WSTester updated to work plus hopefully all the other changes that need to go into...
[jabaws.git] / binaries / src / ViennaRNA / lib / 2Dfold.c
diff --git a/binaries/src/ViennaRNA/lib/2Dfold.c b/binaries/src/ViennaRNA/lib/2Dfold.c
new file mode 100644 (file)
index 0000000..3a4233f
--- /dev/null
@@ -0,0 +1,4024 @@
+/*
+      minimum free energy
+      RNA secondary structure with
+      basepair distance d_1 to reference structure 1 and distance d_2 to reference structure 2
+
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <ctype.h>
+#include <string.h>
+#include "utils.h"
+#include "energy_par.h"
+#include "fold_vars.h"
+#include "fold.h"
+#include "pair_mat.h"
+#include "loop_energies.h"
+#include "mm.h"
+#include "params.h"
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+#include "2Dfold.h"
+
+/*
+#################################
+# GLOBAL VARIABLES              #
+#################################
+*/
+int compute_2Dfold_F3 = 0;
+
+/*
+#################################
+# PRIVATE VARIABLES             #
+#################################
+*/
+
+/*
+#################################
+# PRIVATE FUNCTION DECLARATIONS #
+#################################
+*/
+PRIVATE void  mfe_linear(TwoDfold_vars *vars);
+PRIVATE void  mfe_circ(TwoDfold_vars *vars);
+
+PRIVATE void  initialize_TwoDfold_vars(TwoDfold_vars *vars);
+PUBLIC  void  update_TwoDfold_params(TwoDfold_vars *vars);
+PRIVATE void  make_ptypes(TwoDfold_vars *vars);
+
+PRIVATE void  backtrack_f5(unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars);
+PRIVATE void  backtrack_c(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars);
+PRIVATE void  backtrack_m(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars);
+PRIVATE void  backtrack_m1(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars);
+PRIVATE void  backtrack_fc(int k, int l, char *structure, TwoDfold_vars *vars);
+PRIVATE void  backtrack_m2(unsigned int i, int k, int l, char *structure, TwoDfold_vars *vars);
+
+PRIVATE void  adjustArrayBoundaries(int ***array, int *k_min, int *k_max, int **l_min, int **l_max, int k_min_real, int k_max_real, int *l_min_real, int *l_max_real);
+INLINE  PRIVATE void  preparePosteriorBoundaries(int size, int shift, int *min_k, int *max_k, int **min_l, int **max_l);
+INLINE  PRIVATE void  updatePosteriorBoundaries(int d1, int d2, int *min_k, int *max_k, int **min_l, int **max_l);
+INLINE  PRIVATE void  prepareBoundaries(int min_k_pre, int max_k_pre, int min_l_pre, int max_l_pre, int bpdist, int *min_k, int *max_k, int **min_l, int **max_l);
+INLINE  PRIVATE void  prepareArray(int ***array, int min_k, int max_k, int *min_l, int *max_l);
+INLINE  PRIVATE void  prepareArray2(unsigned long ***array, int min_k, int max_k, int *min_l, int *max_l);
+
+
+
+/*
+#################################
+# BEGIN OF FUNCTION DEFINITIONS #
+#################################
+*/
+
+PUBLIC TwoDfold_vars *get_TwoDfold_variables(const char *seq, const char *structure1, const char *structure2, int circ){
+  unsigned int size, length, i;
+  int *index;
+  TwoDfold_vars *vars;
+  length = strlen(seq);
+  vars = (TwoDfold_vars *)malloc(sizeof(TwoDfold_vars));
+  vars->sequence     = (char *)space(length + 1);
+  strcpy(vars->sequence, seq);
+  vars->seq_length   = length;
+  if(vars->seq_length < 1) nrerror("get_TwoDfold_variables: sequence must be longer than 0");
+  size                        = ((length + 1) * (length + 2)/2);
+
+  vars->reference_pt1   = make_pair_table(structure1);
+  vars->reference_pt2   = make_pair_table(structure2);
+  vars->referenceBPs1   = make_referenceBP_array(vars->reference_pt1, TURN);
+  vars->referenceBPs2   = make_referenceBP_array(vars->reference_pt2, TURN);
+  vars->bpdist          = compute_BPdifferences(vars->reference_pt1, vars->reference_pt2, TURN);
+  vars->do_backtrack    = 1;
+  vars->dangles         = dangles;
+  vars->circ            = circ;
+  vars->temperature     = temperature;
+  vars->ptype           = space(sizeof(char) * size);
+  vars->P               = NULL;
+  vars->S               = NULL;
+  vars->S1              = NULL;
+  vars->my_iindx        = get_iindx(length);
+  index                 = vars->my_iindx;
+  /* compute maximum matching with reference structure 1 disallowed */
+  vars->mm1          = maximumMatchingConstraint(vars->sequence, vars->reference_pt1);
+  /* compute maximum matching with reference structure 2 disallowed */
+  vars->mm2          = maximumMatchingConstraint(vars->sequence, vars->reference_pt2);
+
+  vars->maxD1        = vars->mm1[index[1]-length] + vars->referenceBPs1[index[1]-length];
+  vars->maxD2        = vars->mm2[index[1]-length] + vars->referenceBPs2[index[1]-length];
+
+  /* allocate memory for the energy matrices and min-/max-index helper arrays */
+  vars->E_C              = (int ***) space(sizeof(int **)  * size);
+  vars->l_min_values     = (int **)  space(sizeof(int *)   * size);
+  vars->l_max_values     = (int **)  space(sizeof(int *)   * size);
+  vars->k_min_values     = (int *)   space(sizeof(int)     * size);
+  vars->k_max_values     = (int *)   space(sizeof(int)     * size);
+
+  vars->E_F5             = (int ***) space(sizeof(int **)  * (length + 1));
+  vars->l_min_values_f   = (int **)  space(sizeof(int *)   * (length + 1));
+  vars->l_max_values_f   = (int **)  space(sizeof(int *)   * (length + 1));
+  vars->k_min_values_f   = (int *)   space(sizeof(int)     * (length + 1));
+  vars->k_max_values_f   = (int *)   space(sizeof(int)     * (length + 1));
+
+  if(compute_2Dfold_F3){
+    vars->E_F3             = (int ***) space(sizeof(int **)  * (length + 1));
+    vars->l_min_values_f3  = (int **)  space(sizeof(int *)   * (length + 1));
+    vars->l_max_values_f3  = (int **)  space(sizeof(int *)   * (length + 1));
+    vars->k_min_values_f3  = (int *)   space(sizeof(int)     * (length + 1));
+    vars->k_max_values_f3  = (int *)   space(sizeof(int)     * (length + 1));
+  }
+  else vars->E_F3 = NULL;
+
+  vars->E_M              = (int ***) space(sizeof(int **)  * size);
+  vars->l_min_values_m   = (int **)  space(sizeof(int *)   * size);
+  vars->l_max_values_m   = (int **)  space(sizeof(int *)   * size);
+  vars->k_min_values_m   = (int *)   space(sizeof(int)     * size);
+  vars->k_max_values_m   = (int *)   space(sizeof(int)     * size);
+
+  vars->E_M1             = (int ***) space(sizeof(int **)  * size);
+  vars->l_min_values_m1  = (int **)  space(sizeof(int *)   * size);
+  vars->l_max_values_m1  = (int **)  space(sizeof(int *)   * size);
+  vars->k_min_values_m1  = (int *)   space(sizeof(int)     * size);
+  vars->k_max_values_m1  = (int *)   space(sizeof(int)     * size);
+
+#ifdef COUNT_STATES
+  vars->N_C              = (unsigned long ***) space(sizeof(unsigned long **)  * size);
+  vars->N_F5             = (unsigned long ***) space(sizeof(unsigned long **)  * (length + 1));
+  vars->N_M              = (unsigned long ***) space(sizeof(unsigned long **)  * size);
+  vars->N_M1             = (unsigned long ***) space(sizeof(unsigned long **)  * size);
+#endif
+
+
+  if(circ){
+    vars->E_M2_rem       = (int *)   space(sizeof(int)     * (length + 1));
+    vars->E_M2            = (int ***) space(sizeof(int **)  * (length + 1));
+    vars->l_min_values_m2 = (int **)  space(sizeof(int *)   * (length + 1));
+    vars->l_max_values_m2 = (int **)  space(sizeof(int *)   * (length + 1));
+    vars->k_min_values_m2 = (int *)   space(sizeof(int)     * (length + 1));
+    vars->k_max_values_m2 = (int *)   space(sizeof(int)     * (length + 1));
+  }
+  else{
+    vars->E_M2_rem       = NULL;
+    vars->E_M2            = NULL;
+    vars->l_min_values_m2 = NULL;
+    vars->l_max_values_m2 = NULL;
+    vars->k_min_values_m2 = NULL;
+    vars->k_max_values_m2 = NULL;
+  }
+
+  vars->E_Fc              = NULL;
+  vars->E_FcH             = NULL;
+  vars->E_FcI             = NULL;
+  vars->E_FcM             = NULL;
+
+  vars->E_Fc_rem         = INF;
+  vars->E_FcH_rem        = INF;
+  vars->E_FcI_rem        = INF;
+  vars->E_FcM_rem        = INF;
+
+  vars->E_C_rem          = (int *) space(sizeof(int) * size);
+  vars->E_M_rem          = (int *) space(sizeof(int) * size);
+  vars->E_M1_rem         = (int *) space(sizeof(int) * size);
+  vars->E_F5_rem         = (int *) space(sizeof(int) * (length+1));
+  /* init rest arrays */
+  for(i=0;i<size;i++){
+    vars->E_C_rem[i] = vars->E_M_rem[i] = vars->E_M1_rem[i] = INF;
+  }
+  for(i=0;i<=length;i++)
+    vars->E_F5_rem[i] = INF;
+  if(vars->E_M2_rem)
+    for(i=0;i<=length;i++)
+      vars->E_M2_rem[i] = INF;
+
+  return vars;
+}
+
+PUBLIC void destroy_TwoDfold_variables(TwoDfold_vars *vars){
+  unsigned int i, j, ij;
+  int cnt1;
+  if(vars == NULL) return;
+
+  free(vars->E_C_rem);
+  free(vars->E_M_rem);
+  free(vars->E_M1_rem);
+  free(vars->E_F5_rem);
+  if(vars->E_M2_rem) free(vars->E_M2_rem);
+
+#ifdef _OPENMP
+  #pragma omp sections private(i,j,ij,cnt1)
+  {
+
+  #pragma omp section
+  {
+#endif
+
+#ifdef COUNT_STATES
+  if(vars->N_C != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->N_C[ij]) continue;
+        for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++)
+          if(vars->l_min_values[ij][cnt1] < INF){
+            vars->N_C[ij][cnt1] += vars->l_min_values[ij][cnt1]/2;
+            free(vars->N_C[ij][cnt1]);
+          }
+        if(vars->k_min_values[ij] < INF){
+          vars->N_C[ij] += vars->k_min_values[ij];
+          free(vars->N_C[ij]);
+        }
+      }
+    }
+    free(vars->N_C);
+  }
+#endif
+
+  if(vars->E_C != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->E_C[ij]) continue;
+        for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++)
+          if(vars->l_min_values[ij][cnt1] < INF){
+            vars->E_C[ij][cnt1] += vars->l_min_values[ij][cnt1]/2;
+            free(vars->E_C[ij][cnt1]);
+          }
+        if(vars->k_min_values[ij] < INF){
+          vars->E_C[ij] += vars->k_min_values[ij];
+          free(vars->E_C[ij]);
+          vars->l_min_values[ij] += vars->k_min_values[ij];
+          vars->l_max_values[ij] += vars->k_min_values[ij];
+          free(vars->l_min_values[ij]);
+          free(vars->l_max_values[ij]);
+        }
+      }
+    }
+    free(vars->E_C);
+    free(vars->l_min_values);
+    free(vars->l_max_values);
+    free(vars->k_min_values);
+    free(vars->k_max_values);
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+
+#ifdef COUNT_STATES
+  if(vars->N_M != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->N_M[ij]) continue;
+        for(cnt1 = vars->k_min_values_m[ij]; cnt1 <= vars->k_max_values_m[ij]; cnt1++)
+          if(vars->l_min_values_m[ij][cnt1] < INF){
+            vars->N_M[ij][cnt1] += vars->l_min_values_m[ij][cnt1]/2;
+            free(vars->N_M[ij][cnt1]);
+          }
+        if(vars->k_min_values_m[ij] < INF){
+          vars->N_M[ij] += vars->k_min_values_m[ij];
+          free(vars->N_M[ij]);
+        }
+      }
+    }
+    free(vars->N_M);
+  }
+#endif
+
+  if(vars->E_M != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->E_M[ij]) continue;
+        for(cnt1 = vars->k_min_values_m[ij]; cnt1 <= vars->k_max_values_m[ij]; cnt1++)
+          if(vars->l_min_values_m[ij][cnt1] < INF){
+            vars->E_M[ij][cnt1] += vars->l_min_values_m[ij][cnt1]/2;
+            free(vars->E_M[ij][cnt1]);
+          }
+        if(vars->k_min_values_m[ij] < INF){
+          vars->E_M[ij] += vars->k_min_values_m[ij];
+          free(vars->E_M[ij]);
+          vars->l_min_values_m[ij] += vars->k_min_values_m[ij];
+          vars->l_max_values_m[ij] += vars->k_min_values_m[ij];
+          free(vars->l_min_values_m[ij]);
+          free(vars->l_max_values_m[ij]);
+        }
+      }
+    }
+    free(vars->E_M);
+    free(vars->l_min_values_m);
+    free(vars->l_max_values_m);
+    free(vars->k_min_values_m);
+    free(vars->k_max_values_m);
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+
+#ifdef COUNT_STATES
+  if(vars->N_M1 != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->N_M1[ij]) continue;
+        for(cnt1 = vars->k_min_values_m1[ij]; cnt1 <= vars->k_max_values_m1[ij]; cnt1++)
+          if(vars->l_min_values_m1[ij][cnt1] < INF){
+            vars->N_M1[ij][cnt1] += vars->l_min_values_m1[ij][cnt1]/2;
+            free(vars->N_M1[ij][cnt1]);
+          }
+        if(vars->k_min_values_m1[ij] < INF){
+          vars->N_M1[ij] += vars->k_min_values_m1[ij];
+          free(vars->N_M1[ij]);
+        }
+      }
+    }
+    free(vars->N_M1);
+  }
+#endif
+
+  if(vars->E_M1 != NULL){
+    for(i = 1; i < vars->seq_length; i++){
+      for(j = i; j <= vars->seq_length; j++){
+        ij = vars->my_iindx[i] - j;
+        if(!vars->E_M1[ij]) continue;
+        for(cnt1 = vars->k_min_values_m1[ij]; cnt1 <= vars->k_max_values_m1[ij]; cnt1++)
+          if(vars->l_min_values_m1[ij][cnt1] < INF){
+            vars->E_M1[ij][cnt1] += vars->l_min_values_m1[ij][cnt1]/2;
+            free(vars->E_M1[ij][cnt1]);
+          }
+        if(vars->k_min_values_m1[ij] < INF){
+          vars->E_M1[ij] += vars->k_min_values_m1[ij];
+          free(vars->E_M1[ij]);
+          vars->l_min_values_m1[ij] += vars->k_min_values_m1[ij];
+          vars->l_max_values_m1[ij] += vars->k_min_values_m1[ij];
+          free(vars->l_min_values_m1[ij]);
+          free(vars->l_max_values_m1[ij]);
+        }
+      }
+    }
+    free(vars->E_M1);
+    free(vars->l_min_values_m1);
+    free(vars->l_max_values_m1);
+    free(vars->k_min_values_m1);
+    free(vars->k_max_values_m1);
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(vars->E_M2 != NULL){
+    for(i = 1; i < vars->seq_length-TURN-1; i++){
+      if(!vars->E_M2[i]) continue;
+      for(cnt1 = vars->k_min_values_m2[i]; cnt1 <= vars->k_max_values_m2[i]; cnt1++)
+        if(vars->l_min_values_m2[i][cnt1] < INF){
+          vars->E_M2[i][cnt1] += vars->l_min_values_m2[i][cnt1]/2;
+          free(vars->E_M2[i][cnt1]);
+        }
+      if(vars->k_min_values_m2[i] < INF){
+        vars->E_M2[i] += vars->k_min_values_m2[i];
+        free(vars->E_M2[i]);
+        vars->l_min_values_m2[i] += vars->k_min_values_m2[i];
+        vars->l_max_values_m2[i] += vars->k_min_values_m2[i];
+        free(vars->l_min_values_m2[i]);
+        free(vars->l_max_values_m2[i]);
+      }
+    }
+    free(vars->E_M2);
+    free(vars->l_min_values_m2);
+    free(vars->l_max_values_m2);
+    free(vars->k_min_values_m2);
+    free(vars->k_max_values_m2);
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+
+#ifdef COUNT_STATES
+  if(vars->N_F5 != NULL){
+    for(i = 1; i <= vars->seq_length; i++){
+      if(!vars->N_F5[i]) continue;
+      for(cnt1 = vars->k_min_values_f[i]; cnt1 <= vars->k_max_values_f[i]; cnt1++)
+        if(vars->l_min_values_f[i][cnt1] < INF){
+          vars->N_F5[i][cnt1] += vars->l_min_values_f[i][cnt1]/2;
+          free(vars->N_F5[i][cnt1]);
+        }
+      if(vars->k_min_values_f[i] < INF){
+        vars->N_F5[i] += vars->k_min_values_f[i];
+        free(vars->N_F5[i]);
+      }
+    }
+    free(vars->N_F5);
+  }
+#endif
+
+  if(vars->E_F5 != NULL){
+    for(i = 1; i <= vars->seq_length; i++){
+      if(!vars->E_F5[i]) continue;
+      for(cnt1 = vars->k_min_values_f[i]; cnt1 <= vars->k_max_values_f[i]; cnt1++)
+        if(vars->l_min_values_f[i][cnt1] < INF){
+          vars->E_F5[i][cnt1] += vars->l_min_values_f[i][cnt1]/2;
+          free(vars->E_F5[i][cnt1]);
+        }
+      if(vars->k_min_values_f[i] < INF){
+        vars->E_F5[i] += vars->k_min_values_f[i];
+        free(vars->E_F5[i]);
+        vars->l_min_values_f[i] += vars->k_min_values_f[i];
+        vars->l_max_values_f[i] += vars->k_min_values_f[i];
+        free(vars->l_min_values_f[i]);
+        free(vars->l_max_values_f[i]);
+      }
+    }
+    free(vars->E_F5);
+    free(vars->l_min_values_f);
+    free(vars->l_max_values_f);
+    free(vars->k_min_values_f);
+    free(vars->k_max_values_f);
+  }
+
+  if(vars->E_F3 != NULL){
+    for(i = 1; i <= vars->seq_length; i++){
+      if(!vars->E_F3[i]) continue;
+      for(cnt1 = vars->k_min_values_f3[i]; cnt1 <= vars->k_max_values_f3[i]; cnt1++)
+        if(vars->l_min_values_f3[i][cnt1] < INF){
+          vars->E_F3[i][cnt1] += vars->l_min_values_f3[i][cnt1]/2;
+          free(vars->E_F3[i][cnt1]);
+        }
+      if(vars->k_min_values_f3[i] < INF){
+        vars->E_F3[i] += vars->k_min_values_f3[i];
+        free(vars->E_F3[i]);
+        vars->l_min_values_f3[i] += vars->k_min_values_f3[i];
+        vars->l_max_values_f3[i] += vars->k_min_values_f3[i];
+        free(vars->l_min_values_f3[i]);
+        free(vars->l_max_values_f3[i]);
+      }
+    }
+    free(vars->E_F3);
+    free(vars->l_min_values_f3);
+    free(vars->l_max_values_f3);
+    free(vars->k_min_values_f3);
+    free(vars->k_max_values_f3);
+  }
+
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(vars->E_Fc != NULL){
+    for(cnt1 = vars->k_min_values_fc; cnt1 <= vars->k_max_values_fc; cnt1++)
