = {
/* point addition */
  {"ecm_add_ff",Pecm_add_ff,3},

/* point change sign */
  {"ecm_chsgn_ff",Pecm_chsgn_ff,1},

/* point subtraction */
  {"ecm_sub_ff",Pecm_sub_ff,3},

/* key computation for sort and match */
  {"ecm_compute_all_key_homo_ff",Pecm_compute_all_key_homo_ff,1},

/* exhausitve search of rational points */
  {"ecm_count_order",Pecm_count_order,1},

/* common functions */
  {"nextvect1",Pnextvect1,2},
  {"sort_ktarray",Psort_ktarray,2},
  {"separate_vect",Pseparate_vect,1},
  {"ecm_find_match",Pecm_find_match,2},
  {"ecm_set_addcounter",Pecm_set_addcounter,-1},
  {"sha1",Psha1,-2},
#if 0
  {"sha1_free",Psha1_free,1},
#endif
  {0,0,0},
};

void Psha1(NODE arg,Z *rp)
{
  unsigned char *s;
  unsigned int digest[5];
  size_t bl;
  Z z;
  mpz_t r;

  asir_assert(ARG0(arg),O_N,"sha1_free");  
  z = (Z)ARG0(arg);
  s = (unsigned char *)mpz_export(0,&bl,1,sizeof(unsigned char),1,0,BDY(z));
  sha_memory(s,bl,digest);
  mpz_init(r);
  mpz_import(r,5,1,sizeof(int),0,0,digest);
  MPZTOZ(r,*rp);
}

#if 0
void Psha1_ec(arg,rp)
NODE arg;
Q *rp;
{
#include <fj_crypt.h>
  SHS_CTX context;
  unsigned char *s;
  int i,j,l,bl,n;
  unsigned int t;
  N z,r;
  extern int little_endian;

  asir_assert(ARG0(arg),O_N,"sha1");  
  z = NM((Q)ARG0(arg));
  n = PL(z);
  l = n_bits(z);
  bl = (l+7)/8;
  s = (unsigned char *)MALLOC(bl);
  for ( i = 0, j = bl-1; i < n; i++ ) {
    t = BD(z)[i];
    if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
    if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
    if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
    if ( j >= 0 ) s[j--] = t;
  }
  SHSInit(&context);
  SHSUpdate(&context,s,bl);
  SHSFinal(&context);
  r = NALLOC(5);
  if ( little_endian )
    for ( i = 0; i < 5; i++ ) {
      t = context.digest[4-i];
      BD(r)[i] = (t>>24)|((t&0xff0000)>>8)|((t&0xff00)<<8)|(t<<24);
  } else
    for ( i = 0; i < 5; i++ )
      BD(r)[i] = context.digest[4-i];
  for ( i = 4; i >= 0 && !BD(r)[i]; i-- );
  if ( i < 0 )
    *rp = 0;
  else {
    PL(r) = i+1;
    NTOQ(r,1,*rp);
  }
}
#endif

void Pecm_count_order(NODE arg,Z *rp)
{
  Z p;
  UP2 d;
  Obj a,b;
  unsigned int p0,a0,b0,ord;
  VECT ec;
  Obj *vb;

  switch ( current_ff ) {
    case FF_GFP:
      getmod_lm(&p);
      if ( z_bits((Q)p) > 32 )
        error("ecm_count_order : ground field too large");
      p0 = ZTOS(p);
      ec = (VECT)ARG0(arg);
      vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
      a0 = LMTOS((LM)a);
      b0 = LMTOS((LM)b);
      ord = ecm_count_order_gfp(p0,a0,b0);
      UTOZ(ord,*rp);
      break;
    case FF_GF2N:
      getmod_gf2n(&d);
      if ( degup2(d) > 10 )
        error("ecm_count_order : ground field too large");
      ec = (VECT)ARG0(arg);
      vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
      ord = ecm_count_order_gf2n(d,(GF2N)a,(GF2N)b);
      UTOZ(ord,*rp);
      break;
    default:
      error("ecm_count_order : current_ff is not set");
  }
}

void Pecm_set_addcounter(NODE arg,Z *rp)
{
  if ( arg )
    ecm_addcounter = ZTOS((Q)ARG0(arg));
  UTOZ(ecm_addcounter,*rp);
}

void Pecm_compute_all_key_homo_ff(NODE arg,VECT *rp)
{
  unsigned int *ka;
  int len,i;
  VECT *pa;
  VECT r,v;
  LIST *vb;
  USINT *b;

