/*

EMBLEM and SLIPCASE

Copyright (c) 2013, Fabrizio Riguzzi and Elena Bellodi

This package uses the library cudd, see http://vlsi.colorado.edu/~fabio/CUDD/
for the relative license.

*/

#include "config.h"
#include "cudd_config.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#if HAVE_CUDD_CUDD_H
#include <cudd/cudd.h>
#elif HAVE_CUDD_H
#include "cudd.h"
#endif
#include "YapInterface.h"
#define LOGZERO log(0.000001)
#define CACHE_SLOTS 1
#define UNIQUE_SLOTS 1

typedef struct {
  int nVal, nRule;
  int firstBoolVar;
} variable;

typedef struct {
  DdNode *key;
  double value;
} rowel;

typedef struct {
  int cnt;
  rowel *row;
} tablerow;

tablerow *table;

static variable **vars_ex;
static int **bVar2mVar_ex;
static double *sigma;
static double ***eta;
static double ***eta_temp;
static double **arrayprob;
static int *rules;
static DdManager **mgr_ex;
static int *nVars_ex;
static int nRules;
double *nodes_probs_ex;
double **probs_ex;
static int *boolVars_ex;
tablerow *nodesB;
tablerow *nodesF;
int ex, cycle;
DdNode ***nodesToVisit;
int *NnodesToVisit;
double *example_prob;
static YAP_Bool ret_prob(void);
double Prob(DdNode *node, int comp_par);
static YAP_Bool end_bdd(void);
static YAP_Bool init_test(void);
static YAP_Bool add_var(void);
static YAP_Bool init(void);
static YAP_Bool end(void);
static YAP_Bool EM(void);
static YAP_Bool Q(void);
double ProbPath(DdNode *node, int comp_par, int nex);
static YAP_Bool rec_deref(void);
int indexMvar(DdNode *node);
void Forward(DdNode *node, int nex);
void GetForward(DdNode *node, double ForwProbPath);
void UpdateForward(DdNode *node, int nex);
double GetOutsideExpe(DdNode *root, double ex_prob, int nex);
void Maximization(void);
static double Expectation(DdNode **nodes_ex, int lenNodes);
void init_my_predicates(void);
FILE *open_file(char *filename, const char *mode);
tablerow *init_table(int varcnt);
double *get_value(tablerow *tab, DdNode *node);
void add_or_replace_node(tablerow *tab, DdNode *node, double value);
void add_node(tablerow *tab, DdNode *node, double value);
void destroy_table(tablerow *tab, int varcnt);

static YAP_Bool init(void) {
  int j, i;
  YAP_Term arg1, arg2, list;

  ex = 0;
  cycle = 0;
  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  nRules = YAP_IntOfTerm(arg1);

  vars_ex = NULL;
  nVars_ex = NULL;
  eta = (double ***)malloc(nRules * sizeof(double **));
  eta_temp = (double ***)malloc(nRules * sizeof(double **));
  rules = (int *)malloc(nRules * sizeof(int));
  arrayprob = (double **)malloc(nRules * sizeof(double *));
  probs_ex = NULL;
  bVar2mVar_ex = NULL;
  boolVars_ex = NULL;
  mgr_ex = NULL;
  nodes_probs_ex = NULL;
  list = arg2;
  for (j = 0; j < nRules; j++) {
    rules[j] = YAP_IntOfTerm(YAP_HeadOfTerm(list));
    list = YAP_TailOfTerm(list);
    eta[j] = (double **)malloc((rules[j] - 1) * sizeof(double *));
    eta_temp[j] = (double **)malloc((rules[j] - 1) * sizeof(double *));
    arrayprob[j] = (double *)malloc((rules[j] - 1) * sizeof(double));
    for (i = 0; i < rules[j] - 1; i++) {
      eta[j][i] = (double *)malloc(2 * sizeof(double));
      eta_temp[j][i] = (double *)malloc(2 * sizeof(double));
    }
  }
  return 1;
}

static YAP_Bool init_bdd(void) {
  mgr_ex = (DdManager **)realloc(mgr_ex, (ex + 1) * sizeof(DdManager *));
  mgr_ex[ex] = Cudd_Init(0, 0, UNIQUE_SLOTS, CACHE_SLOTS, 5120);
  Cudd_AutodynEnable(mgr_ex[ex], CUDD_REORDER_GROUP_SIFT);
  Cudd_SetMaxCacheHard(mgr_ex[ex], 0);
  Cudd_SetLooseUpTo(mgr_ex[ex], 0);
  Cudd_SetMinHit(mgr_ex[ex], 15);

  bVar2mVar_ex = (int **)realloc(bVar2mVar_ex, (ex + 1) * sizeof(int *));
  bVar2mVar_ex[ex] = NULL;

  vars_ex = (variable **)realloc(vars_ex, (ex + 1) * sizeof(variable *));
  vars_ex[ex] = NULL;

  nVars_ex = (int *)realloc(nVars_ex, (ex + 1) * sizeof(int));
  nVars_ex[ex] = 0;