+      if(vars->l_min_values_fc[cnt1] < INF){
+        vars->E_Fc[cnt1] += vars->l_min_values_fc[cnt1]/2;
+        free(vars->E_Fc[cnt1]);
+      }
+    if(vars->k_min_values_fc < INF){
+      vars->E_Fc += vars->k_min_values_fc;
+      free(vars->E_Fc);
+      vars->l_min_values_fc += vars->k_min_values_fc;
+      vars->l_max_values_fc += vars->k_min_values_fc;
+      free(vars->l_min_values_fc);
+      free(vars->l_max_values_fc);
+    }
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(vars->E_FcI != NULL){
+    for(cnt1 = vars->k_min_values_fcI; cnt1 <= vars->k_max_values_fcI; cnt1++)
+      if(vars->l_min_values_fcI[cnt1] < INF){
+        vars->E_FcI[cnt1] += vars->l_min_values_fcI[cnt1]/2;
+        free(vars->E_FcI[cnt1]);
+      }
+    if(vars->k_min_values_fcI < INF){
+      vars->E_FcI += vars->k_min_values_fcI;
+      free(vars->E_FcI);
+      vars->l_min_values_fcI += vars->k_min_values_fcI;
+      vars->l_max_values_fcI += vars->k_min_values_fcI;
+      free(vars->l_min_values_fcI);
+      free(vars->l_max_values_fcI);
+    }
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(vars->E_FcH != NULL){
+    for(cnt1 = vars->k_min_values_fcH; cnt1 <= vars->k_max_values_fcH; cnt1++)
+      if(vars->l_min_values_fcH[cnt1] < INF){
+        vars->E_FcH[cnt1] += vars->l_min_values_fcH[cnt1]/2;
+        free(vars->E_FcH[cnt1]);
+      }
+    if(vars->k_min_values_fcH < INF){
+      vars->E_FcH += vars->k_min_values_fcH;
+      free(vars->E_FcH);
+      vars->l_min_values_fcH += vars->k_min_values_fcH;
+      vars->l_max_values_fcH += vars->k_min_values_fcH;
+      free(vars->l_min_values_fcH);
+      free(vars->l_max_values_fcH);
+    }
+  }
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(vars->E_FcM != NULL){
+    for(cnt1 = vars->k_min_values_fcM; cnt1 <= vars->k_max_values_fcM; cnt1++)
+      if(vars->l_min_values_fcM[cnt1] < INF){
+        vars->E_FcM[cnt1] += vars->l_min_values_fcM[cnt1]/2;
+        free(vars->E_FcM[cnt1]);
+      }
+    if(vars->k_min_values_fcM < INF){
+      vars->E_FcM += vars->k_min_values_fcM;
+      free(vars->E_FcM);
+      vars->l_min_values_fcM += vars->k_min_values_fcM;
+      vars->l_max_values_fcM += vars->k_min_values_fcM;
+      free(vars->l_min_values_fcM);
+      free(vars->l_max_values_fcM);
+    }
+  }
+
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+
+  if(vars->P != NULL)             free(vars->P);
+  if(vars->sequence != NULL)      free(vars->sequence);
+  if(vars->reference_pt1 != NULL) free(vars->reference_pt1);
+  if(vars->reference_pt2 != NULL) free(vars->reference_pt2);
+  if(vars->referenceBPs1 != NULL) free(vars->referenceBPs1);
+  if(vars->referenceBPs2 != NULL) free(vars->referenceBPs2);
+  if(vars->ptype != NULL)         free(vars->ptype);
+  if(vars->S != NULL)             free(vars->S);
+  if(vars->S1 != NULL)            free(vars->S1);
+
+  if(vars->mm1 != NULL)           free(vars->mm1);
+  if(vars->mm2 != NULL)           free(vars->mm2);
+  if(vars->bpdist != NULL)        free(vars->bpdist);
+#ifdef _OPENMP
+  }
+  }
+#endif
+
+  if(vars->my_iindx != NULL)      free(vars->my_iindx);
+
+  free(vars);
+}
+
+PRIVATE void initialize_TwoDfold_vars(TwoDfold_vars *vars){
+  update_TwoDfold_params(vars);
+  /* this call updates the params in the ViennaRNA fold.o which is a global, so be careful
+  *  whith calling it parallel... need a workarround or fix of ViennaRNA fold stuff
+  */
+  update_fold_params();
+}
+
+
+PUBLIC TwoDfold_solution **TwoDfold(TwoDfold_vars *vars, int distance1, int distance2){
+  unsigned int i, d1, d2;
+  unsigned int maxD1;
+  unsigned int maxD2;
+  unsigned int length;
+  TwoDfold_solution **output;
+
+  initialize_TwoDfold_vars(vars);
+  if(fabs(vars->P->temperature - temperature)>1e-6) update_TwoDfold_params(vars);
+  vars->S   = encode_sequence(vars->sequence, 0);
+  vars->S1  = encode_sequence(vars->sequence, 1);
+
+  make_ptypes(vars);
+
+  maxD1 = vars->maxD1;
+  maxD2 = vars->maxD2;
+
+  if(distance1 >= 0){
+    if((unsigned int)distance1 > maxD1)
+      fprintf(stderr,
+              "limiting maximum basepair distance 1 to %u\n",
+              maxD1);
+    else
+      maxD1 = (unsigned int)distance1;
+  }
+
+  if(distance2 >= 0){
+    if((unsigned int)distance2 > maxD2)
+      fprintf(stderr,
+              "limiting maximum basepair distance 2 to %u\n",
+              maxD2);
+    else
+      maxD2 = (unsigned int)distance2;
+  }
+
+  vars->maxD1 = maxD1;
+  vars->maxD2 = maxD2;
+  output = (TwoDfold_solution **)space((vars->maxD1+1) * sizeof(TwoDfold_solution *));
+
+  mfe_linear(vars);
+  if(vars->circ) mfe_circ(vars);
+
+  length = vars->seq_length;
+
+  for(d1=0; d1<=maxD1;d1++){
+    output[d1] = (TwoDfold_solution *)space((vars->maxD2+1)*sizeof(TwoDfold_solution));
+#ifdef _OPENMP
+  #pragma omp parallel for private(d2)
+#endif
+    for(d2=0; d2<=maxD2;d2++){
+      output[d1][d2].en = (float)INF/(float)100.;
+      output[d1][d2].s  = NULL;
+    }
+    if(     (d1 >= ((vars->circ) ? vars->k_min_values_fc : vars->k_min_values_f[length]))
+        &&  (d1 <= ((vars->circ) ? vars->k_max_values_fc : vars->k_max_values_f[length]))){
+#ifdef _OPENMP
+  #pragma omp parallel for private(d2, i)
+#endif
+      for(  d2  = ((vars->circ) ? vars->l_min_values_fc[d1] : vars->l_min_values_f[length][d1]);
+            d2 <= ((vars->circ) ? vars->l_max_values_fc[d1] : vars->l_max_values_f[length][d1]);
+            d2 += 2){
+        output[d1][d2].en = (float)((vars->circ) ? vars->E_Fc[d1][d2/2] : vars->E_F5[length][d1][d2/2])/(float)100.;
+        if(vars->do_backtrack && (output[d1][d2].en != (float)INF/(float)100.)){
+          char *mfe_structure = (char *)space(length+1);
+          for(i=0;i<length;i++) mfe_structure[i] = '.';
+          mfe_structure[i] = '\0';
+          (vars->circ) ? backtrack_fc(d1, d2, mfe_structure, vars) : backtrack_f5(length, d1, d2, mfe_structure, vars);
+          output[d1][d2].s = mfe_structure;
+        }
+      }
+    }
+
+  }
+  return output;
+}
+
+PUBLIC TwoDfold_solution *TwoDfoldList(TwoDfold_vars *vars, int distance1, int distance2){
+  unsigned int  i, d1, d2;
+  unsigned int  maxD1;
+  unsigned int  maxD2;
+  unsigned int  length;
+  unsigned int  counter = 0;
+  int           en = 0;
+  TwoDfold_solution *output;
+
+  initialize_TwoDfold_vars(vars);
+  if(fabs(vars->P->temperature - temperature)>1e-6) update_TwoDfold_params(vars);
+  vars->S   = encode_sequence(vars->sequence, 0);
+  vars->S1  = encode_sequence(vars->sequence, 1);
+
+  make_ptypes(vars);
+
+  maxD1 = vars->maxD1;
+  maxD2 = vars->maxD2;
+
+  if(distance1 >= 0){
+    if((unsigned int)distance1 > maxD1)
+      fprintf(stderr,
+              "TwoDfoldList@2Dfold.c: limiting maximum basepair distance 1 to %u\n",
+              maxD1);
+    else
+      maxD1 = (unsigned int)distance1;
+  }
+
+  if(distance2 >= 0){
+    if((unsigned int)distance2 > maxD2)
+      fprintf(stderr,
+              "TwoDfoldList@2Dfold.c: limiting maximum basepair distance 2 to %u\n",
+              maxD2);
+    else
+      maxD2 = (unsigned int)distance2;
+  }
+
+  vars->maxD1 = maxD1;
+  vars->maxD2 = maxD2;
+  output = (TwoDfold_solution *)space((((vars->maxD1+1)*(vars->maxD2+2))/2 + 2) * sizeof(TwoDfold_solution));
+
+  mfe_linear(vars);
+  if(vars->circ) mfe_circ(vars);
+
+  length = vars->seq_length;
+
+  for(d1=0; d1<=maxD1;d1++){
+    if((d1 >= ((vars->circ) ? vars->k_min_values_fc : vars->k_min_values_f[length]))
+        &&  (d1 <= ((vars->circ) ? vars->k_max_values_fc : vars->k_max_values_f[length]))){
+      for(d2  = ((vars->circ) ? vars->l_min_values_fc[d1] : vars->l_min_values_f[length][d1]);
+          d2 <= ((vars->circ) ? vars->l_max_values_fc[d1] : vars->l_max_values_f[length][d1]);
+          d2 += 2){
+        en = ((vars->circ) ? vars->E_Fc[d1][d2/2] : vars->E_F5[length][d1][d2/2]);
+        if(en == INF) continue;
+        output[counter].k   = d1;
+        output[counter].l   = d2;
+        output[counter].en  = (float)en/(float)100.;
+        if(vars->do_backtrack){
+          char *mfe_structure = (char *)space(length+1);
+          for(i=0;i<length;i++) mfe_structure[i] = '.';
+          mfe_structure[i] = '\0';
+          (vars->circ) ? backtrack_fc((int)d1, (int)d2, mfe_structure, vars) : backtrack_f5(length, (int)d1, (int)d2, mfe_structure, vars);
+          output[counter].s = mfe_structure;
+        }
+        else output[counter].s = NULL;
+        counter++;
+      }
+    }
+  }
+
+  /* store entry for remaining partition if it exists */
+  en = ((vars->circ) ? vars->E_Fc_rem : vars->E_F5_rem[length]);
+  if(en != INF){
+    output[counter].k   = -1;
+    output[counter].l   = -1;
+    output[counter].en  =  (float)en/(float)100.;
+    if(vars->do_backtrack){
+      char *mfe_structure = (char *)space(length+1);
+      for(i=0;i<length;i++) mfe_structure[i] = '.';
+      mfe_structure[i] = '\0';
+      (vars->circ) ? backtrack_fc(-1, -1, mfe_structure, vars) : backtrack_f5(length, -1, -1, mfe_structure, vars);
+      output[counter].s = mfe_structure;
+    }
+    else output[counter].s = NULL;
+    counter++;
+  }
+
+  /* insert end-marker entry */
+  output[counter].k = output[counter].l = INF;
+  counter++;
+
+  /* resize to actual dataset amount */
+  output = (TwoDfold_solution*)xrealloc(output, sizeof(TwoDfold_solution) * counter);
+  return output;
+}
+
+
+PUBLIC char *TwoDfold_backtrack_f5(unsigned int j, int k, int l, TwoDfold_vars *vars){
+  unsigned int i;
+  char *mfe_structure = (char *)space(j+1);
+  if(j < TURN + 2) return NULL;
+
+  for(i=0; i < j; i++) mfe_structure[i] = '.';
+  mfe_structure[i] = '\0';
+
+  backtrack_f5(j, k, l, mfe_structure, vars);
+  return mfe_structure;
+}
+
+PRIVATE void mfe_linear(TwoDfold_vars *vars){
+
+  unsigned int  d, i, j, ij, maxD1, maxD2, seq_length, dia, dib, dja, djb, *referenceBPs1, *referenceBPs2, *mm1, *mm2, *bpdist;
+  int           cnt1, cnt2, cnt3, cnt4, d1, d2, energy, dangles, temp2, type, additional_en, *my_iindx, circ;
+  short         *S1, *reference_pt1, *reference_pt2;
+  char          *sequence, *ptype;
+  paramT        *P;
+
+  /* dereferenciate things we often need */
+  P               = vars->P;
+  sequence        = vars->sequence;
+  seq_length      = vars->seq_length;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+  S1              = vars->S1;
+  ptype           = vars->ptype;
+  reference_pt1   = vars->reference_pt1;
+  reference_pt2   = vars->reference_pt2;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+  dangles         = vars->dangles;
+  mm1             = vars->mm1;
+  mm2             = vars->mm2;
+  bpdist          = vars->bpdist;
+  circ            = vars->circ;
+
+  for (d = TURN+2; d <= seq_length; d++) { /* i,j in [1..length] */
+#ifdef _OPENMP
+  #pragma omp parallel for private(additional_en, j, energy, temp2, i, ij, dia,dib,dja,djb,cnt1,cnt2,cnt3,cnt4, d1, d2)
+#endif
+    for (j = d; j <= seq_length; j++) {
+      unsigned int p, q, pq, u, maxp, dij;
+      int type_2, type, tt, no_close, base_d1, base_d2;
+
+      i = j-d+1;
+      dij = j - i - 1;
+      ij = my_iindx[i]-j;
+      type = ptype[ij];
+
+      no_close = (((type==3)||(type==4))&&no_closingGU);
+
+      if (type) {   /* we have a pair */
+        /* increase or decrease distance-to-reference value depending whether (i,j) is included in
+        *  reference or has to be introduced
+        */
+        base_d1 = ((unsigned int)reference_pt1[i] != j) ? 1 : -1;
+        base_d2 = ((unsigned int)reference_pt2[i] != j) ? 1 : -1;
+
+        /* HAIRPIN STRUCTURES */
+
+        /* get distance to reference if closing the hairpin
+        *  d = dbp(T_{i,j}, {i,j})
+        */
+        d1 = base_d1 + referenceBPs1[ij];
+        d2 = base_d2 + referenceBPs2[ij];
+
+        int min_k, max_k, min_l, max_l;
+        int real_min_k, real_max_k, *min_l_real, *max_l_real;
+
+        min_l = min_k = 0;
+        max_k = mm1[ij] + referenceBPs1[ij];
+        max_l = mm2[ij] + referenceBPs2[ij];
+
+        prepareBoundaries(min_k,
+                          max_k,
+                          min_l,
+                          max_l,
+                          bpdist[ij],
+                          &vars->k_min_values[ij],
+                          &vars->k_max_values[ij],
+                          &vars->l_min_values[ij],
+                          &vars->l_max_values[ij]
+                          );
+
+        preparePosteriorBoundaries( vars->k_max_values[ij] - vars->k_min_values[ij] + 1,
+                                    vars->k_min_values[ij],
+                                    &real_min_k,
+                                    &real_max_k,
+                                    &min_l_real,
+                                    &max_l_real
+                                  );
+
+        prepareArray( &vars->E_C[ij],
+                      vars->k_min_values[ij],
+                      vars->k_max_values[ij],
+                      vars->l_min_values[ij],
+                      vars->l_max_values[ij]
+                    );
+
+#ifdef COUNT_STATES
+        prepareArray2( &vars->N_C[ij],
+                      vars->k_min_values[ij],
+                      vars->k_max_values[ij],
+                      vars->l_min_values[ij],
+                      vars->l_max_values[ij]
+                    );
+#endif
+
+        /* d1 and d2 are the distancies to both references introduced by closing a hairpin structure at (i,j) */
+        if((d1 >= 0) && (d2 >= 0)){
+          if(((unsigned int)d1<=maxD1) && ((unsigned int)d2 <= maxD2)){
+            vars->E_C[ij][d1][d2/2] = (no_close) ? FORBIDDEN : E_Hairpin(dij, type, S1[i+1], S1[j-1], sequence+i-1, P);
+            updatePosteriorBoundaries(d1,
+                                      d2,
+                                      &real_min_k,
+                                      &real_max_k,
+                                      &min_l_real,
+                                      &max_l_real
+                                      );
+#ifdef COUNT_STATES
+            vars->N_C[ij][d1][d2/2] = 1;
+#endif
+          }
+          else{
+            vars->E_C_rem[ij] = (no_close) ? FORBIDDEN : E_Hairpin(dij, type, S1[i+1], S1[j-1], sequence+i-1, P);
+          }
+        }
+        /* INTERIOR LOOP STRUCTURES */
+        maxp = MIN2(j-2-TURN,i+MAXLOOP+1);
+        for(p = i+1; p <= maxp; p++){
+          unsigned int minq = p + TURN + 1;
+          unsigned int ln_pre = dij + p;
+          if(ln_pre > minq + MAXLOOP) minq = ln_pre - MAXLOOP - 1;
+          for(q = minq; q < j; q++){
+            pq = my_iindx[p]-q;
+            /* set distance to reference structure... */
+            type_2 = ptype[pq];
+
+            if (type_2==0) continue;
+            type_2 = rtype[type_2];
+
+            /* get distance to reference if closing the interior loop
+            *  d2 = dbp(S_{i,j}, S_{p.q} + {i,j})
+            */
+            d1 = base_d1 + referenceBPs1[ij] - referenceBPs1[pq];
+            d2 = base_d2 + referenceBPs2[ij] - referenceBPs2[pq];
+
+            if(no_closingGU)
+              if(no_close||(type_2==3)||(type_2==4))
+                if((p>i+1)||(q<j-1)) continue;  /* continue unless stack */
+
+            energy = E_IntLoop(p-i-1, j-q-1, type, type_2, S1[i+1], S1[j-1], S1[p-1], S1[q+1], P);
+
+            if(vars->E_C[pq] != NULL){
+              for(cnt1 = vars->k_min_values[pq]; cnt1 <= vars->k_max_values[pq]; cnt1++){
+                for(cnt2 = vars->l_min_values[pq][cnt1]; cnt2 <= vars->l_max_values[pq][cnt1]; cnt2+=2){
+                  if(vars->E_C[pq][cnt1][cnt2/2] != INF){
+                    if(((cnt1 + d1) <= maxD1) && ((cnt2+d2) <= maxD2)){
+                        vars->E_C[ij][cnt1 + d1][(cnt2 + d2)/2] = MIN2( vars->E_C[ij][cnt1 + d1][(cnt2 + d2)/2],
+                                                                        vars->E_C[pq][cnt1][cnt2/2] + energy
+                                                                      );
+                        updatePosteriorBoundaries(cnt1 + d1,
+                                                  cnt2 + d2,
+                                                  &real_min_k,
+                                                  &real_max_k,
+                                                  &min_l_real,
+                                                  &max_l_real
+                                                  );
+#ifdef COUNT_STATES
+                       vars->N_C[ij][cnt1 + d1][(cnt2 + d2)/2] += vars->N_C[pq][cnt1][cnt2/2];
+#endif
+                    }
+                    /* collect all cases where d1+cnt1 or d2+cnt2 exceeds maxD1, maxD2, respectively */
+                    else{
+                      vars->E_C_rem[ij] = MIN2(vars->E_C_rem[ij], vars->E_C[pq][cnt1][cnt2/2] + energy);
+                    }
+                  }
+                }
+              }
+            }
