/* cddcore.c:  Core Procedures for cddlib
   written by Komei Fukuda, fukuda@ifor.math.ethz.ch
   Version 0.94, Aug. 4, 2005
*/

/* cddlib : C-library of the double description method for
   computing all vertices and extreme rays of the polyhedron 
   P= {x :  b - A x >= 0}.  
   Please read COPYING (GNU General Public Licence) and
   the manual cddlibman.tex for detail.
*/

#include "setoper.h"  /* set operation library header (Ver. June 1, 2000 or later) */
#include "cdd.h"
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
#include <string.h>

void dd_CheckAdjacency(dd_ConePtr cone,
    dd_RayPtr *RP1, dd_RayPtr *RP2, dd_boolean *adjacent)
{
  dd_RayPtr TempRay;
  dd_boolean localdebug=dd_FALSE;
  static dd_rowset Face, Face1;
  static dd_rowrange last_m=0;
  
  if (last_m!=cone->m) {
    if (last_m>0){
      set_free(Face); set_free(Face1);
    }
    set_initialize(&Face, cone->m); 
    set_initialize(&Face1, cone->m); 
    last_m=cone->m;
  }

  if (dd_debug) localdebug=dd_TRUE;
  *adjacent = dd_TRUE;
  set_int(Face1, (*RP1)->ZeroSet, (*RP2)->ZeroSet);
  set_int(Face, Face1, cone->AddedHalfspaces);
  if (set_card(Face)< cone->d - 2) {
    *adjacent = dd_FALSE;
    if (localdebug) {
      fprintf(stderr,"non adjacent: set_card(face) %ld < %ld = cone->d.\n",
        set_card(Face),cone->d);
    }
    return;
  }
  else if (cone->parent->NondegAssumed) {
  	*adjacent = dd_TRUE;
  	return;
  }
  TempRay = cone->FirstRay;
  while (TempRay != NULL && *adjacent) {
    if (TempRay != *RP1 && TempRay != *RP2) {
    	set_int(Face1, TempRay->ZeroSet, cone->AddedHalfspaces);
      	if (set_subset(Face, Face1)) *adjacent = dd_FALSE;
    }
    TempRay = TempRay->Next;
  }
}

void dd_Eliminate(dd_ConePtr cone, dd_RayPtr*Ptr)
{
  /*eliminate the record pointed by Ptr^.Next*/
  dd_RayPtr TempPtr;
  dd_colrange j;

  TempPtr = (*Ptr)->Next;
  (*Ptr)->Next = (*Ptr)->Next->Next;
  if (TempPtr == cone->FirstRay)   /*Update the first pointer*/
    cone->FirstRay = (*Ptr)->Next;
  if (TempPtr == cone->LastRay)   /*Update the last pointer*/
    cone->LastRay = *Ptr;

  /* Added, Marc Pfetsch 010219 */
  for (j=0;j < cone->d;j++)
dd_clear(TempPtr->Ray[j]);
  dd_clear(TempPtr->ARay);

  free(TempPtr->Ray);          /* free the ray vector memory */
  set_free(TempPtr->ZeroSet);  /* free the ZeroSet memory */
  free(TempPtr);   /* free the dd_Ray structure memory */
  cone->RayCount--; 
}

void dd_SetInequalitySets(dd_ConePtr cone)
{
  dd_rowrange i;
  
  set_emptyset(cone->GroundSet);
  set_emptyset(cone->EqualitySet);
  set_emptyset(cone->NonequalitySet);  
  for (i = 1; i <= (cone->parent->m); i++){
    set_addelem(cone->GroundSet, i);
    if (cone->parent->EqualityIndex[i]==1) set_addelem(cone->EqualitySet,i);
    if (cone->parent->EqualityIndex[i]==-1) set_addelem(cone->NonequalitySet,i);
  }
}


void dd_AValue(mytype *val, dd_colrange d_size, dd_Amatrix A, mytype *p, dd_rowrange i)
{
  /*return the ith component of the vector  A x p */
  dd_colrange j;
  mytype x;

  dd_init(x); 
  dd_set(*val,dd_purezero);
 /* Changed by Marc Pfetsch 010219 */

  for (j = 0; j < d_size; j++){
    dd_mul(x,A[i - 1][j], p[j]);
    dd_add(*val, *val, x);
  }
  dd_clear(x);
}

void dd_StoreRay1(dd_ConePtr cone, mytype *p, dd_boolean *feasible)
{  /* Original ray storing routine when RelaxedEnumeration is dd_FALSE */
  dd_rowrange i,k,fii=cone->m+1;
  dd_colrange j;
  mytype temp;
  dd_RayPtr RR;
  dd_boolean localdebug=dd_debug;

  dd_init(temp);
  RR=cone->LastRay;
  *feasible = dd_TRUE;
  set_initialize(&(RR->ZeroSet),cone->m);
  for (j = 0; j < cone->d; j++){
    dd_set(RR->Ray[j],p[j]);
  }
  for (i = 1; i <= cone->m; i++) {
    k=cone->OrderVector[i];
    dd_AValue(&temp, cone->d, cone->A, p, k);
    if (localdebug) {
      fprintf(stderr,"dd_StoreRay1: dd_AValue at row %ld =",k);
      dd_WriteNumber(stderr, temp);
      fprintf(stderr,"\n");
    }
    if (dd_EqualToZero(temp)) {
      set_addelem(RR->ZeroSet, k);
      if (localdebug) {
        fprintf(stderr,"recognized zero!\n");
      }
    }
    if (dd_Negative(temp)){
      if (localdebug) {
        fprintf(stderr,"recognized negative!\n");
      }
      *feasible = dd_FALSE;
      if (fii>cone->m) fii=i;  /* the first violating inequality index */
      if (localdebug) {
        fprintf(stderr,"this ray is not feasible, neg comp = %ld\n", fii);
        dd_WriteNumber(stderr, temp);  fprintf(stderr,"\n");
      }
    }
  }
  RR->FirstInfeasIndex=fii;
  RR->feasible = *feasible;
  dd_clear(temp);
}

void dd_StoreRay2(dd_ConePtr cone, mytype *p, 
    dd_boolean *feasible, dd_boolean *weaklyfeasible)
   /* Ray storing routine when RelaxedEnumeration is dd_TRUE.
       weaklyfeasible is true iff it is feasible with
       the strict_inequality conditions deleted. */
{
  dd_RayPtr RR;
  dd_rowrange i,k,fii=cone->m+1;
  dd_colrange j;
  mytype temp;
  dd_boolean localdebug=dd_debug;

  dd_init(temp);
  RR=cone->LastRay;
  if (dd_debug) localdebug=dd_TRUE;
  *feasible = dd_TRUE;
  *weaklyfeasible = dd_TRUE;
  set_initialize(&(RR->ZeroSet),cone->m);
  for (j = 0; j < cone->d; j++){
    dd_set(RR->Ray[j],p[j]);
  }
  for (i = 1; i <= cone->m; i++) {
    k=cone->OrderVector[i];
    dd_AValue(&temp, cone->d, cone->A, p, k);
    if (dd_EqualToZero(temp)){
      set_addelem(RR->ZeroSet, k);
      if (cone->parent->EqualityIndex[k]==-1) 
        *feasible=dd_FALSE;  /* strict inequality required */
    }
/*    if (temp < -zero){ */
    if (dd_Negative(temp)){
      *feasible = dd_FALSE;
      if (fii>cone->m && cone->parent->EqualityIndex[k]>=0) {
        fii=i;  /* the first violating inequality index */
        *weaklyfeasible=dd_FALSE;
      }
    }
  }
  RR->FirstInfeasIndex=fii;
  RR->feasible = *feasible;
  dd_clear(temp);
}


void dd_AddRay(dd_ConePtr cone, mytype *p)
{  
  dd_boolean feasible, weaklyfeasible;
  dd_colrange j;

  if (cone->FirstRay == NULL) {
    cone->FirstRay = (dd_RayPtr) malloc(sizeof(dd_RayType));
    cone->FirstRay->Ray = (mytype *) calloc(cone->d, sizeof(mytype));
    for (j=0; j<cone->d; j++) dd_init(cone->FirstRay->Ray[j]);
    dd_init(cone->FirstRay->ARay);
    if (dd_debug)
      fprintf(stderr,"Create the first ray pointer\n");
    cone->LastRay = cone->FirstRay;
    cone->ArtificialRay->Next = cone->FirstRay;
  } else {
    cone->LastRay->Next = (dd_RayPtr) malloc(sizeof(dd_RayType));
    cone->LastRay->Next->Ray = (mytype *) calloc(cone->d, sizeof(mytype));
    for (j=0; j<cone->d; j++) dd_init(cone->LastRay->Next->Ray[j]);
    dd_init(cone->LastRay->Next->ARay);
    if (dd_debug) fprintf(stderr,"Create a new ray pointer\n");
    cone->LastRay = cone->LastRay->Next;
  }
  cone->LastRay->Next = NULL;
  cone->RayCount++;
  cone->TotalRayCount++;
  if (dd_debug) {
    if (cone->TotalRayCount % 100 == 0) {
      fprintf(stderr,"*Rays (Total, Currently Active, Feasible) =%8ld%8ld%8ld\n",
	 cone->TotalRayCount, cone->RayCount, cone->FeasibleRayCount);
    }
  }
  if (cone->parent->RelaxedEnumeration){
    dd_StoreRay2(cone, p, &feasible, &weaklyfeasible);
    if (weaklyfeasible) (cone->WeaklyFeasibleRayCount)++;
  } else {
    dd_StoreRay1(cone, p, &feasible);
    if (feasible) (cone->WeaklyFeasibleRayCount)++;
    /* weaklyfeasible is equiv. to feasible in this case. */
  }
  if (!feasible) return;
  else {
    (cone->FeasibleRayCount)++;
  }
}