  probs_ex = (double **)realloc(probs_ex, (ex + 1) * sizeof(double *));
  probs_ex[ex] = NULL;

  boolVars_ex = (int *)realloc(boolVars_ex, (ex + 1) * sizeof(int));
  boolVars_ex[ex] = 0;

  return 1;
}

static YAP_Bool end_bdd(void) {

  ex = ex + 1;
  return 1;
}

static YAP_Bool init_test(void) {
  YAP_Term arg1;

  arg1 = YAP_ARG1;
  nRules = YAP_IntOfTerm(arg1);

  ex = 0;
  mgr_ex = (DdManager **)malloc((ex + 1) * sizeof(DdManager *));
  mgr_ex[ex] = Cudd_Init(0, 0, UNIQUE_SLOTS, CACHE_SLOTS, 5120);
  Cudd_AutodynEnable(mgr_ex[ex], CUDD_REORDER_GROUP_SIFT);
  Cudd_SetMaxCacheHard(mgr_ex[ex], 0);
  Cudd_SetLooseUpTo(mgr_ex[ex], 0);
  Cudd_SetMinHit(mgr_ex[ex], 15);

  bVar2mVar_ex = (int **)malloc((ex + 1) * sizeof(int *));
  bVar2mVar_ex[ex] = NULL;

  vars_ex = (variable **)malloc((ex + 1) * sizeof(variable *));
  vars_ex[ex] = NULL;

  nVars_ex = (int *)malloc((ex + 1) * sizeof(int));
  nVars_ex[ex] = 0;

  probs_ex = (double **)malloc((ex + 1) * sizeof(double *));
  probs_ex[ex] = NULL;

  boolVars_ex = (int *)malloc((ex + 1) * sizeof(int));
  boolVars_ex[ex] = 0;

  rules = (int *)malloc(nRules * sizeof(int));

  return 1;
}

static YAP_Bool end_test(void) {
  free(bVar2mVar_ex[ex]);
  free(vars_ex[ex]);
  Cudd_Quit(mgr_ex[ex]);
  free(probs_ex[ex]);
  free(rules);
  free(mgr_ex);
  free(bVar2mVar_ex);
  free(vars_ex);
  free(probs_ex);
  free(nVars_ex);
  free(boolVars_ex);

  return 1;
}

static double Expectation(DdNode **nodes_ex, int lenNodes) {
  int i;
  double rootProb, CLL = 0;

  for (i = 0; i < lenNodes; i++) {
    if (!Cudd_IsConstant(nodes_ex[i])) {
      nodesB = init_table(boolVars_ex[i]);
      nodesF = init_table(boolVars_ex[i]);

      Forward(nodes_ex[i], i);
      rootProb = GetOutsideExpe(nodes_ex[i], example_prob[i], i);

      if (rootProb <= 0.0)
        CLL = CLL + LOGZERO * example_prob[i];
      else
        CLL = CLL + log(rootProb) * example_prob[i];

      nodes_probs_ex[i] = rootProb;
      destroy_table(nodesB, boolVars_ex[i]);
      destroy_table(nodesF, boolVars_ex[i]);
    } else if (nodes_ex[i] == Cudd_ReadLogicZero(mgr_ex[i])) {
      CLL = CLL + LOGZERO * example_prob[i];
      nodes_probs_ex[i] = 0.0;
    } else
      nodes_probs_ex[i] = 1.0;
  }
  return CLL;
}

static YAP_Bool end(void) {
  int r, i;

  for (i = 0; i < ex; i++) {
    Cudd_Quit(mgr_ex[i]);
    free(bVar2mVar_ex[i]);
    free(vars_ex[i]);
    free(probs_ex[i]);
    fflush(stdout);
  }

  free(mgr_ex);
  free(bVar2mVar_ex);
  free(vars_ex);
  free(probs_ex);
  free(nVars_ex);
  free(boolVars_ex);
  for (r = 0; r < nRules; r++) {
    for (i = 0; i < rules[r] - 1; i++) {
      free(eta[r][i]);
      free(eta_temp[r][i]);
    }
    free(eta[r]);
    free(eta_temp[r]);
  }
  free(eta);
  free(eta_temp);
  for (r = 0; r < nRules; r++) {
    free(arrayprob[r]);
  }
  free(arrayprob);
  free(rules);

  return 1;
}

static YAP_Bool ret_prob(void) {
  YAP_Term arg1, arg2, out;
  DdNode *node;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  node = (DdNode *)YAP_IntOfTerm(arg1);

  if (!Cudd_IsConstant(node)) {
    table = init_table(boolVars_ex[ex]);
    out = YAP_MkFloatTerm(Prob(node, 0));
    destroy_table(table, boolVars_ex[ex]);
  } else {
    if (node == Cudd_ReadOne(mgr_ex[ex]))
      out = YAP_MkFloatTerm(1.0);
    else
      out = YAP_MkFloatTerm(0.0);
  }