+            /* collect all contributions where C[pq] already lies outside k_max, l_max boundary */
+            if(vars->E_C_rem[pq] != INF){
+              vars->E_C_rem[ij] = MIN2(vars->E_C_rem[ij], vars->E_C_rem[pq] + energy);
+            }
+          } /* end q-loop */
+        } /* end p-loop */
+
+
+
+        /* MULTI LOOP STRUCTURES */
+        if(!no_close){
+
+          /* dangle energies for multiloop closing stem */
+          tt = rtype[type];
+          temp2 = P->MLclosing;
+          if(dangles == 2)
+            temp2 += E_MLstem(tt, S1[j-1], S1[i+1], P);
+          else
+            temp2 += E_MLstem(tt, -1, -1, P);
+
+          for(u=i+TURN+2; u<j-TURN-2;u++){
+            int i1u   = my_iindx[i+1]-u;
+            int u1j1  = my_iindx[u+1]-j+1;
+            /* check all cases where either M or M1 are already out of scope of maxD1 and/or maxD2 */
+            if(vars->E_M_rem[i1u] != INF){
+              for(cnt3 = vars->k_min_values_m1[u1j1];
+                  cnt3 <= vars->k_max_values_m1[u1j1];
+                  cnt3++)
+                for(cnt4 = vars->l_min_values_m1[u1j1][cnt3];
+                    cnt4 <= vars->l_max_values_m1[u1j1][cnt3];
+                    cnt4+=2){
+                  if(vars->E_M1[u1j1][cnt3][cnt4/2]!= INF){
+                    vars->E_C_rem[ij] = MIN2(vars->E_C_rem[ij],
+                                              vars->E_M_rem[i1u]
+                                            + vars->E_M1[u1j1][cnt3][cnt4/2]
+                                            + temp2
+                                              );
+                  }
+                }
+              if(vars->E_M1_rem[u1j1] != INF){
+                vars->E_C_rem[ij] = MIN2(vars->E_C_rem[ij],
+                                          vars->E_M_rem[i1u]
+                                        + vars->E_M1_rem[u1j1]
+                                        + temp2
+                                          );
+              }
+            }
+            if(vars->E_M1_rem[u1j1] != INF){
+              for(cnt1 = vars->k_min_values_m[i1u];
+                  cnt1 <= vars->k_max_values_m[i1u];
+                  cnt1++)
+                for(cnt2 = vars->l_min_values_m[i1u][cnt1];
+                    cnt2 <= vars->l_max_values_m[i1u][cnt1];
+                    cnt2+=2)
+                  if(vars->E_M[i1u][cnt1][cnt2/2] != INF){
+                    vars->E_C_rem[ij] = MIN2(vars->E_C_rem[ij],
+                                              vars->E_M[i1u][cnt1][cnt2/2]
+                                            + vars->E_M1_rem[u1j1]
+                                            + temp2
+                                              );
+                  }
+            }
+            /* get distance to reference if closing the multiloop
+            *  d = dbp(S_{i,j}, {i,j} + S_{i+1,u} + S_{u+1,j-1})
+            */
+            if(!vars->E_M[i1u]) continue;
+            if(!vars->E_M1[u1j1]) continue;
+
+            d1 = base_d1 + referenceBPs1[ij] - referenceBPs1[i1u] - referenceBPs1[u1j1];
+            d2 = base_d2 + referenceBPs2[ij] - referenceBPs2[i1u] - referenceBPs2[u1j1];
+
+            for(cnt1 = vars->k_min_values_m[i1u];
+                cnt1 <= vars->k_max_values_m[i1u];
+                cnt1++)
+              for(cnt2 = vars->l_min_values_m[i1u][cnt1];
+                  cnt2 <= vars->l_max_values_m[i1u][cnt1];
+                  cnt2+=2)
+                for(cnt3 = vars->k_min_values_m1[u1j1];
+                    cnt3 <= vars->k_max_values_m1[u1j1];
+                    cnt3++)
+                  for(cnt4 = vars->l_min_values_m1[u1j1][cnt3];
+                      cnt4 <= vars->l_max_values_m1[u1j1][cnt3];
+                      cnt4+=2){
+                    if((vars->E_M[i1u][cnt1][cnt2/2] != INF) && (vars->E_M1[u1j1][cnt3][cnt4/2]!= INF)){
+                      if(((cnt1+cnt3+d1) <= maxD1) && ((cnt2+cnt4+d2) <= maxD2)){
+                        vars->E_C[ij][cnt1+cnt3+d1][(cnt2+cnt4+d2)/2] = MIN2( vars->E_C[ij][cnt1+cnt3+d1][(cnt2+cnt4+d2)/2],
+                                                                              vars->E_M[i1u][cnt1][cnt2/2]
+                                                                            + vars->E_M1[u1j1][cnt3][cnt4/2]
+                                                                            + temp2
+                                                                            );
+                        updatePosteriorBoundaries(cnt1 + cnt3 + d1,
+                                                  cnt2 + cnt4 + d2,
+                                                  &real_min_k,
+                                                  &real_max_k,
+                                                  &min_l_real,
+                                                  &max_l_real
+                                                );
+#ifdef COUNT_STATES
+                        vars->N_C[ij][cnt1+cnt3+d1][(cnt2+cnt4+d2)/2] += vars->N_M[i1u][cnt1][cnt2/2] * vars->N_M1[u1j1][cnt3][cnt4/2];
+#endif
+                      }
+                      /* collect all cases where d1+cnt1+cnt3 or d2+cnt2+cnt4 exceeds maxD1, maxD2, respectively */
+                      else{
+                        vars->E_C_rem[ij] = MIN2(  vars->E_C_rem[ij],
+                                                    vars->E_M[i1u][cnt1][cnt2/2]
+                                                  + vars->E_M1[u1j1][cnt3][cnt4/2]
+                                                  + temp2
+                                                  );
+                      }
+                    }
+                  }
+          }
+        }
+
+        /* resize and move memory portions of energy matrix E_C */
+        adjustArrayBoundaries(&vars->E_C[ij],
+                              &vars->k_min_values[ij],
+                              &vars->k_max_values[ij],
+                              &vars->l_min_values[ij],
+                              &vars->l_max_values[ij],
+                              real_min_k,
+                              real_max_k,
+                              min_l_real,
+                              max_l_real
+                              );
+#ifdef COUNT_STATES
+        /* actually we should adjust the array boundaries here but we might never use the count states option more than once so what....*/
+#endif
+      } /* end >> if (pair) << */
+
+
+
+      /* done with c[i,j], now compute fML[i,j] */
+      /* free ends ? -----------------------------------------*/
+
+
+      dia = referenceBPs1[ij] - referenceBPs1[my_iindx[i+1]-j];
+      dib = referenceBPs2[ij] - referenceBPs2[my_iindx[i+1]-j];
+      dja = referenceBPs1[ij] - referenceBPs1[ij+1];
+      djb = referenceBPs2[ij] - referenceBPs2[ij+1];
+
+      if(dangles==2)
+        temp2 = E_MLstem(type, ((i > 1) || circ) ? S1[i-1] : -1, ((j < seq_length) || circ) ? S1[j+1] : -1, P);
+      else
+        temp2 = E_MLstem(type, -1, -1, P);
+
+      int min_k_guess, max_k_guess, min_l_guess, max_l_guess;
+      int min_k_real_m, max_k_real_m, *min_l_real_m, *max_l_real_m;
+      int min_k_real_m1, max_k_real_m1, *min_l_real_m1, *max_l_real_m1;
+
+      min_k_guess = min_l_guess = 0;
+      max_k_guess = mm1[ij] + referenceBPs1[ij];
+      max_l_guess = mm2[ij] + referenceBPs2[ij];
+
+      prepareBoundaries(min_k_guess,
+                        max_k_guess,
+                        min_l_guess,
+                        max_l_guess,
+                        bpdist[ij],
+                        &vars->k_min_values_m[ij],
+                        &vars->k_max_values_m[ij],
+                        &vars->l_min_values_m[ij],
+                        &vars->l_max_values_m[ij]
+                        );
+
+      prepareBoundaries(min_k_guess,
+                        max_k_guess,
+                        min_l_guess,
+                        max_l_guess,
+                        bpdist[ij],
+                        &vars->k_min_values_m1[ij],
+                        &vars->k_max_values_m1[ij],
+                        &vars->l_min_values_m1[ij],
+                        &vars->l_max_values_m1[ij]
+                        );
+
+      preparePosteriorBoundaries( vars->k_max_values_m[ij] - vars->k_min_values_m[ij] + 1,
+                                  vars->k_min_values_m[ij],
+                                  &min_k_real_m,
+                                  &max_k_real_m,
+                                  &min_l_real_m,
+                                  &max_l_real_m
+                                );
+      preparePosteriorBoundaries( vars->k_max_values_m1[ij] - vars->k_min_values_m1[ij] + 1,
+                                  vars->k_min_values_m1[ij],
+                                  &min_k_real_m1,
+                                  &max_k_real_m1,
+                                  &min_l_real_m1,
+                                  &max_l_real_m1
+                                );
+
+      prepareArray( &vars->E_M[ij],
+                    vars->k_min_values_m[ij],
+                    vars->k_max_values_m[ij],
+                    vars->l_min_values_m[ij],
+                    vars->l_max_values_m[ij]
+                  );
+
+      prepareArray( &vars->E_M1[ij],
+                    vars->k_min_values_m1[ij],
+                    vars->k_max_values_m1[ij],
+                    vars->l_min_values_m1[ij],
+                    vars->l_max_values_m1[ij]
+                  );
+#ifdef COUNT_STATES
+      prepareArray2( &vars->N_M[ij],
+                    vars->k_min_values_m[ij],
+                    vars->k_max_values_m[ij],
+                    vars->l_min_values_m[ij],
+                    vars->l_max_values_m[ij]
+                  );
+      prepareArray2( &vars->N_M1[ij],
+                    vars->k_min_values_m1[ij],
+                    vars->k_max_values_m1[ij],
+                    vars->l_min_values_m1[ij],
+                    vars->l_max_values_m1[ij]
+                  );
+#endif
+
+      /* now to the actual computations... */
+      /* 1st E_M[ij] = E_M1[ij] = E_C[ij] + b */
+      if(vars->E_C_rem[ij] != INF){
+        vars->E_M_rem[ij] = vars->E_M1_rem[ij] = temp2 + vars->E_C_rem[ij];
+      }
+      if(vars->E_C[ij])
+        for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++){
+          for(cnt2 = vars->l_min_values[ij][cnt1]; cnt2 <= vars->l_max_values[ij][cnt1]; cnt2+=2){
+            if(vars->E_C[ij][cnt1][cnt2/2] != INF){
+              vars->E_M[ij][cnt1][cnt2/2] = vars->E_M1[ij][cnt1][cnt2/2] = temp2 + vars->E_C[ij][cnt1][cnt2/2];
+              updatePosteriorBoundaries(cnt1,
+                                        cnt2,
+                                        &min_k_real_m,
+                                        &max_k_real_m,
+                                        &min_l_real_m,
+                                        &max_l_real_m
+                                        );
+              updatePosteriorBoundaries(cnt1,
+                                        cnt2,
+                                        &min_k_real_m1,
+                                        &max_k_real_m1,
+                                        &min_l_real_m1,
+                                        &max_l_real_m1
+                                        );
+#ifdef COUNT_STATES
+             vars->N_M[ij][cnt1][cnt2/2] = vars->N_M1[ij][cnt1][cnt2/2] = vars->N_C[ij][cnt1][cnt2/2];
+#endif
+            }
+          }
+        }
+
+      /* 2nd E_M[ij] = MIN(E_M[ij], E_M[i+1,j] + c) */
+      if(vars->E_M_rem[my_iindx[i+1]-j] != INF){
+        vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                  vars->E_M_rem[my_iindx[i+1]-j] + P->MLbase
+                                  );
+      }
+      if(vars->E_M[my_iindx[i+1]-j])
+        for(cnt1 = vars->k_min_values_m[my_iindx[i+1]-j];
+            cnt1 <= vars->k_max_values_m[my_iindx[i+1]-j];
+            cnt1++){
+          for(cnt2 = vars->l_min_values_m[my_iindx[i+1]-j][cnt1];
+              cnt2 <= vars->l_max_values_m[my_iindx[i+1]-j][cnt1];
+              cnt2+=2){
+            if(vars->E_M[my_iindx[i+1]-j][cnt1][cnt2/2] != INF){
+              if(((cnt1 + dia) <= maxD1) && ((cnt2 + dib) <= maxD2)){
+                vars->E_M[ij][cnt1+dia][(cnt2+dib)/2] = MIN2( vars->E_M[ij][cnt1+dia][(cnt2+dib)/2],
+                                                              vars->E_M[my_iindx[i+1]-j][cnt1][cnt2/2] + P->MLbase
+                                                            );
+                updatePosteriorBoundaries(cnt1 + dia,
+                                          cnt2 + dib,
+                                          &min_k_real_m,
+                                          &max_k_real_m,
+                                          &min_l_real_m,
+                                          &max_l_real_m
+                                          );
+#ifdef COUNT_STATES
+                vars->N_M[ij][cnt1+dia][(cnt2+dib)/2] += vars->N_M[my_iindx[i+1]-j][cnt1][cnt2/2];
+#endif
+              }
+              /* collect all cases where dia+cnt1 or dib+cnt2 exceeds maxD1, maxD2, respectively */
+              else{
+                vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                          vars->E_M[my_iindx[i+1]-j][cnt1][cnt2/2] + P->MLbase
+                                          );
+              }
+            }
+          }
+        }
+
+      /* 3rd E_M[ij] = MIN(E_M[ij], E_M[i,j-1] + c) */
+      if(vars->E_M_rem[ij+1] != INF){
+        vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                  vars->E_M_rem[ij+1] + P->MLbase
+                                  );
+      }
+      if(vars->E_M[ij+1])
+        for(cnt1 = vars->k_min_values_m[ij+1];
+            cnt1 <= vars->k_max_values_m[ij+1];
+            cnt1++){
+          for(cnt2 = vars->l_min_values_m[ij+1][cnt1];
+              cnt2 <= vars->l_max_values_m[ij+1][cnt1];
+              cnt2+=2){
+            if(vars->E_M[ij+1][cnt1][cnt2/2] != INF){
+              if(((cnt1 + dja) <= maxD1) && ((cnt2 + djb) <= maxD2)){
+                vars->E_M[ij][cnt1+dja][(cnt2+djb)/2] = MIN2( vars->E_M[ij][cnt1+dja][(cnt2+djb)/2],
+                                                              vars->E_M[ij+1][cnt1][cnt2/2] + P->MLbase
+                                                            );
+                updatePosteriorBoundaries(cnt1 + dja,
+                                          cnt2 + djb,
+                                          &min_k_real_m,
+                                          &max_k_real_m,
+                                          &min_l_real_m,
+                                          &max_l_real_m
+                                          );
+#ifdef COUNT_STATES
+                vars->N_M[ij][cnt1+dja][(cnt2+djb)/2] += vars->N_M[ij+1][cnt1][cnt2/2];
+#endif
+              }
+              /* collect all cases where dja+cnt1 or djb+cnt2 exceeds maxD1, maxD2, respectively */
+              else{
+                vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                          vars->E_M[ij+1][cnt1][cnt2/2] + P->MLbase
+                                          );
+              }
+            }
+          }
+        }
+
+      /* 4th E_M1[ij] = MIN(E_M1[ij], E_M1[i,j-1] + c) */
+      if(vars->E_M1_rem[ij+1] != INF){
+        vars->E_M1_rem[ij] = MIN2( vars->E_M1_rem[ij],
+                                    vars->E_M1_rem[ij+1] + P->MLbase
+                                  );
+      }
+      if(vars->E_M1[ij+1])
+        for(cnt1 = vars->k_min_values_m1[ij+1];
+            cnt1 <= vars->k_max_values_m1[ij+1];
+            cnt1++){
+          for(cnt2 = vars->l_min_values_m1[ij+1][cnt1];
+              cnt2 <= vars->l_max_values_m1[ij+1][cnt1];
+              cnt2+=2){
+            if(vars->E_M1[ij+1][cnt1][cnt2/2] != INF){
+              if(((cnt1 + dja) <= maxD1) && ((cnt2 + djb) <= maxD2)){
+                vars->E_M1[ij][cnt1+dja][(cnt2+djb)/2]  = MIN2( vars->E_M1[ij][cnt1+dja][(cnt2+djb)/2],
+                                                                vars->E_M1[ij+1][cnt1][cnt2/2] + P->MLbase
+                                                              );
+                updatePosteriorBoundaries(cnt1 + dja,
+                                          cnt2 + djb,
+                                          &min_k_real_m1,
+                                          &max_k_real_m1,
+                                          &min_l_real_m1,
+                                          &max_l_real_m1
+                                          );
+#ifdef COUNT_STATES
+                vars->N_M1[ij][cnt1+dja][(cnt2+djb)/2]  += vars->N_M1[ij+1][cnt1][cnt2/2];
+#endif
+              }
+              /* collect all cases where dja+cnt1 or djb+cnt2 exceeds maxD1, maxD2, respectively */
+              else{
+                vars->E_M1_rem[ij] = MIN2( vars->E_M1_rem[ij],