void dd_AddArtificialRay(dd_ConePtr cone)
{  
  dd_Arow zerovector;
  dd_colrange j,d1;
  dd_boolean feasible;

  if (cone->d<=0) d1=1; else d1=cone->d;
  dd_InitializeArow(d1, &zerovector);
  if (cone->ArtificialRay != NULL) {
    fprintf(stderr,"Warning !!!  FirstRay in not nil.  Illegal Call\n");
    free(zerovector); /* 086 */
    return;
  }
  cone->ArtificialRay = (dd_RayPtr) malloc(sizeof(dd_RayType));
  cone->ArtificialRay->Ray = (mytype *) calloc(d1, sizeof(mytype));
  for (j=0; j<d1; j++) dd_init(cone->ArtificialRay->Ray[j]);
  dd_init(cone->ArtificialRay->ARay);

  if (dd_debug) fprintf(stderr,"Create the artificial ray pointer\n");

  cone->LastRay=cone->ArtificialRay;
  dd_StoreRay1(cone, zerovector, &feasible);  
    /* This stores a vector to the record pointed by cone->LastRay */
  cone->ArtificialRay->Next = NULL;
  for (j = 0; j < d1; j++){
    dd_clear(zerovector[j]);
  }
  free(zerovector); /* 086 */
}

void dd_ConditionalAddEdge(dd_ConePtr cone, 
    dd_RayPtr Ray1, dd_RayPtr Ray2, dd_RayPtr ValidFirstRay)
{
  long it,it_row,fii1,fii2,fmin,fmax;
  dd_boolean adjacent,lastchance;
  dd_RayPtr TempRay,Rmin,Rmax;
  dd_AdjacencyType *NewEdge;
  dd_boolean localdebug=dd_FALSE;
  dd_rowset ZSmin, ZSmax;
  static dd_rowset Face, Face1;
  static dd_rowrange last_m=0;
  
  if (last_m!=cone->m) {
    if (last_m>0){
      set_free(Face); set_free(Face1);
    }
    set_initialize(&Face, cone->m);
    set_initialize(&Face1, cone->m);
    last_m=cone->m;
  }
  
  fii1=Ray1->FirstInfeasIndex;
  fii2=Ray2->FirstInfeasIndex;
  if (fii1<fii2){
    fmin=fii1; fmax=fii2;
    Rmin=Ray1;
    Rmax=Ray2;
  }
  else{
    fmin=fii2; fmax=fii1;
    Rmin=Ray2;
    Rmax=Ray1;
  }
  ZSmin = Rmin->ZeroSet;
  ZSmax = Rmax->ZeroSet;
  if (localdebug) {
    fprintf(stderr,"dd_ConditionalAddEdge: FMIN = %ld (row%ld)   FMAX=%ld\n",
      fmin, cone->OrderVector[fmin], fmax);
  }
  if (fmin==fmax){
    if (localdebug) fprintf(stderr,"dd_ConditionalAddEdge: equal FII value-> No edge added\n");
  }
  else if (set_member(cone->OrderVector[fmin],ZSmax)){
    if (localdebug) fprintf(stderr,"dd_ConditionalAddEdge: No strong separation -> No edge added\n");
  }
  else {  /* the pair will be separated at the iteration fmin */
    lastchance=dd_TRUE;
    /* flag to check it will be the last chance to store the edge candidate */
    set_int(Face1, ZSmax, ZSmin);
    (cone->count_int)++;
    if (localdebug){
      fprintf(stderr,"Face: ");
      for (it=1; it<=cone->m; it++) {
        it_row=cone->OrderVector[it];
        if (set_member(it_row, Face1)) fprintf(stderr,"%ld ",it_row);
      }
      fprintf(stderr,"\n");
    }
    for (it=cone->Iteration+1; it < fmin && lastchance; it++){
      it_row=cone->OrderVector[it];
      if (cone->parent->EqualityIndex[it_row]>=0 && set_member(it_row, Face1)){
        lastchance=dd_FALSE;
        (cone->count_int_bad)++;
        if (localdebug){
          fprintf(stderr,"There will be another chance iteration %ld (row %ld) to store the pair\n", it, it_row);
        }
      }
    }
    if (lastchance){
      adjacent = dd_TRUE;
      (cone->count_int_good)++;
      /* adjacent checking */
      set_int(Face, Face1, cone->AddedHalfspaces);
      if (localdebug){
        fprintf(stderr,"Check adjacency\n");
        fprintf(stderr,"AddedHalfspaces: "); set_fwrite(stderr,cone->AddedHalfspaces);
        fprintf(stderr,"Face: ");
        for (it=1; it<=cone->m; it++) {
          it_row=cone->OrderVector[it];
          if (set_member(it_row, Face)) fprintf(stderr,"%ld ",it_row);
        }
        fprintf(stderr,"\n");
      }
      if (set_card(Face)< cone->d - 2) {
        adjacent = dd_FALSE;
      }
      else if (cone->parent->NondegAssumed) {
    	adjacent = dd_TRUE;
      }
      else{
        TempRay = ValidFirstRay;  /* the first ray for adjacency checking */
        while (TempRay != NULL && adjacent) {
          if (TempRay != Ray1 && TempRay != Ray2) {
            set_int(Face1, TempRay->ZeroSet, cone->AddedHalfspaces);
            if (set_subset(Face, Face1)) {
              if (localdebug) set_fwrite(stderr,Face1);
              adjacent = dd_FALSE;
            }
          }
          TempRay = TempRay->Next;
        }
      }
      if (adjacent){
        if (localdebug) fprintf(stderr,"The pair is adjacent and the pair must be stored for iteration %ld (row%ld)\n",
          fmin, cone->OrderVector[fmin]);
        NewEdge=(dd_AdjacencyPtr) malloc(sizeof *NewEdge);
        NewEdge->Ray1=Rmax;  /* save the one remains in iteration fmin in the first */
        NewEdge->Ray2=Rmin;  /* save the one deleted in iteration fmin in the second */
        NewEdge->Next=NULL;
        (cone->EdgeCount)++; 
        (cone->TotalEdgeCount)++;
        if (cone->Edges[fmin]==NULL){
          cone->Edges[fmin]=NewEdge;
          if (localdebug) fprintf(stderr,"Create a new edge list of %ld\n", fmin);
        }else{
          NewEdge->Next=cone->Edges[fmin];
          cone->Edges[fmin]=NewEdge;
        }
      }
    }
  }
}

void dd_CreateInitialEdges(dd_ConePtr cone)
{
  dd_RayPtr Ptr1, Ptr2;
  dd_rowrange fii1,fii2;
  long count=0;
  dd_boolean adj,localdebug=dd_FALSE;

  cone->Iteration=cone->d;  /* CHECK */
  if (cone->FirstRay ==NULL || cone->LastRay==NULL){
    /* fprintf(stderr,"Warning: dd_ CreateInitialEdges called with NULL pointer(s)\n"); */
    goto _L99;
  }
  Ptr1=cone->FirstRay;
  while(Ptr1!=cone->LastRay && Ptr1!=NULL){
    fii1=Ptr1->FirstInfeasIndex;
    Ptr2=Ptr1->Next;
    while(Ptr2!=NULL){
      fii2=Ptr2->FirstInfeasIndex;
      count++;
      if (localdebug) fprintf(stderr,"dd_ CreateInitialEdges: edge %ld \n",count);
      dd_CheckAdjacency(cone, &Ptr1, &Ptr2, &adj);
      if (fii1!=fii2 && adj) 
        dd_ConditionalAddEdge(cone, Ptr1, Ptr2, cone->FirstRay);
      Ptr2=Ptr2->Next;
    }
    Ptr1=Ptr1->Next;
  }
_L99:;  
}


void dd_UpdateEdges(dd_ConePtr cone, dd_RayPtr RRbegin, dd_RayPtr RRend)
/* This procedure must be called after the ray list is sorted
   by dd_EvaluateARay2 so that FirstInfeasIndex's are monotonically
   increasing.
*/
{
  dd_RayPtr Ptr1, Ptr2begin, Ptr2;
  dd_rowrange fii1;
  dd_boolean ptr2found,quit,localdebug=dd_FALSE;
  long count=0,pos1, pos2;
  float workleft,prevworkleft=110.0,totalpairs;

  totalpairs=(cone->ZeroRayCount-1.0)*(cone->ZeroRayCount-2.0)+1.0;
  Ptr2begin = NULL; 
  if (RRbegin ==NULL || RRend==NULL){
    if (1) fprintf(stderr,"Warning: dd_UpdateEdges called with NULL pointer(s)\n");
    goto _L99;
  }
  Ptr1=RRbegin;
  pos1=1;
  do{
    ptr2found=dd_FALSE;
    quit=dd_FALSE;
    fii1=Ptr1->FirstInfeasIndex;
    pos2=2;
    for (Ptr2=Ptr1->Next; !ptr2found && !quit; Ptr2=Ptr2->Next,pos2++){
      if  (Ptr2->FirstInfeasIndex > fii1){
        Ptr2begin=Ptr2;
        ptr2found=dd_TRUE;
      }
      else if (Ptr2==RRend) quit=dd_TRUE;
    }
    if (ptr2found){
      quit=dd_FALSE;
      for (Ptr2=Ptr2begin; !quit ; Ptr2=Ptr2->Next){
        count++;
        if (localdebug) fprintf(stderr,"dd_UpdateEdges: edge %ld \n",count);
        dd_ConditionalAddEdge(cone, Ptr1,Ptr2,RRbegin);
        if (Ptr2==RRend || Ptr2->Next==NULL) quit=dd_TRUE;
      }
    }
    Ptr1=Ptr1->Next;
    pos1++;
    workleft = 100.0 * (cone->ZeroRayCount-pos1) * (cone->ZeroRayCount - pos1-1.0) / totalpairs;
    if (cone->ZeroRayCount>=500 && dd_debug && pos1%10 ==0 && prevworkleft-workleft>=10 ) {
      fprintf(stderr,"*Work of iteration %5ld(/%ld): %4ld/%4ld => %4.1f%% left\n",
	     cone->Iteration, cone->m, pos1, cone->ZeroRayCount, workleft);
      prevworkleft=workleft;
    }    
  }while(Ptr1!=RRend && Ptr1!=NULL);
_L99:;  
}

void dd_FreeDDMemory0(dd_ConePtr cone)
{
  dd_RayPtr Ptr, PrevPtr;
  long count;
  dd_colrange j;
  dd_boolean localdebug=dd_FALSE;
  