  v = (VECT)ARG0(arg);
  len = v->len;
  vb = (LIST *)v->body;
  pa = (VECT *)ALLOCA(len*sizeof(VECT));
  ka = (unsigned int *)ALLOCA(len*sizeof(unsigned int));
  for ( i = 0; i < len; i++ )
    pa[i] = (VECT)BDY(NEXT(BDY(vb[i])));
  switch ( current_ff ) {
    case FF_GFP:
      compute_all_key_homo_gfp(pa,len,ka); break;
    case FF_GF2N:
      compute_all_key_homo_gf2n(pa,len,ka); break;
    default:
      error("ecm_compute_all_key_homo_ff : current_ff is not set");
  }
  MKVECT(r,len); *rp = r;
  b = (USINT *)r->body;
  for ( i = 0; i < len; i++ )
    MKUSINT(b[i],ka[i]);
}

void Psort_ktarray(NODE arg,LIST *rp)
{
  sort_ktarray((VECT)ARG0(arg),(VECT)ARG1(arg),rp);
}

void Pecm_add_ff(NODE arg,VECT *rp)
{
  ecm_add_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
}

void Pecm_sub_ff(NODE arg,VECT *rp)
{
  ecm_sub_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
}

void Pecm_chsgn_ff(NODE arg,VECT *rp)
{
  ecm_chsgn_ff(ARG0(arg),rp);
}

void Pnextvect1(NODE arg,Z *rp)
{
  int index;

  index = nextvect1(ARG0(arg),ARG1(arg));
  STOZ(index,*rp);
}

/* XXX at least n < 32 must hold. What is the strict restriction for n ? */

void Pseparate_vect(NODE arg,LIST *rp)
{
  VECT v;
  int n,i;
  Z *b;
  double *w;
  unsigned int s;
  NODE ns,nc,t,t1;
  Z iq;
  LIST ls,lc;

  v = (VECT)ARG0(arg);
  n = v->len; b = (Z *)v->body;
  w = (double *)ALLOCA(n*sizeof(double));
  for ( i = 0; i < n; i++ )
    w[i] = (double)ZTOS(b[i]);
  s = separate_vect(w,n);
  ns = nc = 0;
  for ( i = n-1; i >= 0; i-- )
    if ( s & (1<<i) ) {
      STOZ(i,iq); MKNODE(t,iq,ns); ns = t;
    } else {
      STOZ(i,iq); MKNODE(t,iq,nc); nc = t;
    }
  MKLIST(ls,ns); MKLIST(lc,nc);
  MKNODE(t,lc,0); MKNODE(t1,ls,t);
  MKLIST(*rp,t1);
}

void Pecm_find_match(NODE arg,LIST *rp)
{
  VECT g,b;
  int ng,nb,i;
  USINT *p;
  unsigned int *kg,*kb;

  g = (VECT)ARG0(arg); ng = g->len;
  kg = (unsigned int *)ALLOCA(ng*sizeof(unsigned int));
  for ( i = 0, p = (USINT *)g->body; i < ng; i++ )
    kg[i] = p[i]?BDY(p[i]):0;
  b = (VECT)ARG1(arg); nb = b->len;
  kb = (unsigned int *)ALLOCA(nb*sizeof(unsigned int));
  for ( i = 0, p = (USINT *)b->body; i < nb; i++ )
    kb[i] = p[i]?BDY(p[i]):0;
  ecm_find_match(kg,ng,kb,nb,rp);
}

void ecm_add_ff(VECT p1,VECT p2,VECT ec,VECT *pr)
{
  if ( !p1 )
    *pr = p2;
  else if ( !p2 )
    *pr = p1;
  else {
    switch ( current_ff ) {
      case FF_GFP:
        ecm_add_gfp(p1,p2,ec,pr); break;
      case FF_GF2N:
        ecm_add_gf2n(p1,p2,ec,pr); break;
      default:
        error("ecm_add_ff : current_ff is not set");
    }
  }
}