+                                            vars->E_M1[ij+1][cnt1][cnt2/2] + P->MLbase
+                                          );
+              }
+            }
+          }
+        }
+
+
+      /* 5th E_M[ij] = MIN(E_M[ij], min(E_M[i,k] + E_M[k+1,j])) */
+      if(j > TURN + 2)
+      for (u = i+1+TURN; u <= j-2-TURN; u++){
+        /* check all cases where M(i,u) and/or M(u+1,j) are already out of scope of maxD1 and/or maxD2 */
+        if(vars->E_M_rem[my_iindx[i]-u] != INF){
+          for(cnt3 = vars->k_min_values_m[my_iindx[u+1]-j];
+              cnt3 <= vars->k_max_values_m[my_iindx[u+1]-j];
+              cnt3++){
+            for(cnt4 = vars->l_min_values_m[my_iindx[u+1]-j][cnt3];
+                cnt4 <= vars->l_max_values_m[my_iindx[u+1]-j][cnt3];
+                cnt4+=2){
+              if(vars->E_M[my_iindx[u+1]-j][cnt3][cnt4/2] != INF){
+                  vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                            vars->E_M_rem[my_iindx[i]-u] + vars->E_M[my_iindx[u+1]-j][cnt3][cnt4/2]
+                                            );
+              }
+            }
+          }
+          if(vars->E_M_rem[my_iindx[u+1]-j] != INF){
+            vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                      vars->E_M_rem[my_iindx[i]-u] + vars->E_M_rem[my_iindx[u+1]-j]
+                                      );
+          }
+        }
+        if(vars->E_M_rem[my_iindx[u+1]-j] != INF){
+          for(cnt1 = vars->k_min_values_m[my_iindx[i]-u];
+              cnt1 <= vars->k_max_values_m[my_iindx[i]-u];
+              cnt1++){
+            for(cnt2 = vars->l_min_values_m[my_iindx[i]-u][cnt1];
+                cnt2 <= vars->l_max_values_m[my_iindx[i]-u][cnt1];
+                cnt2+=2){
+              if(vars->E_M[my_iindx[i]-u][cnt1][cnt2/2] != INF){
+                vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                          vars->E_M[my_iindx[i]-u][cnt1][cnt2/2] + vars->E_M_rem[my_iindx[u+1]-j]
+                                          );
+              }
+            }
+          }
+        }
+        if(!vars->E_M[my_iindx[i]-u]) continue;
+        if(!vars->E_M[my_iindx[u+1]-j]) continue;
+
+        dia = referenceBPs1[ij] - referenceBPs1[my_iindx[i]-u] - referenceBPs1[my_iindx[u+1]-j];
+        dib = referenceBPs2[ij] - referenceBPs2[my_iindx[i]-u] - referenceBPs2[my_iindx[u+1]-j];
+
+        for(cnt1 = vars->k_min_values_m[my_iindx[i]-u];
+            cnt1 <= vars->k_max_values_m[my_iindx[i]-u];
+            cnt1++){
+          for(cnt2 = vars->l_min_values_m[my_iindx[i]-u][cnt1];
+              cnt2 <= vars->l_max_values_m[my_iindx[i]-u][cnt1];
+              cnt2+=2){
+            for(cnt3 = vars->k_min_values_m[my_iindx[u+1]-j];
+                cnt3 <= vars->k_max_values_m[my_iindx[u+1]-j];
+                cnt3++){
+              for(cnt4 = vars->l_min_values_m[my_iindx[u+1]-j][cnt3];
+                  cnt4 <= vars->l_max_values_m[my_iindx[u+1]-j][cnt3];
+                  cnt4+=2){
+                if((vars->E_M[my_iindx[i]-u][cnt1][cnt2/2] != INF) && (vars->E_M[my_iindx[u+1]-j][cnt3][cnt4/2] != INF)){
+                  if(((cnt1 + cnt3 + dia) <= maxD1) && ((cnt2 + cnt4 + dib) <= maxD2)){
+                    vars->E_M[ij][cnt1+cnt3+dia][(cnt2+cnt4+dib)/2] = MIN2( vars->E_M[ij][cnt1+cnt3+dia][(cnt2+cnt4+dib)/2],
+                                                                            vars->E_M[my_iindx[i]-u][cnt1][cnt2/2]
+                                                                          + vars->E_M[my_iindx[u+1]-j][cnt3][cnt4/2]
+                                                                          );
+                    updatePosteriorBoundaries(cnt1 + cnt3 + dia,
+                                              cnt2 + cnt4 + dib,
+                                              &min_k_real_m,
+                                              &max_k_real_m,
+                                              &min_l_real_m,
+                                              &max_l_real_m
+                                              );
+#ifdef COUNT_STATES
+                    vars->N_M[ij][cnt1+cnt3+dia][(cnt2+cnt4+dib)/2] += vars->N_M[my_iindx[i]-u][cnt1][cnt2/2] * vars->N_M1[my_iindx[u+1]-j][cnt3][cnt4/2];
+#endif
+                  }
+                  /* collect all cases where dia+cnt1+cnt3 or dib+cnt2+cnt4 exceeds maxD1, maxD2, respectively */
+                  else{
+                    vars->E_M_rem[ij] = MIN2(vars->E_M_rem[ij],
+                                              vars->E_M[my_iindx[i]-u][cnt1][cnt2/2] + vars->E_M[my_iindx[u+1]-j][cnt3][cnt4/2]
+                                              );
+                  }
+                }
+              }
+            }
+          }
+        }
+      }
+
+      /* thats all folks for the multiloop decomposition... */
+
+      adjustArrayBoundaries(&vars->E_M[ij],
+                            &vars->k_min_values_m[ij],
+                            &vars->k_max_values_m[ij],
+                            &vars->l_min_values_m[ij],
+                            &vars->l_max_values_m[ij],
+                            min_k_real_m,
+                            max_k_real_m,
+                            min_l_real_m,
+                            max_l_real_m
+                            );
+
+      adjustArrayBoundaries(&vars->E_M1[ij],
+                            &vars->k_min_values_m1[ij],
+                            &vars->k_max_values_m1[ij],
+                            &vars->l_min_values_m1[ij],
+                            &vars->l_max_values_m1[ij],
+                            min_k_real_m1,
+                            max_k_real_m1,
+                            min_l_real_m1,
+                            max_l_real_m1
+                            );
+
+#ifdef COUNT_STATES
+        /* actually we should adjust the array boundaries here but we might never use the count states option more than once so what....*/
+#endif
+    } /* end of j-loop */
+  }
+
+  /* calculate energies of 5' and 3' fragments */
+
+  /* prepare first entries in E_F5 */
+  for(cnt1 = 1; cnt1 <= TURN+1; cnt1++){
+    vars->E_F5[cnt1] = (int **)space(sizeof(int *));
+    vars->E_F5[cnt1][0] = (int *)space(sizeof(int));
+    vars->E_F5[cnt1][0][0] = 0;
+    vars->E_F5_rem[cnt1] = INF;
+    vars->k_min_values_f[cnt1] = vars->k_max_values_f[cnt1] = 0;
+    vars->l_min_values_f[cnt1] = (int *)space(sizeof(int));
+    vars->l_max_values_f[cnt1] = (int *)space(sizeof(int));
+    vars->l_min_values_f[cnt1][0] = vars->l_max_values_f[cnt1][0] = 0;
+#ifdef COUNT_STATES
+    vars->N_F5[cnt1] = (unsigned long **)space(sizeof(unsigned long *));
+    vars->N_F5[cnt1][0] = (unsigned long *)space(sizeof(unsigned long));
+    vars->N_F5[cnt1][0][0] = 1;
+#endif
+
+  }
+
+
+
+  for (j=TURN+2; j <= seq_length; j++) {
+
+    unsigned int da = referenceBPs1[my_iindx[1]-j] - referenceBPs1[my_iindx[1]-j+1];
+    unsigned int db = referenceBPs2[my_iindx[1]-j] - referenceBPs2[my_iindx[1]-j+1];
+
+    type=ptype[my_iindx[1]-j];
+    additional_en = 0;
+    if(type){
+      if(dangles == 2)
+        additional_en += E_ExtLoop(type, -1, j < seq_length ? S1[j+1] : -1, P);
+      else
+        additional_en += E_ExtLoop(type, -1, -1, P);
+    }
+
+    /* make min and max k guess for memory allocation */
+    int min_k_guess, max_k_guess, min_l_guess, max_l_guess;
+    int *min_l_real, *max_l_real, min_k_real, max_k_real;
+
+    min_k_guess = min_l_guess = 0;
+    max_k_guess = referenceBPs1[my_iindx[1]-j] + mm1[my_iindx[1]-j];
+    max_l_guess = referenceBPs2[my_iindx[1]-j] + mm2[my_iindx[1]-j];
+
+    prepareBoundaries(min_k_guess,
+                      max_k_guess,
+                      min_l_guess,
+                      max_l_guess,
+                      bpdist[my_iindx[1]-j],
+                      &vars->k_min_values_f[j],
+                      &vars->k_max_values_f[j],
+                      &vars->l_min_values_f[j],
+                      &vars->l_max_values_f[j]
+                      );
+
+    preparePosteriorBoundaries( vars->k_max_values_f[j] - vars->k_min_values_f[j] + 1,
+                                vars->k_min_values_f[j],
+                                &min_k_real,
+                                &max_k_real,
+                                &min_l_real,
+                                &max_l_real
+                              );
+
+    prepareArray( &vars->E_F5[j],
+                  vars->k_min_values_f[j],
+                  vars->k_max_values_f[j],
+                  vars->l_min_values_f[j],
+                  vars->l_max_values_f[j]
+                );
+#ifdef COUNT_STATES
+    prepareArray2( &vars->N_F5[j],
+                  vars->k_min_values_f[j],
+                  vars->k_max_values_f[j],
+                  vars->l_min_values_f[j],
+                  vars->l_max_values_f[j]
+                );
+#endif
+
+    /* begin the actual computation of 5' end energies */
+
+    /* j-1 is unpaired ... */
+    vars->E_F5_rem[j] = vars->E_F5_rem[j-1];
+    for(cnt1 = vars->k_min_values_f[j-1]; cnt1 <= vars->k_max_values_f[j-1]; cnt1++){
+      for(cnt2 = vars->l_min_values_f[j-1][cnt1]; cnt2 <= vars->l_max_values_f[j-1][cnt1]; cnt2+=2){
+        if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
+          vars->E_F5[j][cnt1+da][(cnt2+db)/2] = MIN2( vars->E_F5[j][cnt1+da][(cnt2+db)/2],
+                                                      vars->E_F5[j-1][cnt1][cnt2/2]
+                                                    );
+          updatePosteriorBoundaries(cnt1 + da,
+                                    cnt2 + db,
+                                    &min_k_real,
+                                    &max_k_real,
+                                    &min_l_real,
+                                    &max_l_real
+                                    );
+#ifdef COUNT_STATES
+          vars->N_F5[j][cnt1+da][(cnt2+db)/2] += vars->N_F5[j-1][cnt1][cnt2/2];
+#endif
+        }
+        /* collect all cases where da+cnt1 or db+cnt2 exceeds maxD1, maxD2, respectively */
+        else{
+          vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j], vars->E_F5[j-1][cnt1][cnt2/2]);
+        }
+      }
+    }
+    /* j pairs with 1 */
+    if(vars->E_C_rem[my_iindx[1]-j] != INF){
+      vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j], vars->E_C_rem[my_iindx[1]-j] + additional_en);
+    }
+    if(vars->E_C[my_iindx[1]-j])
+      for(cnt1 = vars->k_min_values[my_iindx[1]-j]; cnt1 <= vars->k_max_values[my_iindx[1]-j]; cnt1++)
+        for(cnt2 = vars->l_min_values[my_iindx[1]-j][cnt1]; cnt2 <= vars->l_max_values[my_iindx[1]-j][cnt1]; cnt2+=2){
+          if(vars->E_C[my_iindx[1]-j][cnt1][cnt2/2] != INF){
+            vars->E_F5[j][cnt1][cnt2/2] = MIN2( vars->E_F5[j][cnt1][cnt2/2],
+                                                vars->E_C[my_iindx[1]-j][cnt1][cnt2/2]+ additional_en
+                                              );
+            updatePosteriorBoundaries(cnt1,
+                                      cnt2,
+                                      &min_k_real,
+                                      &max_k_real,
+                                      &min_l_real,
+                                      &max_l_real
+                                      );
+#ifdef COUNT_STATES
+            vars->N_F5[j][cnt1][cnt2/2] += vars->N_C[my_iindx[1]-j][cnt1][cnt2/2];
+#endif
+          }
+        }
+
+    /* j pairs with some other nucleotide -> see below */
+    for (i=j-TURN-1; i>1; i--) {
+      ij = my_iindx[i]-j;
+      type = ptype[ij];
+      if (type) {
+        if(dangles == 2)
+          additional_en = E_ExtLoop(type, S1[i-1], j < seq_length ? S1[j+1] : -1, P);
+        else
+          additional_en = E_ExtLoop(type, -1, -1, P);
+
+        if(vars->E_C_rem[ij] != INF){
+          for(cnt3 = vars->k_min_values_f[i-1]; cnt3 <= vars->k_max_values_f[i-1]; cnt3++)
+            for(cnt4 = vars->l_min_values_f[i-1][cnt3]; cnt4 <= vars->l_max_values_f[i-1][cnt3]; cnt4+=2){
+              if(vars->E_F5[i-1][cnt3][cnt4/2] != INF){
+                vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j],
+                                          vars->E_F5[i-1][cnt3][cnt4/2] + vars->E_C_rem[ij] + additional_en
+                                          );
+              }
+            }
+          if(vars->E_F5_rem[i-1] != INF){
+            vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j],
+                                      vars->E_F5_rem[i-1] + vars->E_C_rem[ij] + additional_en
+                                      );
+          }
+        }
+        if((vars->E_F5_rem[i-1] != INF) && (vars->E_C[ij])){
+          for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++)
+            for(cnt2 = vars->l_min_values[ij][cnt1]; cnt2 <= vars->l_max_values[ij][cnt1]; cnt2+=2)
+              if(vars->E_C[ij][cnt1][cnt2/2]!= INF){
+                vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j],
+                                          vars->E_F5_rem[i-1] + vars->E_C[ij][cnt1][cnt2/2] + additional_en
+                                          );
+              }
+        }
+        if(!vars->E_C[ij]) continue;
+
+        unsigned int d1a = referenceBPs1[my_iindx[1]-j] - referenceBPs1[ij] - referenceBPs1[my_iindx[1]-i+1];
+        unsigned int d1b = referenceBPs2[my_iindx[1]-j] - referenceBPs2[ij] - referenceBPs2[my_iindx[1]-i+1];
+
+        for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++)
+          for(cnt2 = vars->l_min_values[ij][cnt1]; cnt2 <= vars->l_max_values[ij][cnt1]; cnt2+=2)
+            for(cnt3 = vars->k_min_values_f[i-1]; cnt3 <= vars->k_max_values_f[i-1]; cnt3++)
+              for(cnt4 = vars->l_min_values_f[i-1][cnt3]; cnt4 <= vars->l_max_values_f[i-1][cnt3]; cnt4+=2){
+                if(vars->E_F5[i-1][cnt3][cnt4/2] != INF && vars->E_C[ij][cnt1][cnt2/2]!= INF){
+                  if(((cnt1 + cnt3 + d1a) <= maxD1) && ((cnt2 + cnt4 + d1b) <= maxD2)){
+                    vars->E_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2] = MIN2( vars->E_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2],
+                                                                            vars->E_F5[i-1][cnt3][cnt4/2] + vars->E_C[ij][cnt1][cnt2/2] + additional_en
+                                                                          );
+                    updatePosteriorBoundaries(cnt1 + cnt3 + d1a,
+                                              cnt2 + cnt4 + d1b,
+                                              &min_k_real,
+                                              &max_k_real,
+                                              &min_l_real,
+                                              &max_l_real
+                                              );
+#ifdef COUNT_STATES
+                    vars->N_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2] += vars->N_F5[i-1][cnt3][cnt4/2] * vars->N_C[ij][cnt1][cnt2/2];
+#endif
+                  }
+                  /* collect all cases where d1a+cnt1+cnt3 or d1b+cnt2+cnt4 exceeds maxD1, maxD2, respectively */
+                  else{
+                    vars->E_F5_rem[j] = MIN2(vars->E_F5_rem[j],
+                                              vars->E_F5[i-1][cnt3][cnt4/2] + vars->E_C[ij][cnt1][cnt2/2] + additional_en
+                                              );
+                  }
+                }
+              }
+      }
+    }
+
+    /* resize and move memory portions of energy matrix E_F5 */
+    adjustArrayBoundaries(&vars->E_F5[j],
+                          &vars->k_min_values_f[j],
+                          &vars->k_max_values_f[j],
+                          &vars->l_min_values_f[j],
+                          &vars->l_max_values_f[j],
+                          min_k_real,
+                          max_k_real,
+                          min_l_real,
+                          max_l_real
+                          );
+
+  } /* end of j-loop */
+
+
+  if(compute_2Dfold_F3){
+
+    /* prepare first entries in E_F3 */
+    for(cnt1 = seq_length; cnt1 >= seq_length-TURN-1; cnt1--){
+      vars->E_F3[cnt1]        = (int **)space(sizeof(int *));
+      vars->E_F3[cnt1][0]     = (int *) space(sizeof(int));
+      vars->E_F3[cnt1][0][0]  = 0;
+      vars->k_min_values_f3[cnt1]     = vars->k_max_values_f3[cnt1] = 0;
+      vars->l_min_values_f3[cnt1]     = (int *)space(sizeof(int));
+      vars->l_max_values_f3[cnt1]     = (int *)space(sizeof(int));
+      vars->l_min_values_f3[cnt1][0]  = vars->l_max_values_f3[cnt1][0] = 0;
+    }
+    /* begin calculations */
+    for (j=seq_length-TURN-2; j >= 1; j--){
+
+      unsigned int da = referenceBPs1[my_iindx[j]-seq_length] - referenceBPs1[my_iindx[j+1]-seq_length];
+      unsigned int db = referenceBPs2[my_iindx[j]-seq_length] - referenceBPs2[my_iindx[j+1]-seq_length];
+
+      type=ptype[my_iindx[j]-seq_length];
+      additional_en = 0;
+      if(type){