  /* THIS SHOULD BE REWRITTEN carefully */
  PrevPtr=cone->ArtificialRay;
  if (PrevPtr!=NULL){
    count=0;
    for (Ptr=cone->ArtificialRay->Next; Ptr!=NULL; Ptr=Ptr->Next){
      /* Added Marc Pfetsch 2/19/01 */
      for (j=0;j < cone->d;j++)
dd_clear(PrevPtr->Ray[j]);
      dd_clear(PrevPtr->ARay);

      free(PrevPtr->Ray);
      free(PrevPtr->ZeroSet);
      free(PrevPtr);
      count++;
      PrevPtr=Ptr;
    };
    cone->FirstRay=NULL;
    /* Added Marc Pfetsch 010219 */
    for (j=0;j < cone->d;j++)
dd_clear(cone->LastRay->Ray[j]);
    dd_clear(cone->LastRay->ARay);

    free(cone->LastRay->Ray);
    cone->LastRay->Ray = NULL;
    set_free(cone->LastRay->ZeroSet);
    cone->LastRay->ZeroSet = NULL;
    free(cone->LastRay);
    cone->LastRay = NULL;
    cone->ArtificialRay=NULL;
    if (localdebug) fprintf(stderr,"%ld ray storage spaces freed\n",count);
  }
/* must add (by Sato) */
  free(cone->Edges);
  
  set_free(cone->GroundSet); 
  set_free(cone->EqualitySet); 
  set_free(cone->NonequalitySet); 
  set_free(cone->AddedHalfspaces); 
  set_free(cone->WeaklyAddedHalfspaces); 
  set_free(cone->InitialHalfspaces);
  free(cone->InitialRayIndex);
  free(cone->OrderVector);
  free(cone->newcol);

/* Fixed by Shawn Rusaw.  Originally it was cone->d instead of cone->d_alloc */
  dd_FreeBmatrix(cone->d_alloc,cone->B);
  dd_FreeBmatrix(cone->d_alloc,cone->Bsave);

/* Fixed by Marc Pfetsch 010219*/
  dd_FreeAmatrix(cone->m_alloc,cone->d_alloc,cone->A);
  cone->A = NULL;

  free(cone);
}

void dd_FreeDDMemory(dd_PolyhedraPtr poly)
{
  dd_FreeDDMemory0(poly->child);
  poly->child=NULL;
}

void dd_FreePolyhedra(dd_PolyhedraPtr poly)
{
  dd_bigrange i;

  if ((poly)->child != NULL) dd_FreeDDMemory(poly);
  dd_FreeAmatrix((poly)->m_alloc,poly->d_alloc, poly->A);
  dd_FreeArow((poly)->d_alloc,(poly)->c);
  free((poly)->EqualityIndex);
  if (poly->AincGenerated){
    for (i=1; i<=poly->m1; i++){
      set_free(poly->Ainc[i-1]);
    }
    free(poly->Ainc);
    set_free(poly->Ared);
    set_free(poly->Adom);
    poly->Ainc=NULL;
  }

  free(poly);
}

void dd_Normalize(dd_colrange d_size, mytype *V)
{
  long j,jmin=0;
  mytype temp,min;
  dd_boolean nonzerofound=dd_FALSE;

  if (d_size>0){
    dd_init(min);  dd_init(temp);
    dd_abs(min,V[0]);  jmin=0; /* set the minmizer to 0 */
    if (dd_Positive(min)) nonzerofound=dd_TRUE;
    for (j = 1; j < d_size; j++) {
      dd_abs(temp,V[j]);
      if (dd_Positive(temp)){
        if (!nonzerofound || dd_Smaller(temp,min)){
          nonzerofound=dd_TRUE;
          dd_set(min, temp);  jmin=j;
        }
      }
    }
    if (dd_Positive(min)){
      for (j = 0; j < d_size; j++) dd_div(V[j], V[j], min);
    }
    dd_clear(min); dd_clear(temp);
  }
}


void dd_ZeroIndexSet(dd_rowrange m_size, dd_colrange d_size, dd_Amatrix A, mytype *x, dd_rowset ZS)
{
  dd_rowrange i;
  mytype temp;

  /* Changed by Marc Pfetsch 010219 */
  dd_init(temp);
  set_emptyset(ZS);
  for (i = 1; i <= m_size; i++) {
    dd_AValue(&temp, d_size, A, x, i);
    if (dd_EqualToZero(temp)) set_addelem(ZS, i);
  }

  /* Changed by Marc Pfetsch 010219 */
  dd_clear(temp);
}

void dd_CopyBmatrix(dd_colrange d_size, dd_Bmatrix T, dd_Bmatrix TCOPY)
{
  dd_rowrange i;
  dd_colrange j;

  for (i=0; i < d_size; i++) {
    for (j=0; j < d_size; j++) {
      dd_set(TCOPY[i][j],T[i][j]);
    }
  }
}


void dd_CopyArow(mytype *acopy, mytype *a, dd_colrange d)
{
  dd_colrange j;

  for (j = 0; j < d; j++) {
    dd_set(acopy[j],a[j]);
  }
}

void dd_CopyNormalizedArow(mytype *acopy, mytype *a, dd_colrange d)
{
  dd_CopyArow(acopy, a, d);
  dd_Normalize(d,acopy);
}

void dd_CopyAmatrix(mytype **Acopy, mytype **A, dd_rowrange m, dd_colrange d)
{
  dd_rowrange i;

  for (i = 0; i< m; i++) {
    dd_CopyArow(Acopy[i],A[i],d);
  }
}

void dd_CopyNormalizedAmatrix(mytype **Acopy, mytype **A, dd_rowrange m, dd_colrange d)
{
  dd_rowrange i;

  for (i = 0; i< m; i++) {
    dd_CopyNormalizedArow(Acopy[i],A[i],d);
  }
}

void dd_PermuteCopyAmatrix(mytype **Acopy, mytype **A, dd_rowrange m, dd_colrange d, dd_rowindex roworder)
{
  dd_rowrange i;

  for (i = 1; i<= m; i++) {
    dd_CopyArow(Acopy[i-1],A[roworder[i]-1],d);
  }
}

void dd_PermutePartialCopyAmatrix(mytype **Acopy, mytype **A, dd_rowrange m, dd_colrange d, dd_rowindex roworder,dd_rowrange p, dd_rowrange q)
{
 /* copy the rows of A whose roworder is positive.  roworder[i] is the row index of the copied row. */
  dd_rowrange i,k;

  k=0;
  for (i = 1; i<= m; i++) {
    if (roworder[i]>0) dd_CopyArow(Acopy[roworder[i]-1],A[i-1],d);
  }
}

void dd_InitializeArow(dd_colrange d,dd_Arow *a)
{
  dd_colrange j;

  if (d>0) *a=(mytype*) calloc(d,sizeof(mytype));
  for (j = 0; j < d; j++) {
      dd_init((*a)[j]);
  }
}

void dd_InitializeAmatrix(dd_rowrange m,dd_colrange d,dd_Amatrix *A)
{
  dd_rowrange i;

  if (m>0) (*A)=(mytype**) calloc(m,sizeof(mytype*));
  for (i = 0; i < m; i++) {
    dd_InitializeArow(d,&((*A)[i]));
  }
}

void dd_FreeAmatrix(dd_rowrange m,dd_colrange d,dd_Amatrix A)
{
  dd_rowrange i;
  dd_colrange j;

  for (i = 0; i < m; i++) {
    for (j = 0; j < d; j++) {
      dd_clear(A[i][j]);
    }
  }
  if (A!=NULL) {
    for (i = 0; i < m; i++) {
      free(A[i]);
    }
    free(A);
  }
}

void dd_FreeArow(dd_colrange d, dd_Arow a)
{
  dd_colrange j;

  for (j = 0; j < d; j++) {
    dd_clear(a[j]);
  }
  free(a);
}


void dd_InitializeBmatrix(dd_colrange d,dd_Bmatrix *B)
{
  dd_colrange i,j;

  (*B)=(mytype**) calloc(d,sizeof(mytype*));
  for (j = 0; j < d; j++) {
    (*B)[j]=(mytype*) calloc(d,sizeof(mytype));
  }
  for (i = 0; i < d; i++) {
    for (j = 0; j < d; j++) {
      dd_init((*B)[i][j]);
    }
  }
}

void dd_FreeBmatrix(dd_colrange d,dd_Bmatrix B)
{
  dd_colrange i,j;

  for (i = 0; i < d; i++) {
    for (j = 0; j < d; j++) {
      dd_clear(B[i][j]);
    }
  }
  if (B!=NULL) {
    for (j = 0; j < d; j++) {
      free(B[j]);
    }
    free(B);
  }
}

dd_SetFamilyPtr dd_CreateSetFamily(dd_bigrange fsize, dd_bigrange ssize)
{
  dd_SetFamilyPtr F;
  dd_bigrange i,f0,f1,s0,s1;

  if (fsize<=0) {
    f0=0; f1=1;  
    /* if fsize<=0, the fsize is set to zero and the created size is one */
  } else {
    f0=fsize; f1=fsize;
  }
  if (ssize<=0) {
    s0=0; s1=1;  
    /* if ssize<=0, the ssize is set to zero and the created size is one */
  } else {
    s0=ssize; s1=ssize;
  }