/* ec = [AX,BC]  */

void ecm_add_gf2n(VECT p1,VECT p2,VECT ec,VECT *rp)
{
  GF2N ax,bc,a0,a1,a2,b0,b1,b2;
  GF2N a2b0,a0b2,a2b1,a1b2,a02,a04,a22,a24,a0a2,a0a22,a1a2;
  GF2N t,s,u,r0,r1,r00,r01,r02,r002,r003,r02q;
  VECT r;
  GF2N *vb,*rb;

  ecm_addcounter++;
  /* addition with O  */
  if ( !p1 ) {
    *rp = p2;
    return;
  }
  if ( !p2 ) {
    *rp = p1;
    return;
  }
  vb = (GF2N *)BDY(ec); ax = vb[0]; bc = vb[1];
  vb = (GF2N *)BDY(p1); a0 = vb[0]; a1 = vb[1]; a2 = vb[2];
  vb = (GF2N *)BDY(p2); b0 = vb[0]; b1 = vb[1]; b2 = vb[2];

  mulgf2n(a2,b0,&a2b0); mulgf2n(a0,b2,&a0b2);
  if ( !cmpgf2n(a2b0,a0b2) ) {
    mulgf2n(a2,b1,&a2b1);  
    mulgf2n(a1,b2,&a1b2);  
    if ( !cmpgf2n(a2b1,a1b2) ) {
      if ( !a0 )
        *rp = 0;
      else {
        squaregf2n(a0,&a02); squaregf2n(a02,&a04);
        squaregf2n(a2,&a22); squaregf2n(a22,&a24);
        mulgf2n(a0,a2,&a0a2); squaregf2n(a0a2,&a0a22);
        mulgf2n(bc,a24,&t); addgf2n(a04,t,&r0);
        mulgf2n(a04,a0a2,&t); mulgf2n(a1,a2,&a1a2);
        addgf2n(a02,a1a2,&s); addgf2n(s,a0a2,&u);
        mulgf2n(u,r0,&s); addgf2n(t,s,&r1);
  
        MKVECT(r,3); rb = (GF2N *)r->body;
        mulgf2n(r0,a0a2,&rb[0]); rb[1] = r1; mulgf2n(a0a22,a0a2,&rb[2]);
        *rp = r;
      }
    } else
      *rp = 0;
  } else {
    mulgf2n(a1,b2,&a1b2); addgf2n(a0b2,a2b0,&r00);
    mulgf2n(a2,b1,&t); addgf2n(a1b2,t,&r01); mulgf2n(a2,b2,&r02);
    squaregf2n(r00,&r002); mulgf2n(r002,r00,&r003);

    addgf2n(r00,r01,&t); mulgf2n(t,r01,&s); mulgf2n(s,r02,&t);
    if ( ax ) {
      mulgf2n(r02,ax,&r02q);
      addgf2n(t,r003,&s); mulgf2n(r02q,r002,&t); addgf2n(s,t,&r0);
    } else
      addgf2n(t,r003,&r0);

    mulgf2n(a0b2,r002,&t); addgf2n(t,r0,&s); mulgf2n(r01,s,&t);
    mulgf2n(r002,a1b2,&s); addgf2n(r0,s,&u); mulgf2n(r00,u,&s);
    addgf2n(t,s,&r1);
  
    MKVECT(r,3); rb = (GF2N *)r->body;
    mulgf2n(r0,r00,&rb[0]); rb[1] = r1; mulgf2n(r003,r02,&rb[2]);
    *rp = r;
  }
}

extern LM THREE_LM,FOUR_LM,EIGHT_LM;

/* 0 < p < 2^16, 0 <= a,b < p */

unsigned int ecm_count_order_gfp(unsigned int p,unsigned int a,unsigned int b)
{
  unsigned int x,rhs,ord,t;

  for ( x = 0, ord = 1; x < p; x++ ) {
    DMAR(x,x,a,p,t) /* t = x^2+a mod p */
    DMAR(t,x,b,p,rhs) /* rhs = x*(x^2+a)+b mod p */
    if ( !rhs )  
      ord++;
    else if ( small_jacobi(rhs,p)==1 )
      ord+=2;
  }
  return ord;
}

unsigned int ecm_count_order_gf2n(UP2 d,GF2N a,GF2N b)
{
  error("ecm_count_order_gf2n : not implemented yet");
  /* NOTREACHED */
  return 0;
}

/* ec = [AX,BC]  */

void ecm_add_gfp(VECT p1,VECT p2,VECT ec,VECT *pr)
{
  LM aa,bb,x1,y1,z1,x2,y2,z2,x1z2,v1,y1z2,u1,u2,v2,v3,z1z2;
  LM v2x1z2,a1,x3,y3,z3,w1,s1,s2,s3,s1y1,b1,h1;
  LM t,s,u;
  LM *vb;
  VECT r;

  ecm_addcounter++;
  /* addition with O  */
  if( !p1 ) {
    *pr = p2;
    return;
  }
  if( !p2 ) {
    *pr = p1;
    return;
  }