+        if(dangles == 2)
+          additional_en += E_ExtLoop(type, j > 1 ? S1[j-1] : -1, -1, P);
+        else
+          additional_en += E_ExtLoop(type, -1, -1, P);
+      }
+
+      /* make min and max k guess for memory allocation */
+      int min_k_guess, max_k_guess, min_l_guess, max_l_guess;
+      int *min_l_real, *max_l_real, min_k_real, max_k_real;
+
+      min_k_guess = min_l_guess = 0;
+      max_k_guess = referenceBPs1[my_iindx[j]-seq_length] + mm1[my_iindx[j]-seq_length];
+      max_l_guess = referenceBPs2[my_iindx[j]-seq_length] + mm2[my_iindx[j]-seq_length];
+
+      prepareBoundaries(min_k_guess,
+                        max_k_guess,
+                        min_l_guess,
+                        max_l_guess,
+                        bpdist[my_iindx[j]-seq_length],
+                        &vars->k_min_values_f3[j],
+                        &vars->k_max_values_f3[j],
+                        &vars->l_min_values_f3[j],
+                        &vars->l_max_values_f3[j]
+                        );
+
+      preparePosteriorBoundaries( vars->k_max_values_f3[j] - vars->k_min_values_f3[j] + 1,
+                                  vars->k_min_values_f3[j],
+                                  &min_k_real,
+                                  &max_k_real,
+                                  &min_l_real,
+                                  &max_l_real
+                                );
+
+      prepareArray( &vars->E_F3[j],
+                    vars->k_min_values_f3[j],
+                    vars->k_max_values_f3[j],
+                    vars->l_min_values_f3[j],
+                    vars->l_max_values_f3[j]
+                  );
+      /* begin the actual computation of 5' end energies */
+
+      /* j is unpaired ... */
+      for(cnt1 = vars->k_min_values_f3[j+1]; cnt1 <= vars->k_max_values_f3[j+1]; cnt1++){
+        for(cnt2 = vars->l_min_values_f3[j+1][cnt1]; cnt2 <= vars->l_max_values_f3[j+1][cnt1]; cnt2+=2){
+          vars->E_F3[j][cnt1+da][(cnt2+db)/2] = MIN2( vars->E_F3[j][cnt1+da][(cnt2+db)/2],
+                                                      vars->E_F3[j+1][cnt1][cnt2/2]
+                                                    );
+          updatePosteriorBoundaries(cnt1 + da,
+                                    cnt2 + db,
+                                    &min_k_real,
+                                    &max_k_real,
+                                    &min_l_real,
+                                    &max_l_real
+                                    );
+        }
+      }
+      /* j pairs with n */
+      if(vars->E_C[my_iindx[j]-seq_length])
+        for(cnt1 = vars->k_min_values[my_iindx[j]-seq_length]; cnt1 <= vars->k_max_values[my_iindx[j]-seq_length]; cnt1++)
+          for(cnt2 = vars->l_min_values[my_iindx[j]-seq_length][cnt1]; cnt2 <= vars->l_max_values[my_iindx[j]-seq_length][cnt1]; cnt2+=2){
+            if(vars->E_C[my_iindx[j]-seq_length][cnt1][cnt2/2] != INF){
+              vars->E_F3[j][cnt1][cnt2/2] = MIN2( vars->E_F3[j][cnt1][cnt2/2],
+                                                  vars->E_C[my_iindx[j]-seq_length][cnt1][cnt2/2]+ additional_en
+                                                );
+              updatePosteriorBoundaries(cnt1,
+                                        cnt2,
+                                        &min_k_real,
+                                        &max_k_real,
+                                        &min_l_real,
+                                        &max_l_real
+                                        );
+            }
+          }
+
+      /* j pairs with some other nucleotide -> see below */
+      for (i=j-TURN-1; i>1; i--) {
+        ij = my_iindx[i]-j;
+        if(!vars->E_C[ij]) continue;
+        type = ptype[ij];
+        if (type) {
+          unsigned int d1a = referenceBPs1[my_iindx[1]-j] - referenceBPs1[ij] - referenceBPs1[my_iindx[1]-i+1];
+          unsigned int d1b = referenceBPs2[my_iindx[1]-j] - referenceBPs2[ij] - referenceBPs2[my_iindx[1]-i+1];
+
+          if(dangles == 2)
+            additional_en = E_ExtLoop(type, S1[i-1], j < seq_length ? S1[j+1] : -1, P);
+          else
+            additional_en = E_ExtLoop(type, -1, -1, P);
+
+          for(cnt1 = vars->k_min_values[ij]; cnt1 <= vars->k_max_values[ij]; cnt1++)
+            for(cnt2 = vars->l_min_values[ij][cnt1]; cnt2 <= vars->l_max_values[ij][cnt1]; cnt2+=2)
+              for(cnt3 = vars->k_min_values_f[i-1]; cnt3 <= vars->k_max_values_f[i-1]; cnt3++)
+                for(cnt4 = vars->l_min_values_f[i-1][cnt3]; cnt4 <= vars->l_max_values_f[i-1][cnt3]; cnt4+=2){
+                  if(vars->E_F5[i-1][cnt3][cnt4/2] != INF && vars->E_C[ij][cnt1][cnt2/2]!= INF){
+                    vars->E_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2] = MIN2( vars->E_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2],
+                                                                            vars->E_F5[i-1][cnt3][cnt4/2] + vars->E_C[ij][cnt1][cnt2/2] + additional_en
+                                                                          );
+                    updatePosteriorBoundaries(cnt1 + cnt3 + d1a,
+                                              cnt2 + cnt4 + d1b,
+                                              &min_k_real,
+                                              &max_k_real,
+                                              &min_l_real,
+                                              &max_l_real
+                                              );
+#ifdef COUNT_STATES
+                    vars->N_F5[j][cnt1+cnt3+d1a][(cnt2+cnt4+d1b)/2] += vars->N_F5[i-1][cnt3][cnt4/2] * vars->N_C[ij][cnt1][cnt2/2];
+#endif
+                  }
+                }
+        }
+      }
+
+      /* resize and move memory portions of energy matrix E_F5 */
+      adjustArrayBoundaries(&vars->E_F5[j],
+                            &vars->k_min_values_f[j],
+                            &vars->k_max_values_f[j],
+                            &vars->l_min_values_f[j],
+                            &vars->l_max_values_f[j],
+                            min_k_real,
+                            max_k_real,
+                            min_l_real,
+                            max_l_real
+                            );
+
+    } /* end of j-loop */
+
+
+
+
+  }
+}
+
+
+/*---------------------------------------------------------------------------*/
+
+PUBLIC void update_TwoDfold_params(TwoDfold_vars *vars){
+  if(vars->P) free(vars->P);
+  vars->P = scale_parameters();
+  make_pair_matrix();
+}
+
+/*---------------------------------------------------------------------------*/
+PRIVATE void make_ptypes(TwoDfold_vars *vars) {
+  int n,i,j,k,l;
+
+  n=vars->S[0];
+  for (k=1; k<n-TURN; k++)
+    for (l=1; l<=2; l++) {
+      int type,ntype=0,otype=0;
+      i=k; j = i+TURN+l; if (j>n) continue;
+      type = pair[vars->S[i]][vars->S[j]];
+      while ((i>=1)&&(j<=n)) {
+        if ((i>1)&&(j<n)) ntype = pair[vars->S[i-1]][vars->S[j+1]];
+        if (noLonelyPairs && (!otype) && (!ntype))
+          type = 0; /* i.j can only form isolated pairs */
+        vars->ptype[vars->my_iindx[i]-j] = (char) type;
+        otype =  type;
+        type  = ntype;
+        i--; j++;
+      }
+    }
+}
+
+PRIVATE void backtrack_f5(unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars){
+  int           *my_iindx, energy, type, dangles, cnt1, cnt2, cnt3, cnt4;
+  int           **l_min_values, **l_max_values,**l_min_values_f, **l_max_values_f;
+  int           *k_min_values, *k_max_values,*k_min_values_f, *k_max_values_f;
+  int           ***E_C, ***E_F5;
+  int           *E_C_rem, *E_F5_rem;
+  unsigned int   i, ij, seq_length, maxD1, maxD2;
+  short *S1;
+  unsigned int   *referenceBPs1, *referenceBPs2;
+  char  *ptype;
+  paramT   *P;
+  unsigned int da, db;
+
+  P               = vars->P;
+  seq_length      = vars->seq_length;
+  S1              = vars->S1;
+  ptype           = vars->ptype;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+  dangles         = vars->dangles;
+  E_F5            = vars->E_F5;
+  l_min_values_f  = vars->l_min_values_f;
+  l_max_values_f  = vars->l_max_values_f;
+  k_min_values_f  = vars->k_min_values_f;
+  k_max_values_f  = vars->k_max_values_f;
+
+  E_C             = vars->E_C;
+  l_min_values    = vars->l_min_values;
+  l_max_values    = vars->l_max_values;
+  k_min_values    = vars->k_min_values;
+  k_max_values    = vars->k_max_values;
+
+  E_F5_rem       = vars->E_F5_rem;
+  E_C_rem        = vars->E_C_rem;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+
+  da = referenceBPs1[my_iindx[1]-j] - referenceBPs1[my_iindx[1]-j+1];
+  db = referenceBPs2[my_iindx[1]-j] - referenceBPs2[my_iindx[1]-j+1];
+
+  if(j<TURN+2) return;
+
+  /* F5[j] == F5[j-1] ? */
+  if(k == -1){
+    if(E_F5_rem[j]==INF)
+      return;
+    else if(E_F5_rem[j] == E_F5_rem[j-1]){
+      backtrack_f5(j-1,k,l,structure, vars);
+      return;
+    }
+    else if(E_F5[j-1]){
+      for(cnt1 =  k_min_values_f[j-1];
+        cnt1 <= k_max_values_f[j-1];
+        cnt1++){
+        for(cnt2 = l_min_values_f[j-1][cnt1];
+            cnt2 <= l_max_values_f[j-1][cnt1];
+            cnt2+=2){
+          if(((cnt1 + da) > maxD1) || ((cnt2 + db) > maxD2)){
+            if(E_F5_rem[j] == E_F5[j-1][cnt1][cnt2/2]){
+              backtrack_f5(j-1, cnt1, cnt2, structure, vars);
+              return;
+            }
+          }
+        }
+      }
+    }
+  }
+  else if((k >= da) && (l >= db)){
+    if(E_F5[j-1]){
+      if((k - da >= k_min_values_f[j-1]) && (k - da <= k_max_values_f[j-1])){
+        if((l - db >= l_min_values_f[j-1][k-da]) && (l - db <= l_max_values_f[j-1][k-da]))
+          if(E_F5[j-1][k-da][(l-db)/2] == E_F5[j][k][l/2]){
+            backtrack_f5(j-1, k-da, l-db, structure, vars);
+            return;
+          }
+      }
+    }
+  }
+
+  type = ptype[my_iindx[1]-j];
+  if(type){
+    if(dangles == 2)
+      energy = E_ExtLoop(type, -1, j < seq_length ? S1[j+1] : -1, P);
+    else
+      energy = E_ExtLoop(type, -1, -1, P);
+
+    if(k == -1){
+      if(E_C_rem[my_iindx[1]-j] + energy == E_F5_rem[j]){
+          backtrack_c(1, j, -1, -1, structure, vars);
+          return;
+      }
+    }
+    else if(k >= k_min_values[my_iindx[1]-j] && (k <= k_max_values[my_iindx[1]-j])){
+
+      if((l >= l_min_values[my_iindx[1]-j][k]) && (l <= l_max_values[my_iindx[1]-j][k]))
+        if(E_C[my_iindx[1]-j][k][l/2] + energy == E_F5[j][k][l/2]){
+          backtrack_c(1, j, k, l, structure, vars);
+          return;
+        }
+    }
+  }
+
+  for (i=j-TURN-1; i>1; i--) {
+    ij = my_iindx[i]-j;
+    type = ptype[ij];
+    if (type) {
+      unsigned int d1a = referenceBPs1[my_iindx[1]-j] - referenceBPs1[ij] - referenceBPs1[my_iindx[1]-i+1];
+      unsigned int d1b = referenceBPs2[my_iindx[1]-j] - referenceBPs2[ij] - referenceBPs2[my_iindx[1]-i+1];
+
+      if(dangles == 2)
+        energy = E_ExtLoop(type, S1[i-1], j < seq_length ? S1[j+1] : -1, P);
+      else
+        energy = E_ExtLoop(type, -1, -1, P);
+
+      if(k == -1){
+        if(E_C_rem[ij] != INF){
+          for(cnt1 = k_min_values_f[i-1];
+              cnt1 <= k_max_values_f[i-1];
+              cnt1++){
+            for(cnt2 = l_min_values_f[i-1][cnt1];
+                cnt2 <= l_max_values_f[i-1][cnt1];
+                cnt2+=2){
+              if(E_F5_rem[j] == (E_F5[i-1][cnt1][cnt2/2] + E_C_rem[ij] + energy)){
+                backtrack_f5(i-1, cnt1, cnt2, structure, vars);
+                backtrack_c(i,j,-1,-1,structure, vars);
+                return;
+              }
+            }
+          }
+          if(E_F5_rem[j] == (E_F5_rem[i-1] + E_C_rem[ij] + energy)){
+            backtrack_f5(i-1, -1, -1, structure, vars);
+            backtrack_c(i,j,-1,-1,structure,vars);
+            return;
+          }
+        }
+        if(E_F5_rem[i-1] != INF){
+          for(cnt1 = k_min_values[ij];
+              cnt1 <= k_max_values[ij];
+              cnt1++){
+            for(cnt2 = l_min_values[ij][cnt1];
+                cnt2 <= l_max_values[ij][cnt1];
+                cnt2 += 2){
+               if(E_F5_rem[j] == (E_F5_rem[i-1] + E_C[ij][cnt1][cnt2/2] + energy)){
+                backtrack_f5(i-1,-1,-1,structure,vars);
+                backtrack_c(i,j,cnt1,cnt2,structure,vars);
+                return;
+              }
+            }
+          }
+        }
+        for(cnt1 = k_min_values_f[i-1];
+            cnt1 <= k_max_values_f[i-1];
+            cnt1++)
+          for(cnt2 = l_min_values_f[i-1][cnt1];
+              cnt2 <= l_max_values_f[i-1][cnt1];
+              cnt2 += 2)
+            for(cnt3 = k_min_values[ij];
+                cnt3 <= k_max_values[ij];
+                cnt3++)
+              for(cnt4 = l_min_values[ij][cnt3];
+                  cnt4 <= l_max_values[ij][cnt3];
+                  cnt4 += 2){
+                if(((cnt1 + cnt3 + d1a)>maxD1) || ((cnt2+cnt4+d1b)>maxD2)){
+                  if(E_F5_rem[j] == (E_F5[i-1][cnt1][cnt2/2] + E_C[ij][cnt3][cnt4/2] + energy)){
+                    backtrack_f5(i-1,cnt1,cnt2,structure,vars);
+                    backtrack_c(i,j,cnt3,cnt4,structure,vars);
+                    return;
+                  }
+                }
+              }
+      }
+      else if((k >= d1a) && (l >= d1b)){
+        int k_f_max = MIN2(k-d1a, k_max_values_f[i-1]);
+
+        for(cnt1 = k_min_values_f[i-1]; cnt1 <= k_f_max; cnt1++){
+          int l_f_max = MIN2(l - d1b, l_max_values_f[i-1][cnt1]);
+          for(cnt2 = l_min_values_f[i-1][cnt1]; cnt2 <= l_f_max; cnt2+=2){
+            int k_c = k - d1a - cnt1;
+            if((k_c >= k_min_values[ij]) && (k_c <= k_max_values[ij])){
+              int l_c = l - d1b - cnt2;
+              if((l_c >= l_min_values[ij][k_c]) && (l_c <= l_max_values[ij][k_c])){
+                if(E_F5[j][k][l/2] == (E_F5[i-1][cnt1][cnt2/2] + E_C[ij][k_c][l_c/2] + energy)){
+                  backtrack_f5(i-1, cnt1, cnt2, structure, vars);
+                  backtrack_c(i, j, k_c, l_c, structure, vars);
+                  return;
+                }
+              }
+            }
+          }
+
+        }
+      }
+    }
+  }
+  nrerror("backtracking failed in f5");
+}
+
+PRIVATE void backtrack_c(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars){
+  unsigned int p, q, pq, ij, maxp, maxD1, maxD2;
+  int *my_iindx, type, type_2, energy, no_close, dangles, base_d1, base_d2, d1, d2, cnt1, cnt2, cnt3, cnt4;
+  int           **l_min_values, **l_max_values,**l_min_values_m, **l_max_values_m,**l_min_values_m1, **l_max_values_m1;
+  int           *k_min_values, *k_max_values,*k_min_values_m, *k_max_values_m,*k_min_values_m1, *k_max_values_m1;
+  int           ***E_C, ***E_M, ***E_M1, *E_C_rem, *E_M_rem, *E_M1_rem;
+  short *S1;
+  unsigned int   *referenceBPs1, *referenceBPs2;
+  char  *ptype, *sequence;
+  paramT   *P;
+
+  P               = vars->P;
+  sequence        = vars->sequence;
+  S1              = vars->S1;
+  ptype           = vars->ptype;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+  dangles         = vars->dangles;
+
+  E_C             = vars->E_C;
+  l_min_values    = vars->l_min_values;
+  l_max_values    = vars->l_max_values;
+  k_min_values    = vars->k_min_values;
+  k_max_values    = vars->k_max_values;
+
+  E_M             = vars->E_M;
+  l_min_values_m  = vars->l_min_values_m;
+  l_max_values_m  = vars->l_max_values_m;
+  k_min_values_m  = vars->k_min_values_m;
+  k_max_values_m  = vars->k_max_values_m;
+
+  E_M1            = vars->E_M1;
+  l_min_values_m1 = vars->l_min_values_m1;
+  l_max_values_m1 = vars->l_max_values_m1;
+  k_min_values_m1 = vars->k_min_values_m1;
+  k_max_values_m1 = vars->k_max_values_m1;
+
+  E_C_rem        = vars->E_C_rem;
+  E_M_rem        = vars->E_M_rem;
+  E_M1_rem       = vars->E_M1_rem;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+
+
+  ij = my_iindx[i]-j;
+
+  int e = (k==-1) ? E_C_rem[ij] : E_C[ij][k][l/2];
+
+  type = ptype[ij];
+
+  no_close = (((type==3)||(type==4))&&no_closingGU);
+  structure[i-1] = '(';
+  structure[j-1] = ')';
+
+  base_d1 = ((unsigned int)vars->reference_pt1[i] != j) ? 1 : -1;
+  base_d2 = ((unsigned int)vars->reference_pt2[i] != j) ? 1 : -1;
+
+  base_d1 += referenceBPs1[ij];
+  base_d2 += referenceBPs2[ij];
+
+  if(k == -1){
+    if(((unsigned int)base_d1 > maxD1) || ((unsigned int)base_d2 > maxD2)){
+      if(e == E_Hairpin(j-i-1, type, S1[i+1], S1[j-1], sequence+i-1, P)) return;
+    }
+  }
+  else{
+    if((unsigned int)base_d1 == k)
+      if((unsigned int)base_d2 == l)
+        if(E_Hairpin(j-i-1, type, S1[i+1], S1[j-1], sequence+i-1, P) == e) return;
+  }
+  maxp = MIN2(j-2-TURN,i+MAXLOOP+1);
+  for(p = i+1; p <= maxp; p++){
+    unsigned int minq, ln_pre;
+    minq = p + TURN + 1;
+    ln_pre = j - i - 1;
+    if(ln_pre > minq + MAXLOOP) minq = ln_pre - MAXLOOP - 1;
+    for (q = minq; q < j; q++) {
+      pq = my_iindx[p]-q;
+      type_2 = ptype[pq];