  F=(dd_SetFamilyPtr) malloc (sizeof(dd_SetFamilyType));
  F->set=(set_type*) calloc(f1,sizeof(set_type));
  for (i=0; i<f1; i++) {
    set_initialize(&(F->set[i]), s1);
  }
  F->famsize=f0;
  F->setsize=s0;
  return F;
}


void dd_FreeSetFamily(dd_SetFamilyPtr F)
{
  dd_bigrange i,f1;

  if (F!=NULL){
    if (F->famsize<=0) f1=1; else f1=F->famsize; 
      /* the smallest created size is one */
    for (i=0; i<f1; i++) {
      set_free(F->set[i]);
    }
    free(F->set);
    free(F);
  }
}

dd_MatrixPtr dd_CreateMatrix(dd_rowrange m_size,dd_colrange d_size)
{
  dd_MatrixPtr M;
  dd_rowrange m0,m1;
  dd_colrange d0,d1;

  if (m_size<=0){ 
    m0=0; m1=1;  
    /* if m_size <=0, the number of rows is set to zero, the actual size is 1 */
  } else {
    m0=m_size; m1=m_size;
  }
  if (d_size<=0){ 
    d0=0; d1=1;  
    /* if d_size <=0, the number of cols is set to zero, the actual size is 1 */
  } else {
    d0=d_size; d1=d_size;
  }
  M=(dd_MatrixPtr) malloc (sizeof(dd_MatrixType));
  dd_InitializeAmatrix(m1,d1,&(M->matrix));
  dd_InitializeArow(d1,&(M->rowvec));
  M->rowsize=m0;
  set_initialize(&(M->linset), m1);
  M->colsize=d0;
  M->objective=dd_LPnone;
  M->numbtype=dd_Unknown;
  M->representation=dd_Unspecified;
  return M;
}

void dd_FreeMatrix(dd_MatrixPtr M)
{
  dd_rowrange m1;
  dd_colrange d1;

  if (M!=NULL) {
    if (M->rowsize<=0) m1=1; else m1=M->rowsize;
    if (M->colsize<=0) d1=1; else d1=M->colsize;
    if (M!=NULL) {
      dd_FreeAmatrix(m1,d1,M->matrix);
      dd_FreeArow(d1,M->rowvec);
      set_free(M->linset);
      free(M);
    }
  }
}

void dd_SetToIdentity(dd_colrange d_size, dd_Bmatrix T)
{
  dd_colrange j1, j2;

  for (j1 = 1; j1 <= d_size; j1++) {
    for (j2 = 1; j2 <= d_size; j2++) {
      if (j1 == j2)
        dd_set(T[j1 - 1][j2 - 1],dd_one);
      else
        dd_set(T[j1 - 1][j2 - 1],dd_purezero);
    }
  }
}

void dd_ColumnReduce(dd_ConePtr cone)
{
  dd_colrange j,j1=0;
  dd_rowrange i;
  dd_boolean localdebug=dd_FALSE;

  for (j=1;j<=cone->d;j++) {
    if (cone->InitialRayIndex[j]>0){
      j1=j1+1;
      if (j1<j) {
        for (i=1; i<=cone->m; i++) dd_set(cone->A[i-1][j1-1],cone->A[i-1][j-1]);
        cone->newcol[j]=j1;
        if (localdebug){
          fprintf(stderr,"shifting the column %ld to column %ld\n", j, j1);
        }
          /* shifting forward */
      }
    } else {
      cone->newcol[j]=0;
      if (localdebug) {
        fprintf(stderr,"a generator (or an equation) of the linearity space: ");
        for (i=1; i<=cone->d; i++) dd_WriteNumber(stderr, cone->B[i-1][j-1]);
        fprintf(stderr,"\n");
      }
    }
  }
  cone->d=j1;  /* update the dimension. cone->d_orig remembers the old. */
  dd_CopyBmatrix(cone->d_orig, cone->B, cone->Bsave);  
    /* save the dual basis inverse as Bsave.  This matrix contains the linearity space generators. */
  cone->ColReduced=dd_TRUE;
}

long dd_MatrixRank(dd_MatrixPtr M, dd_rowset ignoredrows, dd_colset ignoredcols, dd_rowset *rowbasis, dd_colset *colbasis)
{
  dd_boolean stop, chosen, localdebug=dd_debug;
  dd_rowset NopivotRow,PriorityRow;
  dd_colset ColSelected;
  dd_Bmatrix B;
  dd_rowindex roworder;
  dd_rowrange r;
  dd_colrange s;
  long rank;

  rank = 0;
  stop = dd_FALSE;
  set_initialize(&ColSelected, M->colsize);
  set_initialize(&NopivotRow, M->rowsize);
  set_initialize(rowbasis, M->rowsize);
  set_initialize(colbasis, M->colsize);
  set_initialize(&PriorityRow, M->rowsize);
  set_copy(NopivotRow,ignoredrows);
  set_copy(ColSelected,ignoredcols);
  dd_InitializeBmatrix(M->colsize, &B);
  dd_SetToIdentity(M->colsize, B);
  roworder=(long *)calloc(M->rowsize+1,sizeof(long*));
  for (r=0; r<M->rowsize; r++){roworder[r+1]=r+1;
  }

  do {   /* Find a set of rows for a basis */
      dd_SelectPivot2(M->rowsize, M->colsize,M->matrix,B,dd_MinIndex,roworder,
       PriorityRow,M->rowsize, NopivotRow, ColSelected, &r, &s, &chosen);
      if (dd_debug && chosen) 
        fprintf(stderr,"Procedure dd_MatrixRank: pivot on (r,s) =(%ld, %ld).\n", r, s);
      if (chosen) {
        set_addelem(NopivotRow, r);
        set_addelem(*rowbasis, r);
        set_addelem(ColSelected, s);
        set_addelem(*colbasis, s);
        rank++;
        dd_GaussianColumnPivot(M->rowsize, M->colsize, M->matrix, B, r, s);
        if (localdebug) dd_WriteBmatrix(stderr,M->colsize,B);
      } else {
        stop=dd_TRUE;
      }
      if (rank==M->colsize) stop = dd_TRUE;
  } while (!stop);
  dd_FreeBmatrix(M->colsize,B);
  free(roworder);
  set_free(ColSelected);
  set_free(NopivotRow);
  set_free(PriorityRow);
  return rank;
}


void dd_FindBasis(dd_ConePtr cone, long *rank)
{
  dd_boolean stop, chosen, localdebug=dd_debug;
  dd_rowset NopivotRow;
  dd_colset ColSelected;
  dd_rowrange r;
  dd_colrange j,s;

  *rank = 0;
  stop = dd_FALSE;
  for (j=0;j<=cone->d;j++) cone->InitialRayIndex[j]=0;
  set_emptyset(cone->InitialHalfspaces);
  set_initialize(&ColSelected, cone->d);
  set_initialize(&NopivotRow, cone->m);
  set_copy(NopivotRow,cone->NonequalitySet);
  dd_SetToIdentity(cone->d, cone->B);
  do {   /* Find a set of rows for a basis */
      dd_SelectPivot2(cone->m, cone->d,cone->A,cone->B,cone->HalfspaceOrder,cone->OrderVector,
       cone->EqualitySet,cone->m, NopivotRow, ColSelected, &r, &s, &chosen);
      if (dd_debug && chosen) 
        fprintf(stderr,"Procedure dd_FindBasis: pivot on (r,s) =(%ld, %ld).\n", r, s);
      if (chosen) {
        set_addelem(cone->InitialHalfspaces, r);
        set_addelem(NopivotRow, r);
        set_addelem(ColSelected, s);
        cone->InitialRayIndex[s]=r;    /* cone->InitialRayIndex[s] stores the corr. row index */
        (*rank)++;
        dd_GaussianColumnPivot(cone->m, cone->d, cone->A, cone->B, r, s);
        if (localdebug) dd_WriteBmatrix(stderr,cone->d,cone->B);
      } else {
        stop=dd_TRUE;
      }
      if (*rank==cone->d) stop = dd_TRUE;
  } while (!stop);
  set_free(ColSelected);
  set_free(NopivotRow);
}


void dd_FindInitialRays(dd_ConePtr cone, dd_boolean *found)
{
  dd_rowset CandidateRows;
  dd_rowrange i;
  long rank;
  dd_RowOrderType roworder_save=dd_LexMin;