  return (YAP_Unify(out, arg2));
}

double Prob(DdNode *node, int comp_par)
/* compute the probability of the expression rooted at node.
table is used to store nodeB for which the probability has alread been computed
so that it is not recomputed
 */
{
  int index, mVarIndex, comp;
  variable v;
  double res;
  double p, pt, pf, BChild0, BChild1;
  double *value_p;
  DdNode *nodekey, *T, *F;

  comp = Cudd_IsComplement(node);
  comp = (comp && !comp_par) || (!comp && comp_par);
  if (Cudd_IsConstant(node)) {
    if (comp)
      return 0.0;
    else
      return 1.0;
  } else {
    nodekey = Cudd_Regular(node);
    value_p = get_value(table, nodekey);
    if (value_p != NULL)
      return *value_p;
    else {
      index = Cudd_NodeReadIndex(node); // Returns the index of the node. The
                                        // node pointer can be either regular or
                                        // complemented.
      // The index field holds the name of the variable that labels the node.
      // The index of a variable is a permanent attribute that reflects the
      // order of creation.
      p = probs_ex[ex][index];
      T = Cudd_T(node);
      F = Cudd_E(node);
      pf = Prob(F, comp);
      pt = Prob(T, comp);
      BChild0 = pf * (1 - p);
      BChild1 = pt * p;
      mVarIndex = bVar2mVar_ex[ex][index];
      v = vars_ex[ex][mVarIndex];
      index = v.firstBoolVar;
      res = BChild0 + BChild1;
      add_node(table, nodekey, res);
      return res;
    }
  }
}

static YAP_Bool add_var(void) {
  YAP_Term arg1, arg2, arg3, arg4, out, probTerm, probTerm_temp;
  variable *v;
  int i;
  double p, p0;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  arg4 = YAP_ARG4;
  nVars_ex[ex] = nVars_ex[ex] + 1;
  vars_ex[ex] =
      (variable *)realloc(vars_ex[ex], nVars_ex[ex] * sizeof(variable));

  v = &vars_ex[ex][nVars_ex[ex] - 1];
  v->nVal = YAP_IntOfTerm(arg1);
  v->nRule = YAP_IntOfTerm(arg3);
  v->firstBoolVar = boolVars_ex[ex];
  probs_ex[ex] = (double *)realloc(
      probs_ex[ex], (((boolVars_ex[ex] + v->nVal - 1) * sizeof(double))));
  bVar2mVar_ex[ex] = (int *)realloc(
      bVar2mVar_ex[ex], ((boolVars_ex[ex] + v->nVal - 1) * sizeof(int)));
  probTerm = arg2;
  p0 = 1;
  for (i = 0; i < v->nVal - 1; i++) {
    //node = Cudd_bddIthVar(mgr_ex[ex], boolVars_ex[ex] + i);
    p = YAP_FloatOfTerm(YAP_HeadOfTerm(probTerm));
    bVar2mVar_ex[ex][boolVars_ex[ex] + i] = nVars_ex[ex] - 1;
    probs_ex[ex][boolVars_ex[ex] + i] = p / p0;
    probTerm_temp = YAP_TailOfTerm(probTerm);
    probTerm = probTerm_temp;
    p0 = p0 * (1 - p / p0);
  }
  boolVars_ex[ex] = boolVars_ex[ex] + v->nVal - 1;
  rules[v->nRule] = v->nVal;
  out = YAP_MkIntTerm((YAP_Int)nVars_ex[ex] - 1);
  return YAP_Unify(out, arg4);
}

static YAP_Bool equality(void) {
  YAP_Term arg1, arg2, arg3, out;
  int varIndex;
  int value;
  int i;
  variable v;
  DdNode *node, *tmp, *var;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  varIndex = YAP_IntOfTerm(arg1);
  value = YAP_IntOfTerm(arg2);
  v = vars_ex[ex][varIndex];
  i = v.firstBoolVar;
  tmp = Cudd_ReadOne(mgr_ex[ex]);
  Cudd_Ref(tmp);
  node = NULL;
  for (i = v.firstBoolVar; i < v.firstBoolVar + value; i++) {
    var = Cudd_bddIthVar(mgr_ex[ex], i);
    node = Cudd_bddAnd(mgr_ex[ex], tmp, Cudd_Not(var));
    Cudd_Ref(node);
    Cudd_RecursiveDeref(mgr_ex[ex], tmp);
    tmp = node;
  }
  if (!(value == v.nVal - 1)) {
    var = Cudd_bddIthVar(mgr_ex[ex], v.firstBoolVar + value);
    node = Cudd_bddAnd(mgr_ex[ex], tmp, var);
    Cudd_Ref(node);
    Cudd_RecursiveDeref(mgr_ex[ex], tmp);
  }
  out = YAP_MkIntTerm((YAP_Int)node);
  return (YAP_Unify(out, arg3));
}

static YAP_Bool one(void) {
  YAP_Term arg, out;
  DdNode *node;

  arg = YAP_ARG1;
  node = Cudd_ReadOne(mgr_ex[ex]);
  Cudd_Ref(node);
  out = YAP_MkIntTerm((YAP_Int)node);
  return (YAP_Unify(out, arg));
}

static YAP_Bool zero(void) {
  YAP_Term arg, out;
  DdNode *node;