+      if (type_2==0) continue;
+      type_2 = rtype[type_2];
+
+      /* d2 = dbp(S_{i,j}, S_{p.q} + {i,j}) */
+      d1 = base_d1 - referenceBPs1[pq];
+      d2 = base_d2 - referenceBPs2[pq];
+
+      energy = E_IntLoop(p-i-1, j-q-1, type, type_2, S1[i+1], S1[j-1], S1[p-1], S1[q+1], P);
+
+
+      if(k == -1){
+        if(E_C_rem[pq] != INF)
+          if(e == (E_C_rem[pq] + energy)){
+            backtrack_c(p,q,-1,-1,structure,vars);
+            return;
+          }
+        if(E_C[pq])
+        for(cnt1 = k_min_values[pq];
+            cnt1 <= k_max_values[pq];
+            cnt1++)
+          for(cnt2 = l_min_values[pq][cnt1];
+              cnt2 <= l_max_values[pq][cnt1];
+              cnt2 += 2){
+            if(((cnt1 + d1) > maxD1) || ((cnt2 + d2) > maxD2)){
+              if(e == (E_C[pq][cnt1][cnt2/2] + energy)){
+                backtrack_c(p,q,cnt1,cnt2,structure,vars);
+                return;
+              }
+            }
+          }
+      }
+      else{
+        if(!E_C[pq]) continue;
+        if(d1 <= k && d2 <= l){
+          if((k-d1 >= k_min_values[pq]) && (k-d1) <= k_max_values[pq])
+            if((l - d2 >= l_min_values[pq][k-d1]) && (l-d2 <= l_max_values[pq][k-d1]))
+              if(E_C[pq][k-d1][(l-d2)/2] + energy == e){
+                backtrack_c(p, q, k-d1, l-d2, structure, vars);
+                return;
+              }
+        }
+      }
+    } /* end q-loop */
+  } /* end p-loop */
+
+  /* multi-loop decomposition ------------------------*/
+  if(!no_close){
+    unsigned int u;
+    int tt;
+    if(k==-1){
+      for(u=i+TURN+2; u<j-TURN-2;u++){
+        int i1u, u1j1;
+        i1u   = my_iindx[i+1]-u;
+        u1j1  = my_iindx[u+1]-j+1;
+        tt = rtype[type];
+        energy = P->MLclosing;
+        if(dangles == 2)
+          energy += E_MLstem(tt, S1[j-1], S1[i+1], P);
+        else
+          energy += E_MLstem(tt, -1, -1, P);
+
+
+        if(E_M_rem[i1u] != INF){
+          if(E_M1[u1j1])
+          for(cnt1 = k_min_values_m1[u1j1];
+              cnt1 <= k_max_values_m1[u1j1];
+              cnt1++)
+            for(cnt2 = l_min_values_m1[u1j1][cnt1];
+                cnt2 <= l_max_values_m1[u1j1][cnt1];
+                cnt2 += 2){
+              if(e == (E_M_rem[i1u] + E_M1[u1j1][cnt1][cnt2/2] + energy)){
+                backtrack_m(i+1,u,-1,-1,structure,vars);
+                backtrack_m1(u+1,j-1,cnt1,cnt2,structure,vars);
+                return;
+              }
+            }
+          if(E_M1_rem[u1j1] != INF){
+            if(e == (E_M_rem[i1u] + E_M1_rem[u1j1] + energy)){
+              backtrack_m(i+1, u, -1, -1, structure, vars);
+              backtrack_m1(u+1, j-1, -1, -1, structure, vars);
+              return;
+            }
+          }
+        }
+        if(E_M1_rem[u1j1] != INF){
+          if(E_M[i1u])
+          for(cnt1 = k_min_values_m[i1u];
+              cnt1 <= k_max_values_m[i1u];
+              cnt1++)
+            for(cnt2 = l_min_values_m[i1u][cnt1];
+                cnt2 <= l_max_values_m[i1u][cnt1];
+                cnt2 += 2)
+              if(e == (E_M[i1u][cnt1][cnt2/2] + E_M1_rem[u1j1] + energy)){
+                backtrack_m(i+1,u,cnt1,cnt2,structure,vars);
+                backtrack_m1(u+1,j-1,-1,-1,structure,vars);
+                return;
+              }
+        }
+
+        /* now all cases where we exceed the maxD1/D2 scope by combination of E_M and E_M1 */
+        if(!E_M[i1u]) continue;
+        if(!E_M1[u1j1]) continue;
+        /* get distance to reference if closing this multiloop
+        *  dist3 = dbp(S_{i,j}, {i,j} + S_{i+1.u} + S_{u+1,j-1})
+        */
+        d1 = base_d1 - referenceBPs1[i1u] - referenceBPs1[u1j1];
+        d2 = base_d2 - referenceBPs2[i1u] - referenceBPs2[u1j1];
+        
+        for(cnt1 = vars->k_min_values_m[i1u];
+            cnt1 <= vars->k_max_values_m[i1u];
+            cnt1++)
+          for(cnt2 = vars->l_min_values_m[i1u][cnt1];
+              cnt2 <= vars->l_max_values_m[i1u][cnt1];
+              cnt2+=2)
+            for(cnt3 = vars->k_min_values_m1[u1j1];
+                cnt3 <= vars->k_max_values_m1[u1j1];
+                cnt3++)
+              for(cnt4 = vars->l_min_values_m1[u1j1][cnt3];
+                  cnt4 <= vars->l_max_values_m1[u1j1][cnt3];
+                  cnt4+=2){
+                if(((cnt1 + cnt3 + d1) > maxD1) || ((cnt2 + cnt4 + d2) > maxD2)){
+                  if(e == (E_M[i1u][cnt1][cnt2/2] + E_M1[u1j1][cnt3][cnt4/2] + energy)){
+                    backtrack_m(i+1,u,cnt1,cnt2,structure,vars);
+                    backtrack_m1(u+1,j-1,cnt3,cnt4,structure,vars);
+                    return;
+                  }
+                }
+              }
+      }
+    }
+    else{
+      for(u=i+TURN+2; u<j-TURN-2;u++){
+        int i1u, u1j1;
+        i1u   = my_iindx[i+1]-u;
+        u1j1  = my_iindx[u+1]-j+1;
+        if(!E_M[i1u]) continue;
+        if(!E_M1[u1j1]) continue;
+
+        /* get distance to reference if closing this multiloop
+        *  dist3 = dbp(S_{i,j}, {i,j} + S_{i+1.u} + S_{u+1,j-1})
+        */
+        d1 = base_d1 - referenceBPs1[i1u] - referenceBPs1[u1j1];
+        d2 = base_d2 - referenceBPs2[i1u] - referenceBPs2[u1j1];
+
+        tt = rtype[type];
+        energy = P->MLclosing;
+        if(dangles == 2)
+          energy += E_MLstem(tt, S1[j-1], S1[i+1], P);
+        else
+          energy += E_MLstem(tt, -1, -1, P);
+
+        if((d1 <= k) && (d2 <= l))
+          for(cnt1 = k_min_values_m[i1u];
+              cnt1 <= MIN2(k-d1, k_max_values_m[i1u]);
+              cnt1++)
+            for(cnt2 = l_min_values_m[i1u][cnt1];
+                cnt2 <= MIN2(l-d2, l_max_values_m[i1u][cnt1]);
+                cnt2+=2)
+              if(     ((k-d1-cnt1) >= k_min_values_m1[u1j1])
+                  &&  ((k-d1-cnt1) <= k_max_values_m1[u1j1]))
+                if(     ((l-d2-cnt2) >= l_min_values_m1[u1j1][k-d1-cnt1])
+                    &&  ((l-d2-cnt2) <= l_max_values_m1[u1j1][k-d1-cnt1]))
+                  if(e == (energy + E_M[i1u][cnt1][cnt2/2] + E_M1[u1j1][k-d1-cnt1][(l-d2-cnt2)/2])){
+                    backtrack_m(i+1, u, cnt1, cnt2, structure, vars);
+                    backtrack_m1(u+1, j-1, k-d1-cnt1, l-d2-cnt2, structure, vars);
+                    return;
+                  }
+      }
+    }
+  }
+  nrerror("backtracking failed in c");
+}
+
+PRIVATE void backtrack_m(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars){
+  unsigned int u, ij, seq_length, base_d1, base_d2, d1, d2, maxD1, maxD2;
+  int *my_iindx, type, energy, dangles,circ, cnt1, cnt2, cnt3, cnt4;
+  int           **l_min_values, **l_max_values,**l_min_values_m, **l_max_values_m;
+  int           *k_min_values, *k_max_values,*k_min_values_m, *k_max_values_m;
+  int           ***E_C, ***E_M, *E_C_rem, *E_M_rem;
+  short *S1;
+  unsigned int   *referenceBPs1, *referenceBPs2;
+  char  *ptype;
+  paramT   *P;
+
+  P           = vars->P;
+  seq_length  = vars->seq_length;
+  S1          = vars->S1;
+  circ        = vars->circ;
+  ptype       = vars->ptype;
+  my_iindx    = vars->my_iindx;
+  referenceBPs1  = vars->referenceBPs1;
+  referenceBPs2  = vars->referenceBPs2;
+  dangles     = vars->dangles;
+
+  E_C             = vars->E_C;
+  l_min_values    = vars->l_min_values;
+  l_max_values    = vars->l_max_values;
+  k_min_values    = vars->k_min_values;
+  k_max_values    = vars->k_max_values;
+
+  E_M             = vars->E_M;
+  l_min_values_m  = vars->l_min_values_m;
+  l_max_values_m  = vars->l_max_values_m;
+  k_min_values_m  = vars->k_min_values_m;
+  k_max_values_m  = vars->k_max_values_m;
+
+  E_C_rem        = vars->E_C_rem;
+  E_M_rem        = vars->E_M_rem;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+
+  ij = my_iindx[i]-j;
+  int e = (k == -1) ? E_M_rem[ij] : E_M[ij][k][l/2];
+
+  base_d1 = referenceBPs1[ij];
+  base_d2 = referenceBPs2[ij];
+
+  if(k == -1){
+    /* new_fML = ML(i+1,j)+c */
+    d1 = base_d1 - referenceBPs1[my_iindx[i+1]-j];
+    d2 = base_d2 - referenceBPs2[my_iindx[i+1]-j];
+    if(E_M_rem[my_iindx[i+1]-j] != INF){
+      if(e == (E_M_rem[my_iindx[i+1]-j] + P->MLbase)){
+        backtrack_m(i+1,j,-1,-1,structure,vars);
+        return;
+      }
+    }
+    if(E_M[my_iindx[i+1]-j])
+    for(cnt1 = k_min_values_m[my_iindx[i+1]-j];
+        cnt1 <= k_max_values_m[my_iindx[i+1]-j];
+        cnt1++)
+      for(cnt2 = l_min_values_m[my_iindx[i+1]-j][cnt1];
+          cnt2 <= l_max_values_m[my_iindx[i+1]-j][cnt1];
+          cnt2 += 2)
+        if(((cnt1 + d1) > maxD1) || ((cnt2 + d2) > maxD2)){
+          if(e == (E_M[my_iindx[i+1]-j][cnt1][cnt2/2] + P->MLbase)){
+            backtrack_m(i+1,j,cnt1,cnt2,structure,vars);
+            return;
+          }
+        }
+
+    /* new_fML = min(ML(i,j-1) + c, new_fML) */
+    d1 = base_d1 - referenceBPs1[ij+1];
+    d2 = base_d2 - referenceBPs2[ij+1];
+    if(E_M_rem[ij+1] != INF){
+      if(e == (E_M_rem[ij+1] + P->MLbase)){
+        backtrack_m(i,j-1,-1,-1,structure,vars);
+        return;
+      }
+    }
+    if(E_M[ij+1])
+    for(cnt1 = k_min_values_m[ij+1];
+        cnt1 <= k_max_values_m[ij+1];
+        cnt1++)
+      for(cnt2 = l_min_values_m[ij+1][cnt1];
+          cnt2 <= l_max_values_m[ij+1][cnt1];
+          cnt2 += 2)
+        if(((cnt1 + d1) > maxD1) || ((cnt2 + d2) > maxD2)){
+          if(e == (E_M[ij+1][cnt1][cnt2/2] + P->MLbase)){
+            backtrack_m(i,j-1,cnt1,cnt2,structure,vars);
+            return;
+          }
+        }
+
+    /* new_fML = min(new_fML, C(i,j)+b) */
+    if(E_C_rem[ij] != INF){
+      type = ptype[ij];
+      if(dangles == 2)
+        energy = E_MLstem(type, ((i > 1) || circ) ? S1[i-1] : -1, ((j < seq_length) || circ) ? S1[j+1] : -1, P);
+      else
+        energy = E_MLstem(type, -1, -1, P);
+      if(e == (E_C_rem[ij] + energy)){
+        backtrack_c(i,j,-1,-1,structure,vars);
+        return;
+      }
+    }
+
+    /* modular decomposition -------------------------------*/
+    for(u = i+1+TURN; u <= j-2-TURN; u++){
+      int iu, uj;
+      iu = my_iindx[i]-u;
+      uj = my_iindx[u+1]-j;
+      type = ptype[uj];
+
+      d1 = base_d1 - referenceBPs1[iu] - referenceBPs1[uj];
+      d2 = base_d2 - referenceBPs2[iu] - referenceBPs2[uj];
+
+      if(dangles == 2)
+        energy = E_MLstem(type, S1[u], (j < seq_length) || circ ? S1[j+1] : -1, P);
+      else
+        energy = E_MLstem(type, -1, -1, P);
+
+      if(E_M_rem[iu] != INF){
+        if(E_C[uj])
+        for(cnt1 = k_min_values[uj];
+            cnt1 <= k_max_values[uj];
+            cnt1++)
+          for(cnt2 = l_min_values[uj][cnt1];
+              cnt2 <= l_max_values[uj][cnt1];
+              cnt2 += 2)
+            if(e == (E_M_rem[iu] + E_C[uj][cnt1][cnt2/2] + energy)){
+              backtrack_m(i,u,-1,-1,structure,vars);
+              backtrack_c(u+1,j,cnt1,cnt2,structure, vars);
+              return;
+            }
+        if(E_C_rem[uj] != INF){
+          if(e == (E_M_rem[iu] + E_C_rem[uj] + energy)){
+            backtrack_m(i,u,-1,-1,structure,vars);
+            backtrack_c(u+1,j,-1,-1,structure,vars);
+            return;
+          }
+        }
+      }
+      if(E_C_rem[uj] != INF){
+        if(E_M[iu])
+        for(cnt1 = k_min_values_m[iu];
+            cnt1 <= k_max_values_m[iu];
+            cnt1++)
+          for(cnt2 = l_min_values_m[iu][cnt1];
+              cnt2 <= l_max_values_m[iu][cnt1];
+              cnt2 += 2)
+            if(e == (E_M[iu][cnt1][cnt2/2] + E_C_rem[uj] + energy)){
+              backtrack_m(i,u,cnt1,cnt2,structure,vars);
+              backtrack_c(u+1,j,-1,-1,structure,vars);
+              return;
+            }
+      }
+
+      if(!E_M[iu]) continue;
+      if(!E_C[uj]) continue;
+
+      for(cnt1 = k_min_values_m[iu];
+          cnt1 <= k_max_values_m[iu];
+          cnt1++)
+        for(cnt2 = l_min_values_m[iu][cnt1];
+            cnt2 <= l_max_values_m[iu][cnt1];
+            cnt2 += 2)
+          for(cnt3 = k_min_values[uj];
+              cnt3 <= k_max_values[uj];
+              cnt3++){
+            for(cnt4 = l_min_values[uj][cnt3];
+                cnt4 <= l_max_values[uj][cnt3];
+                cnt4 += 2)
+              if(((cnt1 + cnt3 + d1) > maxD1) || ((cnt2 + cnt4 + d2) > maxD2))
+                if(e == (E_M[iu][cnt1][cnt2/2] + E_C[uj][cnt3][cnt4/2] + energy)){
+                  backtrack_m(i, u, cnt1, cnt2, structure, vars);
+                  backtrack_c(u+1, j, cnt3, cnt4, structure, vars);
+                  return;
+                }
+          }
+    }
+
+  } /* end if (k == -1) */
+  else{
+    d1 = base_d1 - referenceBPs1[my_iindx[i+1]-j];
+    d2 = base_d2 - referenceBPs2[my_iindx[i+1]-j];
+    /* new_fML = ML(i+1,j)+c */
+    if(d1 <= k && d2 <= l)
+      if((k-d1 >= k_min_values_m[my_iindx[i+1]-j]) && (k-d1 <= k_max_values_m[my_iindx[i+1]-j]))
+        if((l-d2 >= l_min_values_m[my_iindx[i+1]-j][k-d1]) && (l-d2 <= l_max_values_m[my_iindx[i+1]-j][k-d1])){
+          if(E_M[my_iindx[i+1]-j][k-d1][(l-d2)/2] + P->MLbase == e){
+            backtrack_m(i+1, j, k-d1, l-d2, structure, vars);
+            return;
+          }
+        }
+
+    d1 = base_d1 - referenceBPs1[ij+1];
+    d2 = base_d2 - referenceBPs2[ij+1];
+
+    /* new_fML = min(ML(i,j-1) + c, new_fML) */
+    if(E_M[ij+1])
+      if(d1 <= k && d2 <= l)
+        if((k-d1 >= k_min_values_m[ij+1]) && (k-d1 <= k_max_values_m[ij+1]))
+          if((l-d2 >= l_min_values_m[ij+1][k-d1]) && (l-d2 <= l_max_values_m[ij+1][k-d1]))
+            if(E_M[ij+1][k-d1][(l-d2)/2] + P->MLbase == e){
+              backtrack_m(i, j-1, k-d1, l-d2, structure, vars);
+              return;
+            }
+
+    /* new_fML = min(new_fML, C(i,j)+b) */
+    if(E_C[ij]){
+      type = ptype[ij];
+
+      if(dangles == 2)
+        energy = E_MLstem(type, ((i > 1) || circ) ? S1[i-1] : -1, ((j < seq_length) || circ) ? S1[j+1] : -1, P);
+      else
+        energy = E_MLstem(type, -1, -1, P);
+
+      if((k >= k_min_values[ij]) && (k <= k_max_values[ij]))
+        if((l >= l_min_values[ij][k]) && (l <= l_max_values[ij][k])){
+          if(E_C[ij][k][l/2] + energy == e){
+            backtrack_c(i, j, k, l, structure, vars);
+            return;
+          }
+        }
+    }
+
+      /* modular decomposition -------------------------------*/
+
+    for(u = i+1+TURN; u <= j-2-TURN; u++){
+      if(!E_M[my_iindx[i]-u]) continue;
+      if(!E_C[my_iindx[u+1]-j]) continue;
+      type = ptype[my_iindx[u+1]-j];
+
+      d1 = base_d1 - referenceBPs1[my_iindx[i]-u] - referenceBPs1[my_iindx[u+1]-j];
+      d2 = base_d2 - referenceBPs2[my_iindx[i]-u] - referenceBPs2[my_iindx[u+1]-j];
+
+      if(dangles == 2)
+        energy = E_MLstem(type, S1[u], ((j < seq_length) || circ) ? S1[j+1] : -1, P);
+      else
+        energy = E_MLstem(type, -1, -1, P);
+
+      if(d1 <= k && d2 <= l)
+        for(cnt1 = k_min_values_m[my_iindx[i]-u]; cnt1 <= MIN2(k-d1, k_max_values_m[my_iindx[i]-u]); cnt1++)
+          for(cnt2 = l_min_values_m[my_iindx[i]-u][cnt1]; cnt2 <= MIN2(l-d2, l_max_values_m[my_iindx[i]-u][cnt1]); cnt2+=2)
+            if((k-d1-cnt1 >= k_min_values[my_iindx[u+1]-j]) && (k-d1-cnt1 <= k_max_values[my_iindx[u+1]-j]))
+              if((l-d2-cnt2 >= l_min_values[my_iindx[u+1]-j][k-d1-cnt1]) && (l-d2-cnt2 <= l_max_values[my_iindx[u+1]-j][k-d1-cnt1]))
+                if(E_M[my_iindx[i]-u][cnt1][cnt2/2] + E_C[my_iindx[u+1]-j][k-d1-cnt1][(l-d2-cnt2)/2] + energy == e){
+                  backtrack_m(i, u, cnt1, cnt2, structure, vars);
+                  backtrack_c(u+1, j, k-d1-cnt1, l-d2-cnt2, structure, vars);
+                  return;
+                }
+    }
+  }
+  nrerror("backtracking failed in fML\n");
+}
+
+PRIVATE void backtrack_m1(unsigned int i, unsigned int j, int k, int l, char *structure, TwoDfold_vars *vars){
+  unsigned int  ij, seq_length, d1, d2, *referenceBPs1, *referenceBPs2, maxD1, maxD2;
+  int           *my_iindx, **l_min_values, **l_max_values,**l_min_values_m1, **l_max_values_m1;
+  int           *k_min_values, *k_max_values,*k_min_values_m1, *k_max_values_m1, cnt1, cnt2;
+  int           ***E_C, ***E_M1, *E_C_rem, *E_M1_rem, type, dangles, circ, energy, e_m1;
+
+  short         *S1;
+  char          *ptype;
+  paramT        *P;
+
+  P               = vars->P;
+  seq_length      = vars->seq_length;
+  S1              = vars->S1;
+  ptype           = vars->ptype;
+  circ            = vars->circ;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+  dangles         = vars->dangles;
+
+  E_C             = vars->E_C;
+  l_min_values    = vars->l_min_values;
+  l_max_values    = vars->l_max_values;
+  k_min_values    = vars->k_min_values;
+  k_max_values    = vars->k_max_values;
+
+  E_M1            = vars->E_M1;
+  l_min_values_m1 = vars->l_min_values_m1;
+  l_max_values_m1 = vars->l_max_values_m1;
+  k_min_values_m1 = vars->k_min_values_m1;
+  k_max_values_m1 = vars->k_max_values_m1;
+
+  E_C_rem        = vars->E_C_rem;