  *found = dd_FALSE;
  set_initialize(&CandidateRows, cone->m);
  if (cone->parent->InitBasisAtBottom==dd_TRUE) {
    roworder_save=cone->HalfspaceOrder;
    cone->HalfspaceOrder=dd_MaxIndex;
    cone->PreOrderedRun=dd_FALSE;
  }
  else cone->PreOrderedRun=dd_TRUE;
  if (dd_debug) dd_WriteBmatrix(stderr, cone->d, cone->B);
  for (i = 1; i <= cone->m; i++)
    if (!set_member(i,cone->NonequalitySet)) set_addelem(CandidateRows, i);
    /*all rows not in NonequalitySet are candidates for initial cone*/
  dd_FindBasis(cone, &rank);
  if (dd_debug) dd_WriteBmatrix(stderr, cone->d, cone->B);
  if (dd_debug) fprintf(stderr,"dd_FindInitialRays: rank of Amatrix = %ld\n", rank);
  cone->LinearityDim=cone->d - rank;
  if (dd_debug) fprintf(stderr,"Linearity Dimension = %ld\n", cone->LinearityDim);
  if (cone->LinearityDim > 0) {
     dd_ColumnReduce(cone);
     dd_FindBasis(cone, &rank);
  }
  if (!set_subset(cone->EqualitySet,cone->InitialHalfspaces)) {
    if (dd_debug) {
      fprintf(stderr,"Equality set is dependent. Equality Set and an initial basis:\n");
      set_fwrite(stderr,cone->EqualitySet);
      set_fwrite(stderr,cone->InitialHalfspaces);
    };
  }
  *found = dd_TRUE;
  set_free(CandidateRows);
  if (cone->parent->InitBasisAtBottom==dd_TRUE) {
    cone->HalfspaceOrder=roworder_save;
  }
  if (cone->HalfspaceOrder==dd_MaxCutoff||
      cone->HalfspaceOrder==dd_MinCutoff||
      cone->HalfspaceOrder==dd_MixCutoff){
    cone->PreOrderedRun=dd_FALSE;
  } else cone->PreOrderedRun=dd_TRUE;
}

void dd_CheckEquality(dd_colrange d_size, dd_RayPtr*RP1, dd_RayPtr*RP2, dd_boolean *equal)
{
  long j;

  if (dd_debug)
    fprintf(stderr,"Check equality of two rays\n");
  *equal = dd_TRUE;
  j = 1;
  while (j <= d_size && *equal) {
    if (!dd_Equal((*RP1)->Ray[j - 1],(*RP2)->Ray[j - 1]))
      *equal = dd_FALSE;
    j++;
  }
  if (*equal)
    fprintf(stderr,"Equal records found !!!!\n");
}

void dd_CreateNewRay(dd_ConePtr cone, 
    dd_RayPtr Ptr1, dd_RayPtr Ptr2, dd_rowrange ii)
{
  /*Create a new ray by taking a linear combination of two rays*/
  dd_colrange j;
  mytype a1, a2, v1, v2;
  static dd_Arow NewRay;
  static dd_colrange last_d=0;
  dd_boolean localdebug=dd_debug;

  dd_init(a1); dd_init(a2); dd_init(v1); dd_init(v2);
  if (last_d!=cone->d){
    if (last_d>0) {
      for (j=0; j<last_d; j++) dd_clear(NewRay[j]);
      free(NewRay);
    }
    NewRay=(mytype*)calloc(cone->d,sizeof(mytype));
    for (j=0; j<cone->d; j++) dd_init(NewRay[j]);
    last_d=cone->d;
  }

  dd_AValue(&a1, cone->d, cone->A, Ptr1->Ray, ii);
  dd_AValue(&a2, cone->d, cone->A, Ptr2->Ray, ii);
  if (localdebug) {
    fprintf(stderr,"CreatNewRay: Ray1 ="); dd_WriteArow(stderr, Ptr1->Ray, cone->d);
    fprintf(stderr,"CreatNewRay: Ray2 ="); dd_WriteArow(stderr, Ptr2->Ray, cone->d);
  }
  dd_abs(v1,a1);
  dd_abs(v2,a2);
  if (localdebug){
    fprintf(stderr,"dd_AValue1 and ABS");  dd_WriteNumber(stderr,a1); dd_WriteNumber(stderr,v1); fprintf(stderr,"\n");
    fprintf(stderr,"dd_AValue2 and ABS");  dd_WriteNumber(stderr,a2); dd_WriteNumber(stderr,v2); fprintf(stderr,"\n");
  }
  for (j = 0; j < cone->d; j++){
    dd_LinearComb(NewRay[j], Ptr1->Ray[j],v2,Ptr2->Ray[j],v1);
  }
  if (localdebug) {
    fprintf(stderr,"CreatNewRay: New ray ="); dd_WriteArow(stderr, NewRay, cone->d);
  }
  dd_Normalize(cone->d, NewRay);
  if (localdebug) {
    fprintf(stderr,"CreatNewRay: dd_Normalized ray ="); dd_WriteArow(stderr, NewRay, cone->d);
  }
  dd_AddRay(cone, NewRay);
  dd_clear(a1); dd_clear(a2); dd_clear(v1); dd_clear(v2);
}

void dd_EvaluateARay1(dd_rowrange i, dd_ConePtr cone)
/* Evaluate the ith component of the vector  A x RD.Ray 
    and rearrange the linked list so that
    the infeasible rays with respect to  i  will be
    placed consecutively from First 
 */
{
  dd_colrange j;
  mytype temp,tnext;
  dd_RayPtr Ptr, PrevPtr, TempPtr;

  dd_init(temp); dd_init(tnext);
  Ptr = cone->FirstRay;
  PrevPtr = cone->ArtificialRay;
  if (PrevPtr->Next != Ptr) {
    fprintf(stderr,"Error.  Artificial Ray does not point to FirstRay!!!\n");
  }
  while (Ptr != NULL) {
    dd_set(temp,dd_purezero);
    for (j = 0; j < cone->d; j++){
      dd_mul(tnext,cone->A[i - 1][j],Ptr->Ray[j]);
      dd_add(temp,temp,tnext);
    }
    dd_set(Ptr->ARay,temp);
/*    if ( temp <= -zero && Ptr != cone->FirstRay) {*/
    if ( dd_Negative(temp) && Ptr != cone->FirstRay) {
      /* fprintf(stderr,"Moving an infeasible record w.r.t. %ld to FirstRay\n",i); */
      if (Ptr==cone->LastRay) cone->LastRay=PrevPtr;
      TempPtr=Ptr;
      Ptr = Ptr->Next;
      PrevPtr->Next = Ptr;
      cone->ArtificialRay->Next = TempPtr;
      TempPtr->Next = cone->FirstRay;
      cone->FirstRay = TempPtr;
    }
    else {
      PrevPtr = Ptr;
      Ptr = Ptr->Next;
    }
  }
  dd_clear(temp); dd_clear(tnext);
}

void dd_EvaluateARay2(dd_rowrange i, dd_ConePtr cone)
/* Evaluate the ith component of the vector  A x RD.Ray 
   and rearrange the linked list so that
   the infeasible rays with respect to  i  will be
   placed consecutively from First. Also for all feasible rays,
   "positive" rays and "zero" rays will be placed consecutively.
 */
{
  dd_colrange j;
  mytype temp,tnext;
  dd_RayPtr Ptr, NextPtr;
  dd_boolean zerofound=dd_FALSE,negfound=dd_FALSE,posfound=dd_FALSE;

  if (cone==NULL || cone->TotalRayCount<=0) goto _L99;  
  dd_init(temp); dd_init(tnext);
  cone->PosHead=NULL;cone->ZeroHead=NULL;cone->NegHead=NULL;
  cone->PosLast=NULL;cone->ZeroLast=NULL;cone->NegLast=NULL;
  Ptr = cone->FirstRay;
  while (Ptr != NULL) {
    NextPtr=Ptr->Next;  /* remember the Next record */
    Ptr->Next=NULL;     /* then clear the Next pointer */
    dd_set(temp,dd_purezero);
    for (j = 0; j < cone->d; j++){
      dd_mul(tnext,cone->A[i - 1][j],Ptr->Ray[j]);
      dd_add(temp,temp,tnext);
    }
    dd_set(Ptr->ARay,temp);
/*    if ( temp < -zero) {*/
    if ( dd_Negative(temp)) {
      if (!negfound){
        negfound=dd_TRUE;
        cone->NegHead=Ptr;
        cone->NegLast=Ptr;
      }
      else{
        Ptr->Next=cone->NegHead;
        cone->NegHead=Ptr;
      }
    }
/*    else if (temp > zero){*/
    else if (dd_Positive(temp)){
      if (!posfound){
        posfound=dd_TRUE;
        cone->PosHead=Ptr;
        cone->PosLast=Ptr;
      }
      else{  
        Ptr->Next=cone->PosHead;
        cone->PosHead=Ptr;
       }
    }
    else {
      if (!zerofound){
        zerofound=dd_TRUE;
        cone->ZeroHead=Ptr;
        cone->ZeroLast=Ptr;
      }
      else{
        Ptr->Next=cone->ZeroHead;
        cone->ZeroHead=Ptr;
      }
    }
    Ptr=NextPtr;
  }
  /* joining three neg, pos and zero lists */
  if (negfound){                 /* -list nonempty */
    cone->FirstRay=cone->NegHead;
    if (posfound){               /* -list & +list nonempty */
      cone->NegLast->Next=cone->PosHead;
      if (zerofound){            /* -list, +list, 0list all nonempty */
        cone->PosLast->Next=cone->ZeroHead;
        cone->LastRay=cone->ZeroLast;
      } 
      else{                      /* -list, +list nonempty but  0list empty */
        cone->LastRay=cone->PosLast;      
      }
    }
    else{                        /* -list nonempty & +list empty */
      if (zerofound){            /* -list,0list nonempty & +list empty */
        cone->NegLast->Next=cone->ZeroHead;
        cone->LastRay=cone->ZeroLast;
      } 
      else {                      /* -list nonempty & +list,0list empty */
        cone->LastRay=cone->NegLast;
      }
    }
  }
  else if (posfound){            /* -list empty & +list nonempty */
    cone->FirstRay=cone->PosHead;
    if (zerofound){              /* -list empty & +list,0list nonempty */
      cone->PosLast->Next=cone->ZeroHead;
      cone->LastRay=cone->ZeroLast;
    } 
    else{                        /* -list,0list empty & +list nonempty */
      cone->LastRay=cone->PosLast;
    }
  }
  else{                          /* -list,+list empty & 0list nonempty */
    cone->FirstRay=cone->ZeroHead;
    cone->LastRay=cone->ZeroLast;
  }
  cone->ArtificialRay->Next=cone->FirstRay;
  cone->LastRay->Next=NULL;
  dd_clear(temp); dd_clear(tnext);
  _L99:;  
}

void dd_DeleteNegativeRays(dd_ConePtr cone)
/* Eliminate the infeasible rays with respect to  i  which
   are supposed to be consecutive from the head of the dd_Ray list,
   and sort the zero list assumed to be consecutive at the
   end of the list.
 */
{
  dd_rowrange fii,fiitest;
  mytype temp;
  dd_RayPtr Ptr, PrevPtr,NextPtr,ZeroPtr1,ZeroPtr0;
  dd_boolean found, completed, zerofound=dd_FALSE,negfound=dd_FALSE,posfound=dd_FALSE;
  dd_boolean localdebug=dd_FALSE;
  
  dd_init(temp);
  cone->PosHead=NULL;cone->ZeroHead=NULL;cone->NegHead=NULL;
  cone->PosLast=NULL;cone->ZeroLast=NULL;cone->NegLast=NULL;