  arg = YAP_ARG1;
  node = Cudd_ReadLogicZero(mgr_ex[ex]);
  Cudd_Ref(node);
  out = YAP_MkIntTerm((YAP_Int)node);
  return (YAP_Unify(out, arg));
}

static YAP_Bool bdd_not(void) {
  YAP_Term arg1, arg2, out;
  DdNode *node;
  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;

  node = (DdNode *)YAP_IntOfTerm(arg1);
  node = Cudd_Not(node);
  out = YAP_MkIntTerm((YAP_Int)node);
  return (YAP_Unify(out, arg2));
}

static YAP_Bool and (void) {
  YAP_Term arg1, arg2, arg3, out;
  DdNode *node1, *node2, *nodeout;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  node1 = (DdNode *)YAP_IntOfTerm(arg1);
  node2 = (DdNode *)YAP_IntOfTerm(arg2);
  nodeout = Cudd_bddAnd(mgr_ex[ex], node1, node2);
  Cudd_Ref(nodeout);
  out = YAP_MkIntTerm((YAP_Int)nodeout);
  return (YAP_Unify(out, arg3));
}

static YAP_Bool or (void) {
  YAP_Term arg1, arg2, arg3, out;
  DdNode *node1, *node2, *nodeout;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  node1 = (DdNode *)YAP_IntOfTerm(arg1);
  node2 = (DdNode *)YAP_IntOfTerm(arg2);
  nodeout = Cudd_bddOr(mgr_ex[ex], node1, node2);
  Cudd_Ref(nodeout);
  out = YAP_MkIntTerm((YAP_Int)nodeout);
  return (YAP_Unify(out, arg3));
}

static YAP_Bool garbage_collect(void) {
  YAP_Term arg1, arg2, out;
  YAP_Int nodes, clearCache;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  clearCache = YAP_IntOfTerm(arg1);
  nodes = (YAP_Int)cuddGarbageCollect(mgr_ex[ex], clearCache);
  out = YAP_MkIntTerm(nodes);
  return (YAP_Unify(out, arg2));
}

static YAP_Bool bdd_to_add(void) {
  YAP_Term arg1, arg2, out;
  DdNode *node1, *node2;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  node1 = (DdNode *)YAP_IntOfTerm(arg1);
  node2 = Cudd_BddToAdd(mgr_ex[ex], node1);
  out = YAP_MkIntTerm((YAP_Int)node2);
  return (YAP_Unify(out, arg2));
}

static YAP_Bool create_dot(void) {
  const char *onames[] = {"Out"};
  char **inames;
  DdNode *array[1];
  YAP_Term arg1, arg2;
  int i, b, index;
  variable v;
  char numberVar[10], numberBit[10], filename[1000];
  FILE *file;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;

  YAP_StringToBuffer(arg2, filename, 1000);
  inames = (char **)malloc(sizeof(char *) * (boolVars_ex[ex]));
  index = 0;
  for (i = 0; i < nVars_ex[ex]; i++) {
    v = vars_ex[ex][i];
    for (b = 0; b < v.nVal - 1; b++) {
      inames[b + index] = (char *)malloc(sizeof(char) * 20);
      strcpy(inames[b + index], "X");
      sprintf(numberVar, "%d", i);
      strcat(inames[b + index], numberVar);
      strcat(inames[b + index], "_");
      sprintf(numberBit, "%d", b);
      strcat(inames[b + index], numberBit);
    }
    index = index + v.nVal - 1;
  }
  array[0] = (DdNode *)YAP_IntOfTerm(arg1);
  file = open_file(filename, "w");
  Cudd_DumpDot(mgr_ex[ex], 1, array, (const char **)inames, onames, file);
  fclose(file);
  index = 0;
  for (i = 0; i < nVars_ex[ex]; i++) {
    v = vars_ex[ex][i];
    for (b = 0; b < v.nVal - 1; b++) {
      free(inames[b + index]);
    }
    index = index + v.nVal - 1;
  }
  free(inames);
  return 1;
}

static YAP_Bool rec_deref(void) {
  YAP_Term arg1;
  DdNode *node;

  arg1 = YAP_ARG1;
  node = (DdNode *)YAP_IntOfTerm(arg1);
  Cudd_RecursiveDeref(mgr_ex[ex], node);
  return 1;
}

double ProbPath(DdNode *node, int comp_par, int nex) {
  int index, mVarIndex, comp, pos, position, boolVarIndex;
  variable v;
  double res;
  double value, p, pt, pf, BChild0, BChild1, e0, e1;
  double *value_p, **eta_rule;
  DdNode *nodekey, *T, *F;