  /*  set parameters      */

/*  aa = ec[0]; bb = ec[1]; */
  vb = (LM *)BDY(ec); aa = vb[0]; bb = vb[1];

/*  x1 = p1[0]; y1 = p1[1]; z1 = p1[2]; */
  vb = (LM *)BDY(p1); x1 = vb[0]; y1 = vb[1]; z1 = vb[2];

/*  x2 = p2[0]; y2 = p2[1]; z2 = p2[2]; */
  vb = (LM *)BDY(p2); x2 = vb[0]; y2 = vb[1]; z2 = vb[2];

  /* addition */

/*  x1z2 = (x1*z2) %p; */
  mullm(x1,z2,&x1z2);

/*  v1 = (x2*z1-x1z2) %p; */
  lm_lazy = 1;
  mullm(x2,z1,&t); sublm(t,x1z2,&s);
  lm_lazy = 0; simplm(s,&v1);

/*  y1z2 = (y1*z2) %p; */
  mullm(y1,z2,&y1z2);

/*  u1 = (y2*z1-y1z2) %p; */
  lm_lazy = 1;
  mullm(y2,z1,&t); sublm(t,y1z2,&s);
  lm_lazy = 0; simplm(s,&u1);

  if( v1 != 0 ) {
/*    u2 = (u1*u1) %p; */
    mullm(u1,u1,&u2);

/*    v2 = (v1*v1) %p; */
    mullm(v1,v1,&v2);

/*    v3 = (v1*v2) %p; */
    mullm(v1,v2,&v3);

/*    z1z2 = (z1*z2) %p; */
    mullm(z1,z2,&z1z2);

/*    v2x1z2 = (v2*x1z2) %p; */
    mullm(v2,x1z2,&v2x1z2);

/*    a1 = (u2*z1z2-v3-2*v2x1z2) %p; */
    lm_lazy = 1;
    mullm(u2,z1z2,&t); addlm(v2x1z2,v2x1z2,&s);
    addlm(v3,s,&u); sublm(t,u,&s);
    lm_lazy = 0; simplm(s,&a1);

/*    x3 = ( v1 * a1 ) %p; */
    mullm(v1,a1,&x3);

/*    y3 = ( u1 * ( v2x1z2 - a1 ) - v3 * y1z2 ) %p; */
    lm_lazy = 1;
    sublm(v2x1z2,a1,&t); mullm(u1,t,&s); mullm(v3,y1z2,&u); sublm(s,u,&t);
    lm_lazy = 0; simplm(t,&y3);

/*    z3 = ( v3 * z1z2 ) %p; */
    mullm(v3,z1z2,&z3);
  } else if( u1 == 0 ) {
/*    w1 = (aa*z1*z1+3*x1*x1) %p; */
    lm_lazy = 1;
    mullm(z1,z1,&t); mullm(aa,t,&s);
    mullm(x1,x1,&t); mullm(THREE_LM,t,&u); addlm(s,u,&t);
    lm_lazy = 0; simplm(t,&w1);

/*    s1 = (y1*z1) %p; */
    mullm(y1,z1,&s1);

/*    s2 = (s1*s1) %p; */
    mullm(s1,s1,&s2);

/*    s3 = (s1*s2) %p; */
    mullm(s1,s2,&s3);

/*    s1y1 = (s1*y1) %p; */
    mullm(s1,y1,&s1y1);

/*    b1 = (s1y1*x1) %p; */
    mullm(s1y1,x1,&b1);

/*    h1 = (w1*w1-8*b1) %p; */
    lm_lazy = 1;
    mullm(w1,w1,&t); mullm(EIGHT_LM,b1,&s); sublm(t,s,&u);
    lm_lazy = 0; simplm(u,&h1);

/*    x3 = ( 2 * h1 * s1 ) %p; */
    lm_lazy = 1;
    mullm(h1,s1,&t); addlm(t,t,&s);
    lm_lazy = 0; simplm(s,&x3);

/*    y3 = ( w1 * ( 4 * b1 - h1 ) - 8 * s1y1 * s1y1 ) %p; */
    lm_lazy = 1;
    mullm(FOUR_LM,b1,&t); sublm(t,h1,&s); mullm(w1,s,&u);
    mullm(s1y1,s1y1,&t); mullm(EIGHT_LM,t,&s); sublm(u,s,&t);
    lm_lazy = 0; simplm(t,&y3);