  /* Delete the infeasible rays  */
  PrevPtr= cone->ArtificialRay;
  Ptr = cone->FirstRay;
  if (PrevPtr->Next != Ptr) 
    fprintf(stderr,"Error at dd_DeleteNegativeRays: ArtificialRay does not point the FirstRay.\n");
  completed=dd_FALSE;
  while (Ptr != NULL && !completed){
/*    if ( (Ptr->ARay) < -zero ){ */
    if ( dd_Negative(Ptr->ARay)){
      dd_Eliminate(cone, &PrevPtr);
      Ptr=PrevPtr->Next;
    }
    else{
      completed=dd_TRUE;
    }
  }
  
  /* Sort the zero rays */
  Ptr = cone->FirstRay;
  cone->ZeroRayCount=0;
  while (Ptr != NULL) {
    NextPtr=Ptr->Next;  /* remember the Next record */
    dd_set(temp,Ptr->ARay);
    if (localdebug) {fprintf(stderr,"Ptr->ARay :"); dd_WriteNumber(stderr, temp);}
/*    if ( temp < -zero) {*/
    if ( dd_Negative(temp)) {
      if (!negfound){
        fprintf(stderr,"Error: An infeasible ray found after their removal\n");
        negfound=dd_TRUE;
      }
    }
/*    else if (temp > zero){*/
    else if (dd_Positive(temp)){
      if (!posfound){
        posfound=dd_TRUE;
        cone->PosHead=Ptr;
        cone->PosLast=Ptr;
      }
      else{  
        cone->PosLast=Ptr;
       }
    }
    else {
      (cone->ZeroRayCount)++;
      if (!zerofound){
        zerofound=dd_TRUE;
        cone->ZeroHead=Ptr;
        cone->ZeroLast=Ptr;
        cone->ZeroLast->Next=NULL;
      }
      else{/* Find a right position to store the record sorted w.r.t. FirstInfeasIndex */
        fii=Ptr->FirstInfeasIndex; 
        found=dd_FALSE;
        ZeroPtr1=NULL;
        for (ZeroPtr0=cone->ZeroHead; !found && ZeroPtr0!=NULL ; ZeroPtr0=ZeroPtr0->Next){
          fiitest=ZeroPtr0->FirstInfeasIndex;
          if (fiitest >= fii){
            found=dd_TRUE;
          }
          else ZeroPtr1=ZeroPtr0;
        }
        /* fprintf(stderr,"insert position found \n %d  index %ld\n",found, fiitest); */
        if (!found){           /* the new record must be stored at the end of list */
          cone->ZeroLast->Next=Ptr;
          cone->ZeroLast=Ptr;
          cone->ZeroLast->Next=NULL;
        }
        else{
          if (ZeroPtr1==NULL){ /* store the new one at the head, and update the head ptr */
            /* fprintf(stderr,"Insert at the head\n"); */
            Ptr->Next=cone->ZeroHead;
            cone->ZeroHead=Ptr;
          }
          else{                /* store the new one inbetween ZeroPtr1 and 0 */
            /* fprintf(stderr,"Insert inbetween\n");  */
            Ptr->Next=ZeroPtr1->Next;
            ZeroPtr1->Next=Ptr;
          }
        }
        /*
        Ptr->Next=cone->ZeroHead;
        cone->ZeroHead=Ptr;
        */
      }
    }
    Ptr=NextPtr;
  }
  /* joining the pos and zero lists */
  if (posfound){            /* -list empty & +list nonempty */
    cone->FirstRay=cone->PosHead;
    if (zerofound){              /* +list,0list nonempty */
      cone->PosLast->Next=cone->ZeroHead;
      cone->LastRay=cone->ZeroLast;
    } 
    else{                        /* 0list empty & +list nonempty */
      cone->LastRay=cone->PosLast;
    }
  }
  else{                          /* +list empty & 0list nonempty */
    cone->FirstRay=cone->ZeroHead;
    cone->LastRay=cone->ZeroLast;
  }
  cone->ArtificialRay->Next=cone->FirstRay;
  cone->LastRay->Next=NULL;
  dd_clear(temp);
}

void dd_FeasibilityIndices(long *fnum, long *infnum, dd_rowrange i, dd_ConePtr cone)
{
  /*Evaluate the number of feasible rays and infeasible rays*/
  /*  w.r.t the hyperplane  i*/
  dd_colrange j;
  mytype temp, tnext;
  dd_RayPtr Ptr;

  dd_init(temp); dd_init(tnext);
  *fnum = 0;
  *infnum = 0;
  Ptr = cone->FirstRay;
  while (Ptr != NULL) {
    dd_set(temp,dd_purezero);
    for (j = 0; j < cone->d; j++){
      dd_mul(tnext, cone->A[i - 1][j],Ptr->Ray[j]);
      dd_add(temp, temp, tnext);
    }
    if (dd_Nonnegative(temp))
      (*fnum)++;
    else
      (*infnum)++;
    Ptr = Ptr->Next;
  }
  dd_clear(temp); dd_clear(tnext);
}

dd_boolean dd_LexSmaller(mytype *v1, mytype *v2, long dmax)
{ /* dmax is the size of vectors v1,v2 */
  dd_boolean determined, smaller;
  dd_colrange j;

  smaller = dd_FALSE;
  determined = dd_FALSE;
  j = 1;
  do {
    if (!dd_Equal(v1[j - 1],v2[j - 1])) {  /* 086 */
      if (dd_Smaller(v1[j - 1],v2[j - 1])) {  /*086 */
	    smaller = dd_TRUE;
	  }
      determined = dd_TRUE;
    } else
      j++;
  } while (!(determined) && (j <= dmax));
  return smaller;
}


dd_boolean dd_LexLarger(mytype *v1, mytype *v2, long dmax)
{
  return dd_LexSmaller(v2, v1, dmax);
}

dd_boolean dd_LexEqual(mytype *v1, mytype *v2, long dmax)
{ /* dmax is the size of vectors v1,v2 */
  dd_boolean determined, equal;
  dd_colrange j;

  equal = dd_TRUE;
  determined = dd_FALSE;
  j = 1;
  do {
    if (!dd_Equal(v1[j - 1],v2[j - 1])) {  /* 093c */
	equal = dd_FALSE;
        determined = dd_TRUE;
    } else {
      j++;
    }
  } while (!(determined) && (j <= dmax));
  return equal;
}

void dd_AddNewHalfspace1(dd_ConePtr cone, dd_rowrange hnew)
/* This procedure 1 must be used with PreorderedRun=dd_FALSE 
   This procedure is the most elementary implementation of
   DD and can be used with any type of ordering, including
   dynamic ordering of rows, e.g. MaxCutoff, MinCutoff.
   The memory requirement is minimum because it does not
   store any adjacency among the rays.
*/
{
  dd_RayPtr RayPtr0,RayPtr1,RayPtr2,RayPtr2s,RayPtr3;
  long pos1, pos2;
  double prevprogress, progress;
  mytype value1, value2;
  dd_boolean adj, equal, completed;

  dd_init(value1); dd_init(value2);
  dd_EvaluateARay1(hnew, cone);  
   /*Check feasibility of rays w.r.t. hnew 
     and put all infeasible ones consecutively */

  RayPtr0 = cone->ArtificialRay;   /*Pointer pointing RayPrt1*/
  RayPtr1 = cone->FirstRay;        /*1st hnew-infeasible ray to scan and compare with feasible rays*/
  dd_set(value1,cone->FirstRay->ARay);
  if (dd_Nonnegative(value1)) {
    if (cone->RayCount==cone->WeaklyFeasibleRayCount) cone->CompStatus=dd_AllFound;
    goto _L99;        /* Sicne there is no hnew-infeasible ray and nothing to do */
  }
  else {
    RayPtr2s = RayPtr1->Next;/* RayPtr2s must point the first feasible ray */
    pos2=1;
    while (RayPtr2s!=NULL && dd_Negative(RayPtr2s->ARay)) {
      RayPtr2s = RayPtr2s->Next;
      pos2++;
    }
  }
  if (RayPtr2s==NULL) {
    cone->FirstRay=NULL;
    cone->ArtificialRay->Next=cone->FirstRay;
    cone->RayCount=0;
    cone->CompStatus=dd_AllFound;
    goto _L99;   /* All rays are infeasible, and the computation must stop */
  }
  RayPtr2 = RayPtr2s;   /*2nd feasible ray to scan and compare with 1st*/
  RayPtr3 = cone->LastRay;    /*Last feasible for scanning*/
  prevprogress=-10.0;
  pos1 = 1;
  completed=dd_FALSE;
  while ((RayPtr1 != RayPtr2s) && !completed) {
    dd_set(value1,RayPtr1->ARay);
    dd_set(value2,RayPtr2->ARay);
    dd_CheckEquality(cone->d, &RayPtr1, &RayPtr2, &equal);
    if ((dd_Positive(value1) && dd_Negative(value2)) || (dd_Negative(value1) && dd_Positive(value2))){
      dd_CheckAdjacency(cone, &RayPtr1, &RayPtr2, &adj);
      if (adj) dd_CreateNewRay(cone, RayPtr1, RayPtr2, hnew);
    }
    if (RayPtr2 != RayPtr3) {
      RayPtr2 = RayPtr2->Next;
      continue;
    }
    if (dd_Negative(value1) || equal) {
      dd_Eliminate(cone, &RayPtr0);
      RayPtr1 = RayPtr0->Next;
      RayPtr2 = RayPtr2s;
    } else {
      completed=dd_TRUE;
    }
    pos1++;
    progress = 100.0 * ((double)pos1 / pos2) * (2.0 * pos2 - pos1) / pos2;
    if (progress-prevprogress>=10 && pos1%10==0 && dd_debug) {
      fprintf(stderr,"*Progress of iteration %5ld(/%ld):   %4ld/%4ld => %4.1f%% done\n",
	     cone->Iteration, cone->m, pos1, pos2, progress);
      prevprogress=progress;
    }
  }
  if (cone->RayCount==cone->WeaklyFeasibleRayCount) cone->CompStatus=dd_AllFound;
  _L99:;
  dd_clear(value1); dd_clear(value2);
}