  comp = Cudd_IsComplement(node);
  comp = (comp && !comp_par) || (!comp && comp_par);
  if (Cudd_IsConstant(node)) {
    value = Cudd_V(node);
    if (comp) {
      return 0.0;
    } else {
      return 1.0;
    }
  } else {
    nodekey = Cudd_Regular(node);
    value_p = get_value(nodesB, nodekey);
    if (value_p != NULL) {
      return *value_p;
    } else {
      index = Cudd_NodeReadIndex(node);
      p = probs_ex[nex][index];
      T = Cudd_T(node);
      F = Cudd_E(node);
      pf = ProbPath(F, comp, nex);
      pt = ProbPath(T, comp, nex);
      BChild0 = pf * (1 - p);
      BChild1 = pt * p;
      value_p = get_value(nodesF, nodekey);
      e0 = (*value_p) * BChild0;
      e1 = (*value_p) * BChild1;
      mVarIndex = bVar2mVar_ex[nex][index];
      v = vars_ex[nex][mVarIndex];
      pos = index - v.firstBoolVar;
      eta_rule = eta_temp[v.nRule];
      eta_rule[pos][0] = eta_rule[pos][0] + e0;
      eta_rule[pos][1] = eta_rule[pos][1] + e1;
      res = BChild0 + BChild1;
      add_node(nodesB, nodekey, res);
      position = Cudd_ReadPerm(mgr_ex[nex], index);
      position = position + 1;
      boolVarIndex = Cudd_ReadInvPerm(
          mgr_ex[nex], position); // Returns the index of the variable currently
                                  // in the i-th position of the order.
      if (position < boolVars_ex[nex]) {
        sigma[position] = sigma[position] + e0 + e1;
      }
      if (!Cudd_IsConstant(T)) {
        index = Cudd_NodeReadIndex(T);
        position = Cudd_ReadPerm(mgr_ex[nex], index);
        sigma[position] = sigma[position] - e1;
      }

      if (!Cudd_IsConstant(F)) {
        index = Cudd_NodeReadIndex(F);
        position = Cudd_ReadPerm(mgr_ex[nex], index);
        sigma[position] = sigma[position] - e0;
      }

      return res;
    }
  }
}

void Forward(DdNode *root, int nex) {
  int i, j;

  if (boolVars_ex[nex]) {
    nodesToVisit = (DdNode ***)malloc(sizeof(DdNode **) * boolVars_ex[nex]);
    NnodesToVisit = (int *)malloc(sizeof(int) * boolVars_ex[nex]);
    nodesToVisit[0] = (DdNode **)malloc(sizeof(DdNode *));
    nodesToVisit[0][0] = root;
    NnodesToVisit[0] = 1;
    for (i = 1; i < boolVars_ex[nex]; i++) {
      nodesToVisit[i] = NULL;
      NnodesToVisit[i] = 0;
    }
    add_node(nodesF, Cudd_Regular(root), 1);
    for (i = 0; i < boolVars_ex[nex]; i++) {
      for (j = 0; j < NnodesToVisit[i]; j++)
        UpdateForward(nodesToVisit[i][j], nex);
    }
    for (i = 0; i < boolVars_ex[nex]; i++) {
      free(nodesToVisit[i]);
    }
    free(nodesToVisit);
    free(NnodesToVisit);
  } else {
    add_node(nodesF, Cudd_Regular(root), 1);
  }
}

void UpdateForward(DdNode *node, int nex) {
  int index, position, mVarIndex;
  DdNode *T, *E, *nodereg;
  variable v;
  double *value_p, *value_p_T, *value_p_F, p;

  if (Cudd_IsConstant(node)) {
    return;
  } else {
    index = Cudd_NodeReadIndex(node);
    mVarIndex = bVar2mVar_ex[nex][index];
    v = vars_ex[nex][mVarIndex];
    p = probs_ex[nex][index];
    nodereg = Cudd_Regular(node);
    value_p = get_value(nodesF, nodereg);
    if (value_p == NULL) {
      printf("Error\n");
      return;
    } else {
      T = Cudd_T(node);
      E = Cudd_E(node);
      if (!Cudd_IsConstant(T)) {
        value_p_T = get_value(nodesF, T);
        if (value_p_T != NULL) {
          *value_p_T = *value_p_T + *value_p * p;
        } else {
          add_or_replace_node(nodesF, Cudd_Regular(T), *value_p * p);
          index = Cudd_NodeReadIndex(T);
          position = Cudd_ReadPerm(mgr_ex[nex], index);
          nodesToVisit[position] = (DdNode **)realloc(
              nodesToVisit[position],
              (NnodesToVisit[position] + 1) * sizeof(DdNode *));
          nodesToVisit[position][NnodesToVisit[position]] = T;
          NnodesToVisit[position] = NnodesToVisit[position] + 1;
        }
      }
      if (!Cudd_IsConstant(E)) {
        value_p_F = get_value(nodesF, Cudd_Regular(E));

        if (value_p_F != NULL) {
          *value_p_F = *value_p_F + *value_p * (1 - p);
        } else {
          add_or_replace_node(nodesF, Cudd_Regular(E), *value_p * (1 - p));
          index = Cudd_NodeReadIndex(E);
          position = Cudd_ReadPerm(mgr_ex[nex], index);
          nodesToVisit[position] = (DdNode **)realloc(
              nodesToVisit[position],
              (NnodesToVisit[position] + 1) * sizeof(DdNode *));
          nodesToVisit[position][NnodesToVisit[position]] = E;
          NnodesToVisit[position] = NnodesToVisit[position] + 1;
        }
      }
      return;
    }
  }
}