+  E_M1_rem       = vars->E_M1_rem;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+
+  ij    = my_iindx[i]-j;
+  e_m1  = (k == -1) ? E_M1_rem[ij] : E_M1[ij][k][l/2];
+
+  type = ptype[ij];
+  d1 = referenceBPs1[ij] - referenceBPs1[ij+1];
+  d2 = referenceBPs2[ij] - referenceBPs2[ij+1];
+
+  if(dangles == 2)
+    energy = E_MLstem(type, (i > 1) || circ ? S1[i-1] : -1, (j < seq_length) || circ ? S1[j+1] : -1, P);
+  else
+    energy = E_MLstem(type, -1, -1, P);
+
+  if(k == -1){
+    if(E_C_rem[ij] != INF){
+      if(e_m1 == (E_C_rem[ij] + energy)){
+        backtrack_c(i,j,-1,-1,structure,vars);
+        return;
+      }
+    }
+    if(E_M1_rem[ij+1] != INF){
+      if(e_m1 == (E_M1_rem[ij+1] + P->MLbase)){
+        backtrack_m1(i,j-1,-1,-1,structure,vars);
+        return;
+      }
+    }
+    for(cnt1 = k_min_values_m1[ij+1];
+        cnt1 <= k_max_values_m1[ij+1];
+        cnt1++)
+      for(cnt2 = l_min_values_m1[ij+1][cnt1];
+          cnt2 <= l_max_values_m1[ij+1][cnt1];
+          cnt2 += 2)
+        if(((cnt1 + d1) > maxD1) || ((cnt2 + d2) > maxD2)){
+          if(e_m1  == (E_M1[ij+1][cnt1][cnt2/2] + P->MLbase)){
+            backtrack_m1(i,j-1,cnt1,cnt2,structure,vars);
+            return;
+          }
+        }
+  }
+  else{
+    if(E_C[ij])
+      if((k >= k_min_values[ij]) && (k <= k_max_values[ij]))
+        if((l >= l_min_values[ij][k]) && (l <= l_max_values[ij][k]))
+          if(E_C[ij][k][l/2] + energy == e_m1){
+            backtrack_c(i, j, k, l, structure, vars);
+            return;
+          }
+
+    if(d1 <= k && d2 <= l)
+      if((k-d1 >= k_min_values_m1[ij+1]) && (k-d1 <= k_max_values_m1[ij+1]))
+        if((l-d2 >= l_min_values_m1[ij+1][k-d1]) && (l-d2 <= l_max_values_m1[ij+1][k-d1]))
+          if(E_M1[ij+1][k-d1][(l-d2)/2] + P->MLbase == e_m1){
+            backtrack_m1(i, j-1, k-d1, l-d2, structure, vars);
+            return;
+          }
+  }
+  nrerror("backtack failed in m1\n");
+}
+
+PRIVATE void backtrack_fc(int k, int l, char *structure, TwoDfold_vars *vars){
+  unsigned int   d, i, j, seq_length, base_d1, base_d2, d1, d2, maxD1, maxD2;
+  int   *my_iindx, energy, cnt1, cnt2, cnt3, cnt4;
+  short *S1;
+  unsigned int   *referenceBPs1, *referenceBPs2;
+  char  *sequence, *ptype;
+  int **E_Fc, **E_FcH, **E_FcI, **E_FcM, ***E_C, ***E_M, ***E_M2;
+  int *E_C_rem, *E_M_rem, *E_M2_rem, E_Fc_rem, E_FcH_rem, E_FcI_rem, E_FcM_rem;
+  int **l_min_values, **l_max_values, *k_min_values, *k_max_values;
+  int **l_min_values_m, **l_max_values_m, *k_min_values_m, *k_max_values_m;
+  int **l_min_values_m2, **l_max_values_m2, *k_min_values_m2, *k_max_values_m2;
+  int *l_min_values_fcH, *l_max_values_fcH, k_min_values_fcH, k_max_values_fcH;
+  int *l_min_values_fcI, *l_max_values_fcI, k_min_values_fcI, k_max_values_fcI;
+  int *l_min_values_fcM, *l_max_values_fcM, k_min_values_fcM, k_max_values_fcM;
+  paramT   *P;
+  P                 = vars->P;
+  sequence          = vars->sequence;
+  seq_length        = vars->seq_length;
+  S1                = vars->S1;
+  ptype             = vars->ptype;
+  my_iindx          = vars->my_iindx;
+  referenceBPs1     = vars->referenceBPs1;
+  referenceBPs2     = vars->referenceBPs2;
+
+  base_d1           = referenceBPs1[my_iindx[1]-seq_length];
+  base_d2           = referenceBPs2[my_iindx[1]-seq_length];
+
+  E_C               = vars->E_C;
+  l_min_values      = vars->l_min_values;
+  l_max_values      = vars->l_max_values;
+  k_min_values      = vars->k_min_values;
+  k_max_values      = vars->k_max_values;
+
+  E_M               = vars->E_M;
+  l_min_values_m    = vars->l_min_values_m;
+  l_max_values_m    = vars->l_max_values_m;
+  k_min_values_m    = vars->k_min_values_m;
+  k_max_values_m    = vars->k_max_values_m;
+
+  E_M2              = vars->E_M2;
+  l_min_values_m2   = vars->l_min_values_m2;
+  l_max_values_m2   = vars->l_max_values_m2;
+  k_min_values_m2   = vars->k_min_values_m2;
+  k_max_values_m2   = vars->k_max_values_m2;
+
+  E_Fc              = vars->E_Fc;
+
+  E_FcI             = vars->E_FcI;
+  l_min_values_fcI  = vars->l_min_values_fcI;
+  l_max_values_fcI  = vars->l_max_values_fcI;
+  k_min_values_fcI  = vars->k_min_values_fcI;
+  k_max_values_fcI  = vars->k_max_values_fcI;
+
+  E_FcH             = vars->E_FcH;
+  l_min_values_fcH  = vars->l_min_values_fcH;
+  l_max_values_fcH  = vars->l_max_values_fcH;
+  k_min_values_fcH  = vars->k_min_values_fcH;
+  k_max_values_fcH  = vars->k_max_values_fcH;
+
+  E_FcM             = vars->E_FcM;
+  l_min_values_fcM  = vars->l_min_values_fcM;
+  l_max_values_fcM  = vars->l_max_values_fcM;
+  k_min_values_fcM  = vars->k_min_values_fcM;
+  k_max_values_fcM  = vars->k_max_values_fcM;
+
+  E_C_rem          = vars->E_C_rem;
+  E_M_rem          = vars->E_M_rem;
+  E_M2_rem         = vars->E_M2_rem;
+  E_Fc_rem         = vars->E_Fc_rem;
+  E_FcH_rem        = vars->E_FcH_rem;
+  E_FcI_rem        = vars->E_FcI_rem;
+  E_FcM_rem        = vars->E_FcM_rem;
+  maxD1             = vars->maxD1;
+  maxD2             = vars->maxD2;
+
+
+  if(k==-1){
+    /* check if mfe might be open chain */
+    if(E_Fc_rem == 0)
+      if((referenceBPs1[my_iindx[1]-seq_length] > maxD1) || (referenceBPs2[my_iindx[1]-seq_length] > maxD2))
+        return;
+
+    /* check for hairpin configurations */
+    if(E_Fc_rem == E_FcH_rem){
+      for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+        for (j = d; j <= seq_length; j++) {
+          unsigned int u, ij;
+          int type, no_close;
+          char loopseq[10];
+          i = j-d+1;
+          ij = my_iindx[i]-j;
+          u = seq_length-j + i-1;
+          if (u<TURN) continue;
+          type = ptype[ij];
+          no_close = (((type==3)||(type==4))&&no_closingGU);
+          type=rtype[type];
+          if (!type) continue;
+          if(no_close) continue;
+
+          d1 = base_d1 - referenceBPs1[ij];
+          d2 = base_d2 - referenceBPs2[ij];
+          if (u<7) {
+            strcpy(loopseq , sequence+j-1);
+            strncat(loopseq, sequence, i);
+          }
+          energy = E_Hairpin(u, type, S1[j+1], S1[i-1],  loopseq, P);
+
+          if(E_C_rem[ij] != INF){
+            if(E_Fc_rem == (E_C_rem[ij] + energy)){
+              backtrack_c(i,j,-1,-1,structure,vars);
+              return;
+            }
+          }
+          if(E_C[ij])
+            for(cnt1 = k_min_values[ij];
+                cnt1 <= k_max_values[ij];
+                cnt1++)
+              for(cnt2 = l_min_values[ij][cnt1];
+                  cnt2 <= l_max_values[ij][cnt1];
+                  cnt2 += 2)
+                if(((cnt1 + d1) > maxD1) || ((cnt2 + d2) > maxD2))
+                  if(E_Fc_rem == (E_C[ij][cnt1][cnt2/2] + energy)){
+                    backtrack_c(i,j,cnt1,cnt2,structure,vars);
+                    return;
+                  }
+        }
+    }
+
+    /* check for interior loop configurations */
+    if(E_Fc_rem == E_FcI_rem){
+      for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+        for (j = d; j <= seq_length; j++) {
+          unsigned int u, ij, p, q, pq;
+          int type, type_2;
+          i = j-d+1;
+          ij = my_iindx[i]-j;
+          u = seq_length-j + i-1;
+          if (u<TURN) continue;
+          type = rtype[(unsigned int)ptype[ij]];
+          if (!type) continue;
+
+          for(p = j+1; p < seq_length ; p++){
+            unsigned int u1, qmin, ln_pre;
+            u1 = p-j-1;
+            if (u1+i-1>MAXLOOP) break;
+            qmin = p + TURN + 1;
+            ln_pre = u1 + i + seq_length;
+            if(ln_pre > qmin + MAXLOOP) qmin = ln_pre - MAXLOOP - 1;
+            for(q = qmin; q <= seq_length; q++){
+              unsigned int u2;
+              pq = my_iindx[p]-q;
+              type_2 = rtype[(unsigned int)ptype[pq]];
+              if (type_2==0) continue;
+              u2 = i-1 + seq_length-q;
+              if (u1+u2>MAXLOOP) continue;
+              energy = E_IntLoop(u1, u2, type, type_2, S1[j+1], S1[i-1], S1[p-1], S1[q+1], P);
+              if(E_C_rem[ij] != INF){
+                if(E_C[pq])
+                  for(cnt1 = k_min_values[pq];
+                      cnt1 <= k_max_values[pq];
+                      cnt1++)
+                    for(cnt2 = l_min_values[pq][cnt1];
+                        cnt2 <= l_max_values[pq][cnt1];
+                        cnt2 += 2)
+                      if(E_Fc_rem == (E_C_rem[ij] + E_C[pq][cnt1][cnt2/2] + energy)){
+                        backtrack_c(i,j,-1,-1,structure,vars);
+                        backtrack_c(p,q,cnt1,cnt2,structure,vars);
+                        return;
+                      }
+                if(E_C_rem[pq] != INF){
+                  if(E_Fc_rem == (E_C_rem[ij] + E_C_rem[pq] + energy)){
+                    backtrack_c(i,j,-1,-1,structure,vars);
+                    backtrack_c(p,q,-1,-1,structure,vars);
+                    return;
+                  }
+                }
+              }
+              if(E_C_rem[pq] != INF){
+                if(E_C[ij])
+                  for(cnt1 = k_min_values[ij];
+                      cnt1 <= k_max_values[ij];
+                      cnt1++)
+                    for(cnt2 = l_min_values[ij][cnt1];
+                        cnt2 <= l_max_values[ij][cnt1];
+                        cnt2 += 2)
+                      if(E_Fc_rem == (E_C[ij][cnt1][cnt2/2] + E_C_rem[pq] + energy)){
+                        backtrack_c(i,j,cnt1,cnt2,structure,vars);
+                        backtrack_c(p,q,-1,-1,structure,vars);
+                        return;
+                      }
+              }
+
+              if(!(E_C[ij])) continue;
+              if(!(E_C[pq])) continue;
+
+              /* get distance to reference if closing the interior loop
+              *  d2a = dbp(T1_[1,n}, T1_{p,q} + T1_{i,j})
+              *  d2b = dbp(T2_[1,n}, T2_{p,q} + T2_{i,j})
+              */
+              d1 = base_d1 - referenceBPs1[ij] - referenceBPs1[pq];
+              d2 = base_d2 - referenceBPs2[ij] - referenceBPs2[pq];
+              for(cnt1 = k_min_values[ij];
+                  cnt1 <= k_max_values[ij];
+                  cnt1++)
+                for(cnt2 = l_min_values[ij][cnt1];
+                    cnt2 <= l_max_values[ij][cnt1];
+                    cnt2 += 2)
+                  for(cnt3 = k_min_values[pq];
+                      cnt3 <= k_max_values[pq];
+                      cnt3++)
+                    for(cnt4 = l_min_values[pq][cnt3];
+                        cnt4 <= l_max_values[pq][cnt3];
+                        cnt4 += 2)
+                      if(((cnt1 + cnt3 + d1) > maxD1) || ((cnt2 + cnt4 + d2) > maxD2))
+                        if(E_Fc_rem == (E_C[ij][cnt1][cnt2/2] + E_C[pq][cnt3][cnt4/2] + energy)){
+                          backtrack_c(i, j, cnt1, cnt2, structure, vars);
+                          backtrack_c(p, q, cnt3, cnt4, structure, vars);
+                          return;
+                        }
+            } /* end for p */
+          } /* end for q */
+        }
+
+    }
+
+    /* check for multi loop configurations */
+    if(E_Fc_rem == E_FcM_rem){
+      if(seq_length > 2*TURN)
+        for (i=TURN+1; i<seq_length-2*TURN; i++) {
+          /* get distancies to references
+          * d3a = dbp(T1_[1,n}, T1_{1,k} + T1_{k+1, n})
+          * d3b = dbp(T2_[1,n}, T2_{1,k} + T2_{k+1, n})
+          */
+          if(E_M_rem[my_iindx[1]-i] != INF){
+            if(E_M2[i+1])
+              for(cnt1 = k_min_values_m2[i+1];
+                  cnt1 <= k_max_values_m2[i+1];
+                  cnt1++)
+                for(cnt2 = l_min_values_m2[i+1][cnt1];
+                    cnt2 <= l_max_values_m2[i+1][cnt1];
+                    cnt2 += 2)
+                  if(E_Fc_rem == (E_M_rem[my_iindx[1]-i] + E_M2[i+1][cnt1][cnt2/2] + P->MLclosing)){
+                    backtrack_m(1,i,-1,-1,structure,vars);
+                    backtrack_m2(i+1,cnt1,cnt2,structure,vars);
+                    return;
+                  }
+            if(E_M2_rem[i+1] != INF){
+              if(E_Fc_rem == (E_M_rem[my_iindx[1]-i] + E_M2_rem[i+1] + P->MLclosing)){
+                backtrack_m(1,i,-1,-1,structure,vars);
+                backtrack_m2(i+1,-1,-1,structure,vars);
+                return;
+              }
+            }
+          }
+          if(E_M2_rem[i+1] != INF){
+            if(E_M[my_iindx[1]-i])
+              for(cnt1 = k_min_values_m[my_iindx[1]-i];
+                  cnt1 <= k_max_values_m[my_iindx[1]-i];
+                  cnt1++)
+                for(cnt2 = l_min_values_m[my_iindx[1]-i][cnt1];
+                    cnt2 <= l_max_values_m[my_iindx[1]-i][cnt1];
+                    cnt2 += 2)
+                  if(E_Fc_rem == (E_M[my_iindx[1]-i][cnt1][cnt2/2] + E_M2_rem[i+1] + P->MLclosing)){
+                    backtrack_m(1,i,cnt1,cnt2,structure,vars);
+                    backtrack_m2(i+1,-1,-1,structure,vars);
+                    return;
+                  }
+          }
+
+          if(!(E_M[my_iindx[1]-i])) continue;
+          if(!(E_M2[i+1])) continue;
+
+          d1 = base_d1 - referenceBPs1[my_iindx[1]-i] - referenceBPs1[my_iindx[i+1]-seq_length];
+          d2 = base_d2 - referenceBPs2[my_iindx[1]-i] - referenceBPs2[my_iindx[i+1]-seq_length];
+          for(cnt1 = k_min_values_m[my_iindx[1]-i];
+              cnt1 <= k_max_values_m[my_iindx[1]-i];
+              cnt1++)
+            for(cnt2 = l_min_values_m[my_iindx[1]-i][cnt1];
+                cnt2 <= l_max_values_m[my_iindx[1]-i][cnt1];
+                cnt2 += 2)
+              for(cnt3 = k_min_values_m2[i+1];
+                  cnt3 <= k_max_values_m2[i+1];
+                  cnt3++)
+                for(cnt4 = l_min_values_m2[i+1][cnt3];
+                    cnt4 <= l_max_values_m2[i+1][cnt3];
+                    cnt4 += 2)
+                  if(((cnt1 + cnt3 + d1) > maxD1) || ((cnt2 + cnt4 + d2) > maxD2)){
+                    if(E_Fc_rem == (E_M[my_iindx[1]-i][cnt1][cnt2/2] + E_M2[i+1][cnt3][cnt4/2] + P->MLclosing)){
+                      backtrack_m(1, i, cnt1, cnt2, structure, vars);
+                      backtrack_m2(i+1, cnt3, cnt4, structure, vars);
+                      return;
+                    }
+                  }
+        }
+    }
+  }
+  else{
+    /* open chain ? */
+    if(E_Fc[k][l/2] == 0)
+      if((k == referenceBPs1[my_iindx[1]-seq_length]) && (l == referenceBPs2[my_iindx[1]-seq_length])){
+        return;
+      }
+    if((k >= k_min_values_fcH) && (k <= k_max_values_fcH)){
+      if((l >= l_min_values_fcH[k]) && (l <= l_max_values_fcH[k]))
+        if(E_Fc[k][l/2] == E_FcH[k][l/2]){
+          for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+            for (j = d; j <= seq_length; j++) {
+              unsigned int u, ij;
+              int type, no_close;
+              char loopseq[10];
+              i = j-d+1;
+              ij = my_iindx[i]-j;
+              if (!E_C[ij]) continue;
+              u = seq_length-j + i-1;
+              if (u<TURN) continue;
+
+              type = ptype[ij];
+
+              no_close = (((type==3)||(type==4))&&no_closingGU);
+
+              type=rtype[type];
+
+              if (!type) continue;
+              if(no_close) continue;
+
+              d1 = base_d1 - referenceBPs1[ij];
+              d2 = base_d2 - referenceBPs2[ij];
+              if (u<7) {
+                strcpy(loopseq , sequence+j-1);
+                strncat(loopseq, sequence, i);
+              }
+              energy = E_Hairpin(u, type, S1[j+1], S1[i-1],  loopseq, P);
+              if((k >= d1) && (l >= d2))
+                if((k-d1 >= k_min_values[ij]) && (k-d1 <= k_max_values[ij]))
+                  if((l-d2 >= l_min_values[ij][k-d1]) && (l-d2 <= l_max_values[ij][k-d1])){
+                    if(E_Fc[k][l/2] == E_C[ij][k-d1][(l-d2)/2] + energy){
+                      backtrack_c(i, j, k-d1, l-d2, structure, vars);
+                      return;
+                    }
+                  }
+            }
+        }
+    }
+
+    if((k >= k_min_values_fcI) && (k <= k_max_values_fcI)){
+      if((l >= l_min_values_fcI[k]) && (l <= l_max_values_fcI[k]))
+        if(E_Fc[k][l/2] == E_FcI[k][l/2]){
+          for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+            for (j = d; j <= seq_length; j++) {
+              unsigned int u, ij, p, q, pq;
+              int type, type_2;
+              i = j-d+1;
+              ij = my_iindx[i]-j;
+              if(!E_C[ij]) continue;
+              u = seq_length-j + i-1;
+              if (u<TURN) continue;
+
+              type = ptype[ij];
+
+              type=rtype[type];
+
+              if (!type) continue;
+
+              for(p = j+1; p < seq_length ; p++){
+                unsigned int u1, qmin, ln_pre;
+                u1 = p-j-1;
+                if (u1+i-1>MAXLOOP) break;
+                qmin = p + TURN + 1;
+                ln_pre = u1 + i + seq_length;