void dd_AddNewHalfspace2(dd_ConePtr cone, dd_rowrange hnew)
/* This procedure must be used under PreOrderedRun mode */
{
  dd_RayPtr RayPtr0,RayPtr1,RayPtr2;
  dd_AdjacencyType *EdgePtr, *EdgePtr0;
  long pos1;
  dd_rowrange fii1, fii2;
  dd_boolean localdebug=dd_FALSE;

  dd_EvaluateARay2(hnew, cone);
   /* Check feasibility of rays w.r.t. hnew 
      and sort them. ( -rays, +rays, 0rays)*/

  if (cone->PosHead==NULL && cone->ZeroHead==NULL) {
    cone->FirstRay=NULL;
    cone->ArtificialRay->Next=cone->FirstRay;
    cone->RayCount=0;
    cone->CompStatus=dd_AllFound;
    goto _L99;   /* All rays are infeasible, and the computation must stop */
  }
  
  if (localdebug){
    pos1=0;
    fprintf(stderr,"(pos, FirstInfeasIndex, A Ray)=\n");
    for (RayPtr0=cone->FirstRay; RayPtr0!=NULL; RayPtr0=RayPtr0->Next){
      pos1++;
      fprintf(stderr,"(%ld,%ld,",pos1,RayPtr0->FirstInfeasIndex);
      dd_WriteNumber(stderr,RayPtr0->ARay); 
      fprintf(stderr,") ");
   }
    fprintf(stderr,"\n");
  }
  
  if (cone->ZeroHead==NULL) cone->ZeroHead=cone->LastRay;

  EdgePtr=cone->Edges[cone->Iteration];
  while (EdgePtr!=NULL){
    RayPtr1=EdgePtr->Ray1;
    RayPtr2=EdgePtr->Ray2;
    fii1=RayPtr1->FirstInfeasIndex;   
    dd_CreateNewRay(cone, RayPtr1, RayPtr2, hnew);
    fii2=cone->LastRay->FirstInfeasIndex;
    if (fii1 != fii2) 
      dd_ConditionalAddEdge(cone,RayPtr1,cone->LastRay,cone->PosHead);
    EdgePtr0=EdgePtr;
    EdgePtr=EdgePtr->Next;
    free(EdgePtr0);
    (cone->EdgeCount)--;
  }
  cone->Edges[cone->Iteration]=NULL;
  
  dd_DeleteNegativeRays(cone);
    
  set_addelem(cone->AddedHalfspaces, hnew);

  if (cone->Iteration<cone->m){
    if (cone->ZeroHead!=NULL && cone->ZeroHead!=cone->LastRay){
      if (cone->ZeroRayCount>200 && dd_debug) fprintf(stderr,"*New edges being scanned...\n");
      dd_UpdateEdges(cone, cone->ZeroHead, cone->LastRay);
    }
  }

  if (cone->RayCount==cone->WeaklyFeasibleRayCount) cone->CompStatus=dd_AllFound;
_L99:;
}


void dd_SelectNextHalfspace0(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*A natural way to choose the next hyperplane.  Simply the largest index*/
  long i;
  dd_boolean determined;

  i = cone->m;
  determined = dd_FALSE;
  do {
    if (set_member(i, excluded))
      i--;
    else
      determined = dd_TRUE;
  } while (!determined && i>=1);
  if (determined) 
    *hnext = i;
  else
    *hnext = 0;
}

void dd_SelectNextHalfspace1(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Natural way to choose the next hyperplane.  Simply the least index*/
  long i;
  dd_boolean determined;

  i = 1;
  determined = dd_FALSE;
  do {
    if (set_member(i, excluded))
      i++;
    else
      determined = dd_TRUE;
  } while (!determined && i<=cone->m);
  if (determined) 
    *hnext = i;
  else 
    *hnext=0;
}

void dd_SelectNextHalfspace2(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Choose the next hyperplane with maximum infeasibility*/
  long i, fea, inf, infmin, fi=0;   /*feasibility and infeasibility numbers*/

  infmin = cone->RayCount + 1;
  for (i = 1; i <= cone->m; i++) {
    if (!set_member(i, excluded)) {
      dd_FeasibilityIndices(&fea, &inf, i, cone);
      if (inf < infmin) {
	infmin = inf;
	fi = fea;
	*hnext = i;
      }
    }
  }
  if (dd_debug) {
    fprintf(stderr,"*infeasible rays (min) =%5ld, #feas rays =%5ld\n", infmin, fi);
  }
}

void dd_SelectNextHalfspace3(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Choose the next hyperplane with maximum infeasibility*/
  long i, fea, inf, infmax, fi=0;   /*feasibility and infeasibility numbers*/
  dd_boolean localdebug=dd_debug;

  infmax = -1;
  for (i = 1; i <= cone->m; i++) {
    if (!set_member(i, excluded)) {
      dd_FeasibilityIndices(&fea, &inf, i, cone);
      if (inf > infmax) {
	infmax = inf;
	fi = fea;
	*hnext = i;
      }
    }
  }
  if (localdebug) {
    fprintf(stderr,"*infeasible rays (max) =%5ld, #feas rays =%5ld\n", infmax, fi);
  }
}

void dd_SelectNextHalfspace4(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Choose the next hyperplane with the most unbalanced cut*/
  long i, fea, inf, max, tmax, fi=0, infi=0;
      /*feasibility and infeasibility numbers*/

  max = -1;
  for (i = 1; i <= cone->m; i++) {
    if (!set_member(i, excluded)) {
      dd_FeasibilityIndices(&fea, &inf, i, cone);
      if (fea <= inf)
        tmax = inf;
      else
        tmax = fea;
      if (tmax > max) {
        max = tmax;
        fi = fea;
        infi = inf;
        *hnext = i;
      }
    }
  }
  if (!dd_debug)
    return;
  if (max == fi) {
    fprintf(stderr,"*infeasible rays (min) =%5ld, #feas rays =%5ld\n", infi, fi);
  } else {
    fprintf(stderr,"*infeasible rays (max) =%5ld, #feas rays =%5ld\n", infi, fi);
  }
}

void dd_SelectNextHalfspace5(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Choose the next hyperplane which is lexico-min*/
  long i, minindex;
  mytype *v1, *v2;

  minindex = 0;
  v1 = NULL;
  for (i = 1; i <= cone->m; i++) {
    if (!set_member(i, excluded)) {
	  v2 = cone->A[i - 1];
      if (minindex == 0) {
	    minindex = i;
	    v1=v2;
      } else if (dd_LexSmaller(v2,v1,cone->d)) {
        minindex = i;
	    v1=v2;
      }
    }
  }
  *hnext = minindex;
}


void dd_SelectNextHalfspace6(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hnext)
{
  /*Choose the next hyperplane which is lexico-max*/
  long i, maxindex;
  mytype *v1, *v2;

  maxindex = 0;
  v1 = NULL;
  for (i = 1; i <= cone->m; i++) {
    if (!set_member(i, excluded)) {
      v2= cone->A[i - 1];
      if (maxindex == 0) {
        maxindex = i;
        v1=v2;
      } else if (dd_LexLarger(v2, v1, cone->d)) {
        maxindex = i;
        v1=v2;
     }
    }
  }
  *hnext = maxindex;
}

void dd_UniqueRows(dd_rowindex OV, long p, long r, dd_Amatrix A, long dmax, dd_rowset preferred, long *uniqrows)
{
 /* Select a subset of rows of A (with range [p, q] up to dimension dmax) by removing duplicates.
    When a row subset preferred is nonempty, those row indices in the set have priority.  If
    two priority rows define the same row vector, one is chosen.
    For a selected unique row i, OV[i] returns a new position of the unique row i. 
    For other nonuniqu row i, OV[i] returns a negative of the original row j dominating i.
    Thus the original contents of OV[p..r] will be rewritten.  Other components remain the same.
    *uniqrows returns the number of unique rows.
*/
  long i,iuniq,j;
  mytype *x;
  dd_boolean localdebug=dd_FALSE;
  
  if (p<=0 || p > r) goto _L99;
  iuniq=p; j=1;  /* the first unique row candidate */
  x=A[p-1];
  OV[p]=j;  /* tentative row index of the candidate */
  for (i=p+1;i<=r; i++){
    if (!dd_LexEqual(x,A[i-1],dmax)) {
      /* a new row vector found. */
      iuniq=i;
      j=j+1;
      OV[i]=j;    /* Tentatively register the row i.  */
      x=A[i-1];
    } else {
      /* rows are equal */
      if (set_member(i, preferred) && !set_member(iuniq, preferred)){
        OV[iuniq]=-i;  /* the row iuniq is dominated by the row i */
        iuniq=i;  /* the row i is preferred.  Change the candidate. */
        OV[i]=j;  /* the row i is tentatively registered. */
        x=A[i-1];
      } else {
        OV[i]=-iuniq;  /* the row iuniq is dominated by the row i */
      }
    }
  }
  *uniqrows=j;
  if (localdebug){
    printf("The number of unique rows are %ld\n with order vector",*uniqrows);
    for (i=p;i<=r; i++){
      printf(" %ld:%ld ",i,OV[i]);
    }
    printf("\n");
  }
  _L99:;
}