int indexMvar(DdNode *node) {
  int index, mVarIndex;

  index = Cudd_NodeReadIndex(node);
  mVarIndex = bVar2mVar_ex[ex][index];
  return mVarIndex;
}

double GetOutsideExpe(DdNode *root, double ex_prob, int nex) {
  int i, j, mVarIndex, bVarIndex;
  double **eta_rule;
  double theta, rootProb, T = 0;

  sigma = (double *)malloc(boolVars_ex[nex] * sizeof(double));

  for (j = 0; j < boolVars_ex[nex]; j++) {
    sigma[j] = 0;
  }
  for (j = 0; j < nRules; j++) {
    for (i = 0; i < rules[j] - 1; i++) {
      eta_temp[j][i][0] = 0;
      eta_temp[j][i][1] = 0;
    }
  }
  rootProb = ProbPath(root, 0, nex);
  if (rootProb > 0.0) {
    for (j = 0; j < boolVars_ex[nex]; j++) {
      T += sigma[j];
      bVarIndex = Cudd_ReadInvPerm(mgr_ex[nex], j);
      if (bVarIndex == -1) {
        bVarIndex = j;
      }

      mVarIndex = bVar2mVar_ex[nex][bVarIndex];
      eta_rule = eta_temp[vars_ex[nex][mVarIndex].nRule];
      for (i = 0; i < vars_ex[nex][mVarIndex].nVal - 1; i++) {
        theta = probs_ex[nex][bVarIndex];
        eta_rule[i][0] = eta_rule[i][0] + T * (1 - theta);
        eta_rule[i][1] = eta_rule[i][1] + T * theta;
      }
    }

    for (j = 0; j < nRules; j++) {
      for (i = 0; i < rules[j] - 1; i++) {
        eta[j][i][0] = eta[j][i][0] + eta_temp[j][i][0] * ex_prob / rootProb;
        eta[j][i][1] = eta[j][i][1] + eta_temp[j][i][1] * ex_prob / rootProb;
      }
    }
  }
  free(sigma);
  return rootProb;
}

void Maximization(void) {
  int r, i, j, e;
  double sum = 0;
  double *probs_rule, **eta_rule;

  for (r = 0; r < nRules; r++) {
    eta_rule = eta[r];
    for (i = 0; i < rules[r] - 1; i++) {
      sum = (eta_rule[i][0] + eta_rule[i][1]);
      if (sum == 0.0) {
        arrayprob[r][i] = 0;
      } else
        arrayprob[r][i] = eta_rule[i][1] / sum;
    }
  }

  for (e = 0; e < ex; e++) {
    for (j = 0; j < nVars_ex[e]; j++) {
      r = vars_ex[e][j].nRule;
      probs_rule = arrayprob[r];
      for (i = 0; i < rules[r] - 1; i++) {
        probs_ex[e][vars_ex[e][j].firstBoolVar + i] = probs_rule[i];
      }
    }
  }
}

static YAP_Bool randomize(void) {
  int i, j, e, rule;
  double *theta, p0;
  double pmass, par;
  double **Theta_rules;

  Theta_rules = (double **)malloc(nRules * sizeof(double *));

  for (j = 0; j < nRules; j++) {
    Theta_rules[j] = (double *)malloc(rules[j] * sizeof(double));
  }

  for (j = 0; j < nRules; j++) {
    theta = Theta_rules[j];
    pmass = 0;
    for (i = 0; i < rules[j] - 1; i++) {
      par = ((double)rand()) / RAND_MAX * (1 - pmass);
      pmass = pmass + par;
      theta[i] = par;
    }
    theta[rules[j] - 1] = 1 - pmass;
  }
  for (e = 0; e < ex; e++) {
    for (j = 0; j < nVars_ex[e]; j++) {
      rule = vars_ex[e][j].nRule;
      theta = Theta_rules[rule];
      p0 = 1;
      for (i = 0; i < vars_ex[e][j].nVal - 1; i++) {
        probs_ex[e][vars_ex[e][j].firstBoolVar + i] = theta[i] / p0;
        p0 = p0 * (1 - theta[i] / p0);
      }
    }
  }
  for (j = 0; j < nRules; j++) {
    free(Theta_rules[j]);
  }
  free(Theta_rules);
  return 1;
}

static YAP_Bool EM(void) {
  YAP_Term arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, out1, out2, out3,
      nodesTerm, ruleTerm, tail, pair, compoundTerm;
  DdNode *node1, **nodes_ex;
  int r, lenNodes, i, iter;
  long iter1;
  double CLL0 = -2.2 * pow(10, 10); //-inf
  double CLL1 = -1.7 * pow(10, 8);  //+inf
  double p, p0, **eta_rule, ea, er;
  double ratio, diff;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  arg4 = YAP_ARG4;
  arg5 = YAP_ARG5;
  arg6 = YAP_ARG6;
  arg7 = YAP_ARG7;
  arg8 = YAP_ARG8;