/*    z3 = ( 8 * s3 ) %p; */
    mullm(EIGHT_LM,s3,&z3);
  } else {
    *pr = 0;
    return;
  }
  if ( !z3 )
    *pr = 0;
  else {
    MKVECT(r,3); *pr = r;
    vb = (LM *)BDY(r); vb[0] = x3; vb[1] = y3; vb[2] = z3;
  }
}

void ecm_chsgn_ff(VECT p,VECT *pr)
{
  Obj x,y,z;
  LM tl;
  GF2N tg;
  Obj *vb;
  VECT r;

  if( !p ) {
    *pr = 0;
    return;
  }

  /*  x = p[0]; y = p[1]; z = p[2]; */
  vb = (Obj *)BDY(p); x = vb[0]; y = vb[1]; z = vb[2];
  switch ( current_ff ) {
    case FF_GFP:
      if ( !y ) 
        *pr = p;
      else {
        chsgnlm((LM)y,&tl);
        MKVECT(r,3); *pr = r;
        vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tl; vb[2] = z;
      }
      break;
    case FF_GF2N:
      addgf2n((GF2N)x,(GF2N)y,&tg);
      MKVECT(r,3); *pr = r;
      vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tg; vb[2] = z;
      break;
    default:
      error("ecm_chsgn_ff : current_ff is not set");
  }
}

void ecm_sub_ff(VECT p1,VECT p2,VECT ec,VECT *pr)
{
  VECT mp2;

  ecm_chsgn_ff(p2,&mp2);
  ecm_add_ff(p1,mp2,ec,pr);
}

/* tplist = [[t,p],...]; t:interger, p=[p0,p1]:point (vector)  */

int comp_kip(struct oKeyIndexPair *a,struct oKeyIndexPair *b)
{
  unsigned int ka,kb;

  ka = a->key; kb = b->key;
  if ( ka > kb )
    return 1;
  else if ( ka < kb )
    return -1;
  else
    return 0;
}

#define EC_GET_XZ(p,x,z) \
  if ( !(p) ) {\
    (x)=0; (z)=(LM)ONE;\
  } else { \
    LM *vb;\
    vb = (LM *)BDY((VECT)(p));\
    (x) = vb[0]; (z) = vb[2];\
  }

#define EC_GET_XZ_GF2N(p,x,z) \
  if ( !(p) ) {\
    (x)=0; (z)=(GF2N)ONE;\
  } else { \
    GF2N *vb;\
    vb = (GF2N *)BDY((VECT)(p));\
    (x) = vb[0]; (z) = vb[2];\
  }

void compute_all_key_homo_gfp(VECT *pa,int len,unsigned int *ka)
{
  LM *b,*x,*z;
  int i;
  LM t,s,m;

  b = (LM *)ALLOCA((len+1)*sizeof(LM));
  x = (LM *)ALLOCA(len*sizeof(LM));
  z = (LM *)ALLOCA(len*sizeof(LM));
  b[0] = ONELM;
  for ( i = 1; i <= len; i++ ) {
    EC_GET_XZ(pa[i-1],x[i-1],z[i-1]);
    mullm(b[i-1],z[i-1],&b[i]);
  }
  /* b[0] = 1 */
  divlm(b[0],b[len],&m);
  for ( i = len-1; i >= 0; i-- ) {
    mullm(m,b[i],&s); mullm(s,x[i],&t); s = t;
    ka[i] = LMTOS(s); ka[i] |= 0x80000000;
    mullm(m,z[i],&s); m = s;
  }
}

void compute_all_key_homo_gf2n(VECT *pa,int len,unsigned int *ka)
{
  GF2N *b,*x,*z;
  int i;
  GF2N t,s,m;

  b = (GF2N *)ALLOCA((len+1)*sizeof(Q));
  x = (GF2N *)ALLOCA(len*sizeof(Q));
  z = (GF2N *)ALLOCA(len*sizeof(Q));
  MKGF2N(ONEUP2,b[0]);
  for ( i = 1; i <= len; i++ ) {
    EC_GET_XZ_GF2N(pa[i-1],x[i-1],z[i-1]);
    mulgf2n(b[i-1],z[i-1],&b[i]);
  }
  invgf2n(b[len],&m);
  for ( i = len-1; i >= 0; i-- ) {
    mulgf2n(m,b[i],&s); mulgf2n(s,x[i],&t); s = t;
    ka[i] = s ? s->body->b[0] : 0; ka[i] |= 0x80000000;
    mulgf2n(m,z[i],&s); m = s;
  }
}