long dd_Partition(dd_rowindex OV, long p, long r, dd_Amatrix A, long dmax)
{
  mytype *x;
  long i,j,ovi;
  
  x=A[OV[p]-1];

  i=p-1;
  j=r+1;
  while (dd_TRUE){
    do{
      j--;
    } while (dd_LexLarger(A[OV[j]-1],x,dmax));
    do{
      i++;
    } while (dd_LexSmaller(A[OV[i]-1],x,dmax));
    if (i<j){
      ovi=OV[i];
      OV[i]=OV[j];
      OV[j]=ovi;
    }
    else{
      return j;
    }
  }
}

void dd_QuickSort(dd_rowindex OV, long p, long r, dd_Amatrix A, long dmax)
{
  long q;
  
  if (p < r){
    q = dd_Partition(OV, p, r, A, dmax);
    dd_QuickSort(OV, p, q, A, dmax);
    dd_QuickSort(OV, q+1, r, A, dmax);
  }
}


#ifndef RAND_MAX 
#define RAND_MAX 32767 
#endif

void dd_RandomPermutation(dd_rowindex OV, long t, unsigned int seed)
{
  long k,j,ovj;
  double u,xk,r,rand_max=(double) RAND_MAX;
  dd_boolean localdebug=dd_FALSE;

  srand(seed);
  for (j=t; j>1 ; j--) {
    r=rand();
    u=r/rand_max;
    xk=(double)(j*u +1);
    k=(long)xk;
    if (localdebug) fprintf(stderr,"u=%g, k=%ld, r=%g, randmax= %g\n",u,k,r,rand_max);
    ovj=OV[j];
    OV[j]=OV[k];
    OV[k]=ovj;
    if (localdebug) fprintf(stderr,"row %ld is exchanged with %ld\n",j,k); 
  }
}

void dd_ComputeRowOrderVector(dd_ConePtr cone)
{
  long i,itemp;

  cone->OrderVector[0]=0;
  switch (cone->HalfspaceOrder){
  case dd_MaxIndex:
    for(i=1; i<=cone->m; i++) cone->OrderVector[i]=cone->m-i+1;
    break;

  case dd_MinIndex: 
    for(i=1; i<=cone->m; i++) cone->OrderVector[i]=i;    
    break;

  case dd_LexMin: case dd_MinCutoff: case dd_MixCutoff: case dd_MaxCutoff:
    for(i=1; i<=cone->m; i++) cone->OrderVector[i]=i;
    dd_RandomPermutation(cone->OrderVector, cone->m, cone->rseed);
    dd_QuickSort(cone->OrderVector, 1, cone->m, cone->A, cone->d);
    break;

  case dd_LexMax:
    for(i=1; i<=cone->m; i++) cone->OrderVector[i]=i;
    dd_RandomPermutation(cone->OrderVector, cone->m, cone->rseed);
    dd_QuickSort(cone->OrderVector, 1, cone->m, cone->A, cone->d);
    for(i=1; i<=cone->m/2;i++){   /* just reverse the order */
      itemp=cone->OrderVector[i];
      cone->OrderVector[i]=cone->OrderVector[cone->m-i+1];
      cone->OrderVector[cone->m-i+1]=itemp;
    }
    break;

  case dd_RandomRow:
    for(i=1; i<=cone->m; i++) cone->OrderVector[i]=i;
    dd_RandomPermutation(cone->OrderVector, cone->m, cone->rseed);
    break;

  }
}

void dd_UpdateRowOrderVector(dd_ConePtr cone, dd_rowset PriorityRows)
/* Update the RowOrder vector to shift selected rows
in highest order.
*/
{
  dd_rowrange i,j,k,j1=0,oj=0;
  long rr;
  dd_boolean found, localdebug=dd_FALSE;
  
  if (dd_debug) localdebug=dd_TRUE;
  found=dd_TRUE;
  rr=set_card(PriorityRows);
  if (localdebug) set_fwrite(stderr,PriorityRows);
  for (i=1; i<=rr; i++){
    found=dd_FALSE;
    for (j=i; j<=cone->m && !found; j++){
      oj=cone->OrderVector[j];
      if (set_member(oj, PriorityRows)){
        found=dd_TRUE;
        if (localdebug) fprintf(stderr,"%ldth in sorted list (row %ld) is in PriorityRows\n", j, oj);
        j1=j;
      }
    }
    if (found){
      if (j1>i) {
        /* shift everything lower: ov[i]->cone->ov[i+1]..ov[j1-1]->cone->ov[j1] */
        for (k=j1; k>=i; k--) cone->OrderVector[k]=cone->OrderVector[k-1];
        cone->OrderVector[i]=oj;
        if (localdebug){
          fprintf(stderr,"OrderVector updated to:\n");
          for (j = 1; j <= cone->m; j++) fprintf(stderr," %2ld", cone->OrderVector[j]);
          fprintf(stderr,"\n");
        }
      }
    } else {
      fprintf(stderr,"UpdateRowOrder: Error.\n");
      goto _L99;
    }
  }
_L99:;
}

void dd_SelectPreorderedNext(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hh)
{
  dd_rowrange i,k;
  
  *hh=0;
  for (i=1; i<=cone->m && *hh==0; i++){
    k=cone->OrderVector[i];
    if (!set_member(k, excluded)) *hh=k ;
  }
}

void dd_SelectNextHalfspace(dd_ConePtr cone, dd_rowset excluded, dd_rowrange *hh)
{
  if (cone->PreOrderedRun){
    if (dd_debug) {
      fprintf(stderr,"debug dd_SelectNextHalfspace: Use PreorderNext\n");
    }
    dd_SelectPreorderedNext(cone, excluded, hh);
  }
  else {
    if (dd_debug) {
      fprintf(stderr,"debug dd_SelectNextHalfspace: Use DynamicOrderedNext\n");
    }

    switch (cone->HalfspaceOrder) {

    case dd_MaxIndex:
      dd_SelectNextHalfspace0(cone, excluded, hh);
      break;

    case dd_MinIndex:
      dd_SelectNextHalfspace1(cone, excluded, hh);
      break;

    case dd_MinCutoff:
      dd_SelectNextHalfspace2(cone, excluded, hh);
      break;

    case dd_MaxCutoff:
      dd_SelectNextHalfspace3(cone, excluded, hh);
      break;

    case dd_MixCutoff:
      dd_SelectNextHalfspace4(cone, excluded, hh);
      break;

    default:
      dd_SelectNextHalfspace0(cone, excluded, hh);
      break;
    }
  }
}

dd_boolean dd_Nonnegative(mytype val)
{
/*  if (val>=-dd_zero) return dd_TRUE;  */
  if (dd_cmp(val,dd_minuszero)>=0) return dd_TRUE;
  else return dd_FALSE;
}

dd_boolean dd_Nonpositive(mytype val)
{
/*  if (val<=dd_zero) return dd_TRUE;  */
  if (dd_cmp(val,dd_zero)<=0) return dd_TRUE;
  else return dd_FALSE;
}

dd_boolean dd_Positive(mytype val)
{
  return !dd_Nonpositive(val);
}

dd_boolean dd_Negative(mytype val)
{
  return !dd_Nonnegative(val);
}

dd_boolean dd_EqualToZero(mytype val)
{
  return (dd_Nonnegative(val) && dd_Nonpositive(val));
}

dd_boolean dd_Nonzero(mytype val)
{
  return (dd_Positive(val) || dd_Negative(val));
}

dd_boolean dd_Equal(mytype val1,mytype val2)
{
  return (!dd_Larger(val1,val2) && !dd_Smaller(val1,val2));
}

dd_boolean dd_Larger(mytype val1,mytype val2)
{
  mytype temp;
  dd_boolean answer;

  dd_init(temp);
  dd_sub(temp,val1, val2);
  answer=dd_Positive(temp);
  dd_clear(temp);
  return answer;
}

dd_boolean dd_Smaller(mytype val1,mytype val2)
{
  return dd_Larger(val2,val1);
}

void dd_abs(mytype absval, mytype val)
{
  if (dd_Negative(val)) dd_neg(absval,val);
  else dd_set(absval,val); 
}

void dd_LinearComb(mytype lc, mytype v1, mytype c1, mytype v2, mytype c2)
/*  lc := v1 * c1 + v2 * c2   */
{
  mytype temp;

  dd_init(temp);
  dd_mul(lc,v1,c1);
  dd_mul(temp,v2,c2); 
  dd_add(lc,lc,temp);
  dd_clear(temp);
}

void dd_InnerProduct(mytype prod, dd_colrange d, dd_Arow v1, dd_Arow v2)
{
  mytype temp;
  dd_colrange j;
  dd_boolean localdebug=dd_FALSE;

  dd_init(temp);
  dd_set_si(prod, 0);
  for (j = 0; j < d; j++){
    dd_mul(temp,v1[j],v2[j]); 
    dd_add(prod,prod,temp);
  }
  if (localdebug) {
    fprintf(stderr,"InnerProduct:\n"); 
    dd_WriteArow(stderr, v1, d);
    dd_WriteArow(stderr, v2, d);
    fprintf(stderr,"prod ="); 
    dd_WriteNumber(stderr, prod);
    fprintf(stderr,"\n");
  }
  
  dd_clear(temp);
}

/* end of cddcore.c */