  nodesTerm = arg1;
  ea = YAP_FloatOfTerm(arg2);
  er = YAP_FloatOfTerm(arg3);
  lenNodes = YAP_IntOfTerm(arg4);
  iter = YAP_IntOfTerm(arg5);

  nodes_ex = (DdNode **)malloc(lenNodes * sizeof(DdNode *));
  nodes_probs_ex = (double *)malloc(lenNodes * sizeof(double));
  example_prob = (double *)malloc(lenNodes * sizeof(double));

  for (i = 0; i < lenNodes; i++) {
    pair = YAP_HeadOfTerm(nodesTerm);
    node1 = (DdNode *)YAP_IntOfTerm(YAP_HeadOfTerm(pair));
    nodes_ex[i] = node1;
    pair = YAP_TailOfTerm(pair);
    example_prob[i] = YAP_FloatOfTerm(YAP_HeadOfTerm(pair));
    nodesTerm = YAP_TailOfTerm(nodesTerm);
  }
  diff = CLL1 - CLL0;
  ratio = diff / fabs(CLL0);
  if (iter == -1)
    iter1 = 2147000000;
  else
    iter1 = iter;

  while ((diff > ea) && (ratio > er) && (cycle < iter1)) {
    cycle++;
    for (r = 0; r < nRules; r++) {
      for (i = 0; i < rules[r] - 1; i++) {
        eta_rule = eta[r];
        eta_rule[i][0] = 0;
        eta_rule[i][1] = 0;
      }
    }
    CLL0 = CLL1;
    CLL1 = Expectation(nodes_ex, lenNodes);
    Maximization();
    diff = CLL1 - CLL0;
    ratio = diff / fabs(CLL0);
  }
  out2 = YAP_TermNil();
  for (r = 0; r < nRules; r++) {
    tail = YAP_TermNil();
    p0 = 1;
    for (i = 0; i < rules[r] - 1; i++) {
      p = arrayprob[r][i] * p0;
      tail = YAP_MkPairTerm(YAP_MkFloatTerm(p), tail);
      p0 = p0 * (1 - arrayprob[r][i]);
    }
    tail = YAP_MkPairTerm(YAP_MkFloatTerm(p0), tail);
    ruleTerm = YAP_MkIntTerm(r);
    compoundTerm =
        YAP_MkPairTerm(ruleTerm, YAP_MkPairTerm(tail, YAP_TermNil()));
    out2 = YAP_MkPairTerm(compoundTerm, out2);
  }
  out3 = YAP_TermNil();
  for (i = 0; i < lenNodes; i++) {
    out3 = YAP_MkPairTerm(YAP_MkFloatTerm(nodes_probs_ex[i]), out3);
  }
  YAP_Unify(out3, arg8);

  out1 = YAP_MkFloatTerm(CLL1);
  YAP_Unify(out1, arg6);
  free(nodes_ex);
  free(example_prob);
  free(nodes_probs_ex);

  return (YAP_Unify(out2, arg7));
}

static YAP_Bool Q(void) {
  YAP_Term arg1, arg2, arg3, arg4, out, out1, term, nodesTerm, ruleTerm, tail,
      pair, compoundTerm;
  DdNode *node1, **nodes_ex;
  int r, lenNodes, i;
  double p1, p0, **eta_rule, CLL;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  arg3 = YAP_ARG3;
  arg4 = YAP_ARG4;

  nodesTerm = arg1;
  lenNodes = YAP_IntOfTerm(arg2);

  nodes_ex = (DdNode **)malloc(lenNodes * sizeof(DdNode *));
  example_prob = (double *)malloc(lenNodes * sizeof(double));

  for (i = 0; i < lenNodes; i++) {
    pair = YAP_HeadOfTerm(nodesTerm);
    node1 = (DdNode *)YAP_IntOfTerm(YAP_HeadOfTerm(pair));
    nodes_ex[i] = node1;
    pair = YAP_TailOfTerm(pair);
    example_prob[i] = YAP_FloatOfTerm(YAP_HeadOfTerm(pair));
    nodesTerm = YAP_TailOfTerm(nodesTerm);
  }

  for (r = 0; r < nRules; r++) {
    for (i = 0; i < rules[r] - 1; i++) {
      eta_rule = eta[r];
      eta_rule[i][0] = 0;
      eta_rule[i][1] = 0;
    }
  }
  CLL = Expectation(nodes_ex, lenNodes);
  out = YAP_TermNil();

  for (r = 0; r < nRules; r++) {
    tail = YAP_TermNil();
    eta_rule = eta[r];
    for (i = 0; i < rules[r] - 1; i++) {
      p0 = eta_rule[i][0];
      p1 = eta_rule[i][1];
      term = YAP_MkPairTerm(YAP_MkFloatTerm(p0),
                            YAP_MkPairTerm(YAP_MkFloatTerm(p1), YAP_TermNil()));
      tail = YAP_MkPairTerm(term, tail);
    }

    ruleTerm = YAP_MkIntTerm(r);
    compoundTerm =
        YAP_MkPairTerm(ruleTerm, YAP_MkPairTerm(tail, YAP_TermNil()));
    out = YAP_MkPairTerm(compoundTerm, out);
  }