unsigned int separate_vect(double *v,int n)
{
  unsigned int max = 1<<n;
  unsigned int i,j,i0;
  double all,a,total,m;

  for ( i = 0, all = 1; i < (unsigned int)n; i++ )
    all *= v[i];

  for ( i = 0, m = 0; i < max; i++ ) {
    for ( a = 1, j = 0; j < (unsigned int)n; j++ )
      if ( i & (1<<j) )
        a *= v[j];
    total = a+(all/a)*2;
    if ( !m || total < m ) {
      m = total;
      i0 = i;
    }
  }
  return i0;
}

void ecm_find_match(unsigned int *g,int ng,unsigned int *b,int nb,LIST *r)
{
  int i,j;
  Z iq,jq;
  NODE n0,n1,c0,c;
  LIST l;

  for ( i = 0, c0 = 0; i < ng; i++ ) {
    j = find_match(g[i],b,nb);
    if ( j >= 0 ) {
      STOZ(i,iq); STOZ(j,jq);
      MKNODE(n1,jq,0); MKNODE(n0,iq,n1); MKLIST(l,n0);
      NEXTNODE(c0,c);
      BDY(c) = (pointer)l;
    }
  }
  if ( c0 )
    NEXT(c) = 0;
  MKLIST(*r,c0);
}

int find_match(unsigned int k,unsigned int *key,int n)
{
  int s,e,m;

  for ( s = 0, e = n; (e-s) > 1; ) {
    m = (s+e)/2;
    if ( k==key[m] )
      return m;
    else if ( k > key[m] )
      s = m;
    else
      e = m;
  }
  if ( k == key[s] )
    return s;
  else
    return -1;
}

int nextvect1(VECT vect,VECT bound)
{
  int size,i,a;
  Z *vb,*bb;

  size = vect->len;
  vb = (Z *)vect->body;
  bb = (Z *)bound->body;
  for ( i = size-1; i >= 0; i-- )
    if ( (a=ZTOS(vb[i])) < ZTOS(bb[i]) ) {
      a++; STOZ(a,vb[i]);
      break;
    } else
      vb[i] = 0;
  return i;
}

void sort_ktarray(VECT karray,VECT tarray,LIST *rp)
{
  NODE r,r1;
  int i,i0,k,len,same,tsame;
  struct oKeyIndexPair *kip;
  VECT key,value,v;
  Q *tb,*samebuf;
  USINT *kb;
  Obj *svb;
  USINT *skb;

  len = karray->len;
  kb = (USINT *)karray->body;

  kip = (struct oKeyIndexPair *)ALLOCA(len*sizeof(struct oKeyIndexPair));
  for ( i = 0; i < len; i++ ) {
    kip[i].key = BDY(kb[i]); kip[i].index = i;
  }
  qsort((void *)kip,len,sizeof(struct oKeyIndexPair),
    (int (*)(const void *,const void *))comp_kip);

  for ( same = tsame = i = i0 = 0, k = 1; i < len; i++, tsame++ )
    if ( kip[i0].key != kip[i].key ) {
      i0 = i; k++;
      same = MAX(tsame,same);
      tsame = 0;
    }
  same = MAX(tsame,same);
  samebuf = (Q *)ALLOCA(same*sizeof(Q));

  MKVECT(key,k); skb = (USINT *)BDY(key);
  MKVECT(value,k); svb = (Obj *)BDY(value);

  tb = (Q *)tarray->body;
  for ( same = i = i0 = k = 0; i <= len; i++ ) {
    if ( i == len || kip[i0].key != kip[i].key ) {
      skb[k] = kb[kip[i0].index];
      if ( same > 1 ) {
        MKVECT(v,same);
        bcopy((char *)samebuf,(char *)v->body,same*sizeof(Q));
        svb[k] = (Obj)v;
      } else
        svb[k] = (Obj)samebuf[0];
      i0 = i;
      k++;
      same = 0;
      if ( i == len )
        break;
    }
    samebuf[same++] = tb[kip[i].index];
  }
  MKNODE(r1,value,0); MKNODE(r,key,r1); MKLIST(*rp,r);
}