  free(nodes_ex);
  free(example_prob);

  out1 = YAP_MkFloatTerm(CLL);
  YAP_Unify(out1, arg4);
  return (YAP_Unify(out, arg3));
}

static YAP_Bool paths_to_non_zero(void) {
  double paths;
  YAP_Term arg1, arg2, out;
  DdNode *node;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  node = (DdNode *)YAP_IntOfTerm(arg1);
  paths = Cudd_CountPathsToNonZero(node);
  out = YAP_MkFloatTerm(paths);
  return (YAP_Unify(out, arg2));
}

static YAP_Bool paths(void) {
  double paths;
  YAP_Term arg1, arg2, out;
  DdNode *node;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  node = (DdNode *)YAP_IntOfTerm(arg1);
  paths = Cudd_CountPath(node);
  out = YAP_MkFloatTerm(paths);
  return (YAP_Unify(out, arg2));
}

static YAP_Bool dag_size(void) {
  int size;
  YAP_Term arg1, arg2, out;
  DdNode *node;

  arg1 = YAP_ARG1;
  arg2 = YAP_ARG2;
  node = (DdNode *)YAP_IntOfTerm(arg1);
  size = Cudd_DagSize(node);
  out = YAP_MkIntTerm(size);
  return (YAP_Unify(out, arg2));
}

void init_my_predicates()
/* function required by YAP for intitializing the predicates defined by a C
   function*/
{
  srand(10);

  YAP_UserCPredicate("init", init, 2);
  YAP_UserCPredicate("init_bdd", init_bdd, 0);
  YAP_UserCPredicate("end", end, 0);
  YAP_UserCPredicate("end_bdd", end_bdd, 0);
  YAP_UserCPredicate("add_var", add_var, 4);
  YAP_UserCPredicate("equality", equality, 3);
  YAP_UserCPredicate("and", and, 3);
  YAP_UserCPredicate("one", one, 1);
  YAP_UserCPredicate("zero", zero, 1);
  YAP_UserCPredicate("or", or, 3);
  YAP_UserCPredicate("bdd_not", bdd_not, 2);
  YAP_UserCPredicate("create_dot", create_dot, 2);
  YAP_UserCPredicate("init_test", init_test, 1);
  YAP_UserCPredicate("end_test", end_test, 0);
  YAP_UserCPredicate("ret_prob", ret_prob, 2);
  YAP_UserCPredicate("em", EM, 8);
  YAP_UserCPredicate("q", Q, 4);
  YAP_UserCPredicate("randomize", randomize, 0);
  YAP_UserCPredicate("deref", rec_deref, 1);
  YAP_UserCPredicate("garbage_collect", garbage_collect, 2);
  YAP_UserCPredicate("bdd_to_add", bdd_to_add, 2);
  YAP_UserCPredicate("paths_to_non_zero", paths_to_non_zero, 2);
  YAP_UserCPredicate("paths", paths, 2);
  YAP_UserCPredicate("dag_size", dag_size, 2);
}
FILE *open_file(char *filename, const char *mode)
/* opens a file */
{
  FILE *fp;

  if ((fp = fopen(filename, mode)) == NULL) {
    perror(filename);
    exit(1);
  }
  return fp;
}

tablerow *init_table(int varcnt) {
  int i;
  tablerow *tab;

  tab = (tablerow *)malloc(sizeof(rowel) * varcnt);
  for (i = 0; i < varcnt; i++) {
    tab[i].row = NULL;
    tab[i].cnt = 0;
  }
  return tab;
}

void add_node(tablerow *tab, DdNode *node, double value) {
  int index = Cudd_NodeReadIndex(node);

  tab[index].row =
      (rowel *)realloc(tab[index].row, (tab[index].cnt + 1) * sizeof(rowel));
  tab[index].row[tab[index].cnt].key = node;
  tab[index].row[tab[index].cnt].value = value;
  tab[index].cnt += 1;
}

void add_or_replace_node(tablerow *tab, DdNode *node, double value) {
  int i;
  int index = Cudd_NodeReadIndex(node);
  for (i = 0; i < tab[index].cnt; i++) {
    if (tab[index].row[i].key == node) {
      tab[index].row[i].value = value;
      return;
    }
  }
  tab[index].row =
      (rowel *)realloc(tab[index].row, (tab[index].cnt + 1) * sizeof(rowel));
  tab[index].row[tab[index].cnt].key = node;
  tab[index].row[tab[index].cnt].value = value;
  tab[index].cnt += 1;
}

double *get_value(tablerow *tab, DdNode *node) {
  int i;
  int index = Cudd_NodeReadIndex(node);

  for (i = 0; i < tab[index].cnt; i++) {
    if (tab[index].row[i].key == node) {
      return &tab[index].row[i].value;
    }
  }
  return NULL;
}

void destroy_table(tablerow *tab, int varcnt) {
  int i;

  for (i = 0; i < varcnt; i++) {
    free(tab[i].row);
  }
  free(tab);
}