+                if(ln_pre > qmin + MAXLOOP) qmin = ln_pre - MAXLOOP - 1;
+                for(q = qmin; q <= seq_length; q++){
+                  unsigned int u2;
+                  pq = my_iindx[p]-q;
+                  if(!E_C[pq]) continue;
+                  type_2 = rtype[(unsigned int)ptype[pq]];
+                  if (type_2==0) continue;
+                  u2 = i-1 + seq_length-q;
+                  if (u1+u2>MAXLOOP) continue;
+                  /* get distance to reference if closing the interior loop
+                  *  d2a = dbp(T1_[1,n}, T1_{p,q} + T1_{i,j})
+                  *  d2b = dbp(T2_[1,n}, T2_{p,q} + T2_{i,j})
+                  */
+                  d1 = base_d1 - referenceBPs1[ij] - referenceBPs1[pq];
+                  d2 = base_d2 - referenceBPs2[ij] - referenceBPs2[pq];
+                  energy = E_IntLoop(u1, u2, type, type_2, S1[j+1], S1[i-1], S1[p-1], S1[q+1], P);
+                  if((k >= d1) && (l >= d2))
+                    for(cnt1 = k_min_values[ij]; cnt1 <= MIN2(k_max_values[ij], k - d1); cnt1++)
+                      for(cnt2 = l_min_values[ij][cnt1]; cnt2 <= MIN2(l_max_values[ij][cnt1], l - d2); cnt2+=2)
+                        if((k - d1 - cnt1 >= k_min_values[pq]) && (k - d1 - cnt1 <= k_max_values[pq]))
+                          if((l - d2 - cnt2 >= l_min_values[pq][k-d1-cnt1]) && (l - d2 - cnt2 <= l_max_values[pq][k-d1-cnt1])){
+                            if((E_C[ij][cnt1][cnt2/2] + E_C[pq][k-d1-cnt1][(l-d2-cnt2)/2] + energy) == E_Fc[k][l/2]){
+                              backtrack_c(i, j, cnt1, cnt2, structure, vars);
+                              backtrack_c(p, q, k - d1 - cnt1, l - d2 - cnt2, structure, vars);
+                              return;
+                            }
+                          }
+                }
+              }
+            }
+        }
+    }
+
+    if((k >= k_min_values_fcM) && (k <= k_max_values_fcM)){
+      if((l >= l_min_values_fcM[k]) && (l <= l_max_values_fcM[k]))
+        if(E_Fc[k][l/2] == E_FcM[k][l/2]){
+          if(seq_length > 2*TURN)
+            for (i=TURN+1; i<seq_length-2*TURN; i++) {
+              /* get distancies to references
+              * d3a = dbp(T1_[1,n}, T1_{1,k} + T1_{k+1, n})
+              * d3b = dbp(T2_[1,n}, T2_{1,k} + T2_{k+1, n})
+              */
+              if(!E_M[my_iindx[1]-i]) continue;
+              if(!E_M2[i+1]) continue;
+              d1 = base_d1 - referenceBPs1[my_iindx[1]-i] - referenceBPs1[my_iindx[i+1]-seq_length];
+              d2 = base_d2 - referenceBPs2[my_iindx[1]-i] - referenceBPs2[my_iindx[i+1]-seq_length];
+              if((k >= d1) && (l >= d2))
+                for(cnt1 = k_min_values_m[my_iindx[1]-i]; cnt1 <= MIN2(k_max_values_m[my_iindx[1]-i], k-d1); cnt1++)
+                  for(cnt2 = l_min_values_m[my_iindx[1]-i][cnt1]; cnt2 <= MIN2(l_max_values_m[my_iindx[1]-i][cnt1], l-d2); cnt2+=2)
+                    if((k - d1 - cnt1 >= k_min_values_m2[i+1]) && (k - d1 - cnt1 <= k_max_values_m2[i+1]))
+                      if((l - d2 - cnt2 >= l_min_values_m2[i+1][k-d1-cnt1]) && (l - d2 - cnt2 <= l_max_values_m2[i+1][k-d1-cnt1]))
+                        if((E_M[my_iindx[1]-i][cnt1][cnt2/2] + E_M2[i+1][k-d1-cnt1][(l-d2-cnt2)/2] + P->MLclosing) == E_FcM[k][l/2]){
+                          backtrack_m(1, i, cnt1, cnt2, structure, vars);
+                          backtrack_m2(i+1, k - d1 - cnt1, l - d2 - cnt2, structure, vars);
+                          return;
+                        }
+            }
+        }
+    }
+  }
+  nrerror("backtack failed in fc\n");
+}
+
+
+PRIVATE void backtrack_m2(unsigned int i, int k, int l, char *structure, TwoDfold_vars *vars){
+  unsigned int   j, ij, j3, n;
+  unsigned int   *referenceBPs1, *referenceBPs2;
+  unsigned int d1, d2, base_d1, base_d2, maxD1, maxD2;
+  int *my_iindx, cnt1, cnt2, cnt3, cnt4;
+  int ***E_M1, ***E_M2, *E_M2_rem, *E_M1_rem, e;
+  int **l_min_values_m1, **l_max_values_m1, *k_min_values_m1, *k_max_values_m1;
+
+  n               = vars->seq_length;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+
+  E_M1            = vars->E_M1;
+  l_min_values_m1 = vars->l_min_values_m1;
+  l_max_values_m1 = vars->l_max_values_m1;
+  k_min_values_m1 = vars->k_min_values_m1;
+  k_max_values_m1 = vars->k_max_values_m1;
+
+  E_M1_rem        = vars->E_M1_rem;
+
+  E_M2            = vars->E_M2;
+
+  E_M2_rem        = vars->E_M2_rem;
+
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+
+  base_d1 = referenceBPs1[my_iindx[i]-n];
+  base_d2 = referenceBPs2[my_iindx[i]-n];
+
+  if(k == -1){
+    e = E_M2_rem[i];
+    for (j=i+TURN+1; j<n-TURN-1; j++){
+      if(E_M1_rem[my_iindx[i]-j] != INF){
+        if(E_M1[my_iindx[j+1]-n])
+          for(cnt1 = k_min_values_m1[my_iindx[j+1]-n];
+              cnt1 <= k_max_values_m1[my_iindx[j+1]-n];
+              cnt1++)
+            for(cnt2 = l_min_values_m1[my_iindx[j+1]-n][cnt1];
+                cnt2 <= l_max_values_m1[my_iindx[j+1]-n][cnt1];
+                cnt2++)
+              if(e == E_M1_rem[my_iindx[i]-j] + E_M1[my_iindx[j+1]-n][cnt1][cnt2/2]){
+                backtrack_m1(i, j, k, l, structure, vars);
+                backtrack_m1(j+1, n, cnt1, cnt2, structure, vars);
+                return;
+              }
+        if(E_M1_rem[my_iindx[j+1]-n] != INF){
+          if(e == E_M1_rem[my_iindx[i]-j] + E_M1_rem[my_iindx[j+1]-n]){
+            backtrack_m1(i, j, k, l, structure, vars);
+            backtrack_m1(j+1, n, k, l, structure, vars);
+            return;
+          }
+        }
+      }
+      if(E_M1_rem[my_iindx[j+1]-n] != INF){
+        if(E_M1[my_iindx[i]-j])
+          for(cnt1 = k_min_values_m1[my_iindx[i]-j];
+              cnt1 <= k_max_values_m1[my_iindx[i]-j];
+              cnt1++)
+            for(cnt2 = l_min_values_m1[my_iindx[i]-j][cnt1];
+                cnt2 <= l_max_values_m1[my_iindx[i]-j][cnt1];
+                cnt2 += 2)
+              if(e == E_M1[my_iindx[i]-j][cnt1][cnt2/2] + E_M1_rem[my_iindx[j+1]-n]){
+                backtrack_m1(i, j, cnt1, cnt2, structure, vars);
+                backtrack_m1(j+1, n, k, l, structure, vars);
+                return;
+              }
+      }
+
+
+      if(!E_M1[my_iindx[i]-j]) continue;
+      if(!E_M1[my_iindx[j+1]-n]) continue;
+
+      d1 = referenceBPs1[my_iindx[i]-n] - referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[j+1]-n];
+      d2 = referenceBPs2[my_iindx[i]-n] - referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[j+1]-n];
+
+      for(cnt1 = k_min_values_m1[my_iindx[i]-j]; cnt1 <= k_max_values_m1[my_iindx[i]-j]; cnt1++)
+        for(cnt2 = l_min_values_m1[my_iindx[i]-j][cnt1]; cnt2 <= l_max_values_m1[my_iindx[i]-j][cnt1]; cnt2+=2){
+          for(cnt3 = k_min_values_m1[my_iindx[j+1]-n]; cnt3 <= k_max_values_m1[my_iindx[j+1]-n]; cnt3++)
+            for(cnt4 = l_min_values_m1[my_iindx[j+1]-n][cnt3]; cnt4 <= l_max_values_m1[my_iindx[j+1]-n][cnt3]; cnt4+=2){
+              if(((cnt1 + cnt3 + d1) > maxD1) || ((cnt2 + cnt4 + d2) > maxD2)){
+                if(e == E_M1[my_iindx[i]-j][cnt1][cnt2/2] + E_M1[my_iindx[j+1]-n][cnt3][cnt4/2]){
+                  backtrack_m1(i, j, cnt1, cnt2, structure, vars);
+                  backtrack_m1(j+1, n, cnt3, cnt4, structure, vars);
+                  return;
+                }
+              }
+            }
+        }
+    }
+  }
+  else{
+    for(j=i+TURN+1; j<n-TURN-1; j++){
+      if(!E_M1[my_iindx[i]-j]) continue;
+      if(!E_M1[my_iindx[j+1]-n]) continue;
+
+      ij = my_iindx[i]-j;
+      j3 = my_iindx[j+1]-n;
+      d1 = base_d1 - referenceBPs1[ij] - referenceBPs1[j3];
+      d2 = base_d2 - referenceBPs2[ij] - referenceBPs2[j3];
+
+      for(cnt1 = k_min_values_m1[ij]; cnt1 <= MIN2(k_max_values_m1[ij], k - d1); cnt1++)
+        for(cnt2 = l_min_values_m1[ij][cnt1]; cnt2 <= MIN2(l_max_values_m1[ij][cnt1], l-d2); cnt2+=2)
+          if((k - d1 - cnt1 >= k_min_values_m1[j3]) && (k - d1 - cnt1 <= k_max_values_m1[j3]))
+            if((l - d2 - cnt2 >= l_min_values_m1[j3][k - d1 - cnt1]) && (l - d2 - cnt2 <= l_max_values_m1[j3][k-d1-cnt1]))
+              if(E_M1[ij][cnt1][cnt2/2] + E_M1[j3][k-d1-cnt1][(l-d2-cnt2)/2] == E_M2[i][k][l/2]){
+                backtrack_m1(i, j, cnt1, cnt2, structure, vars);
+                backtrack_m1(j+1, n, k-d1-cnt1, l-d2-cnt2, structure, vars);
+                return;
+              }
+    }
+  }
+  nrerror("backtack failed in m2\n");
+}
+
+PRIVATE void mfe_circ(TwoDfold_vars *vars){
+  unsigned int  d, i, j, maxD1, maxD2, seq_length, *referenceBPs1, *referenceBPs2, d1, d2, base_d1, base_d2, *mm1, *mm2, *bpdist;
+  int           *my_iindx, energy, cnt1, cnt2, cnt3, cnt4;
+  short         *S1;
+  char          *sequence, *ptype;
+  int           ***E_C, ***E_M, ***E_M1;
+  int           *E_C_rem, *E_M_rem, *E_M1_rem;
+  int           **l_min_values, **l_max_values, **l_min_values_m, **l_max_values_m, **l_min_values_m1, **l_max_values_m1;
+  int           *k_min_values, *k_max_values,*k_min_values_m, *k_max_values_m,*k_min_values_m1, *k_max_values_m1;
+
+  paramT        *P;
+
+  P               = vars->P;
+  sequence        = vars->sequence;
+  seq_length      = vars->seq_length;
+  maxD1           = vars->maxD1;
+  maxD2           = vars->maxD2;
+  S1              = vars->S1;
+  ptype           = vars->ptype;
+  my_iindx        = vars->my_iindx;
+  referenceBPs1   = vars->referenceBPs1;
+  referenceBPs2   = vars->referenceBPs2;
+  mm1             = vars->mm1;
+  mm2             = vars->mm2;
+  bpdist          = vars->bpdist;
+
+  E_C             = vars->E_C;
+  l_min_values    = vars->l_min_values;
+  l_max_values    = vars->l_max_values;
+  k_min_values    = vars->k_min_values;
+  k_max_values    = vars->k_max_values;
+
+  E_M             = vars->E_M;
+  l_min_values_m  = vars->l_min_values_m;
+  l_max_values_m  = vars->l_max_values_m;
+  k_min_values_m  = vars->k_min_values_m;
+  k_max_values_m  = vars->k_max_values_m;
+
+  E_M1            = vars->E_M1;
+  l_min_values_m1 = vars->l_min_values_m1;
+  l_max_values_m1 = vars->l_max_values_m1;
+  k_min_values_m1 = vars->k_min_values_m1;
+  k_max_values_m1 = vars->k_max_values_m1;
+
+  E_C_rem        = vars->E_C_rem;
+  E_M_rem        = vars->E_M_rem;
+  E_M1_rem       = vars->E_M1_rem;
+
+#ifdef _OPENMP
+  #pragma omp parallel for private(d1,d2,cnt1,cnt2,cnt3,cnt4,j, i)
+#endif
+  for(i=1; i<seq_length-TURN-1; i++){
+    /* guess memory requirements for M2 */
+
+    int min_k, max_k, max_l, min_l;
+    int min_k_real, max_k_real, *min_l_real, *max_l_real;
+
+    min_k = min_l = 0;
+    max_k = mm1[my_iindx[i]-seq_length] + referenceBPs1[my_iindx[i] - seq_length];
+    max_l = mm2[my_iindx[i]-seq_length] + referenceBPs2[my_iindx[i] - seq_length];
+
+    prepareBoundaries(min_k,
+                      max_k,
+                      min_l,
+                      max_l,
+                      bpdist[my_iindx[i] - seq_length],
+                      &vars->k_min_values_m2[i],
+                      &vars->k_max_values_m2[i],
+                      &vars->l_min_values_m2[i],
+                      &vars->l_max_values_m2[i]
+                      );
+
+    prepareArray( &vars->E_M2[i],
+                  vars->k_min_values_m2[i],
+                  vars->k_max_values_m2[i],
+                  vars->l_min_values_m2[i],
+                  vars->l_max_values_m2[i]
+                 );
+
+    preparePosteriorBoundaries( vars->k_max_values_m2[i] - vars->k_min_values_m2[i] + 1,
+                                vars->k_min_values_m2[i],
+                                &min_k_real,
+                                &max_k_real,
+                                &min_l_real,
+                                &max_l_real
+                              );
+
+    /* begin filling of M2 array */
+    for (j=i+TURN+1; j<seq_length-TURN-1; j++){
+      if(E_M1_rem[my_iindx[i]-j] != INF){
+        if(E_M1[my_iindx[j+1]-seq_length])
+          for(cnt1 = k_min_values_m1[my_iindx[j+1]-seq_length];
+              cnt1 <= k_max_values_m1[my_iindx[j+1]-seq_length];
+              cnt1++)
+            for(cnt2 = l_min_values_m1[my_iindx[j+1]-seq_length][cnt1];
+                cnt2 <= l_max_values_m1[my_iindx[j+1]-seq_length][cnt1];
+                cnt2++)
+              vars->E_M2_rem[i] = MIN2(vars->E_M2_rem[i],
+                                  E_M1_rem[my_iindx[i]-j] + E_M1[my_iindx[j+1]-seq_length][cnt1][cnt2/2]
+                                  );
+        if(E_M1_rem[my_iindx[j+1]-seq_length] != INF)
+          vars->E_M2_rem[i] = MIN2(vars->E_M2_rem[i], E_M1_rem[my_iindx[i]-j] + E_M1_rem[my_iindx[j+1]-seq_length]);
+      }
+      if(E_M1_rem[my_iindx[j+1]-seq_length] != INF){
+        if(E_M1[my_iindx[i]-j])
+          for(cnt1 = k_min_values_m1[my_iindx[i]-j];
+              cnt1 <= k_max_values_m1[my_iindx[i]-j];
+              cnt1++)
+            for(cnt2 = l_min_values_m1[my_iindx[i]-j][cnt1];
+                cnt2 <= l_max_values_m1[my_iindx[i]-j][cnt1];
+                cnt2 += 2)
+              vars->E_M2_rem[i] = MIN2(vars->E_M2_rem[i],
+                                  E_M1[my_iindx[i]-j][cnt1][cnt2/2] + E_M1_rem[my_iindx[j+1]-seq_length]
+                                  );
+      }
+
+
+      if(!E_M1[my_iindx[i]-j]) continue;
+      if(!E_M1[my_iindx[j+1]-seq_length]) continue;
+
+      d1 = referenceBPs1[my_iindx[i]-seq_length] - referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[j+1]-seq_length];
+      d2 = referenceBPs2[my_iindx[i]-seq_length] - referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[j+1]-seq_length];
+
+      for(cnt1 = k_min_values_m1[my_iindx[i]-j]; cnt1 <= k_max_values_m1[my_iindx[i]-j]; cnt1++)
+        for(cnt2 = l_min_values_m1[my_iindx[i]-j][cnt1]; cnt2 <= l_max_values_m1[my_iindx[i]-j][cnt1]; cnt2+=2){
+          for(cnt3 = k_min_values_m1[my_iindx[j+1]-seq_length]; cnt3 <= k_max_values_m1[my_iindx[j+1]-seq_length]; cnt3++)
+            for(cnt4 = l_min_values_m1[my_iindx[j+1]-seq_length][cnt3]; cnt4 <= l_max_values_m1[my_iindx[j+1]-seq_length][cnt3]; cnt4+=2){
+              if(((cnt1 + cnt3 + d1) <= maxD1) && ((cnt2 + cnt4 + d2) <= maxD2)){
+                vars->E_M2[i][cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2] = MIN2( vars->E_M2[i][cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2],
+                                                                        E_M1[my_iindx[i]-j][cnt1][cnt2/2] + E_M1[my_iindx[j+1]-seq_length][cnt3][cnt4/2]
+                                                                      );
+                updatePosteriorBoundaries(cnt1+cnt3+d1,
+                                          cnt2+cnt4+d2,
+                                          &min_k_real,
+                                          &max_k_real,
+                                          &min_l_real,
+                                          &max_l_real
+                                          );
+              }
+              else{
+                vars->E_M2_rem[i] = MIN2(vars->E_M2_rem[i],
+                                    E_M1[my_iindx[i]-j][cnt1][cnt2/2] + E_M1[my_iindx[j+1]-seq_length][cnt3][cnt4/2]
+                                    );
+              }
+            }
+        }
+    }
+
+    /* resize and move memory portions of energy matrix E_M2 */
+    adjustArrayBoundaries(&vars->E_M2[i],
+                          &vars->k_min_values_m2[i],
+                          &vars->k_max_values_m2[i],
+                          &vars->l_min_values_m2[i],
+                          &vars->l_max_values_m2[i],
+                          min_k_real,
+                          max_k_real,
+                          min_l_real,
+                          max_l_real
+                          );
+  } /* end for i */
+
+  base_d1 = referenceBPs1[my_iindx[1]-seq_length];
+  base_d2 = referenceBPs2[my_iindx[1]-seq_length];
+
+  /* guess memory requirements for E_FcH, E_FcI and E_FcM */
+
+  int min_k, max_k, max_l, min_l;
+  int min_k_real, max_k_real, min_k_real_fcH, max_k_real_fcH, min_k_real_fcI, max_k_real_fcI, min_k_real_fcM, max_k_real_fcM;
+  int *min_l_real, *max_l_real, *min_l_real_fcH, *max_l_real_fcH, *min_l_real_fcI, *max_l_real_fcI,*min_l_real_fcM, *max_l_real_fcM;
+
+  min_k = min_l = 0;
+
+  max_k = mm1[my_iindx[1] - seq_length] + referenceBPs1[my_iindx[1] - seq_length];
+  max_l = mm2[my_iindx[1] - seq_length] + referenceBPs2[my_iindx[1] - seq_length];
+
+#ifdef _OPENMP
+  #pragma omp sections
+  {
+
+  #pragma omp section
+  {
+#endif
+  prepareBoundaries(min_k,
+                    max_k,
+                    min_l,
+                    max_l,
+                    bpdist[my_iindx[1] - seq_length],
+                    &vars->k_min_values_fc,
+                    &vars->k_max_values_fc,
+                    &vars->l_min_values_fc,
+                    &vars->l_max_values_fc
+                    );
+  prepareArray( &vars->E_Fc,
+                vars->k_min_values_fc,
+                vars->k_max_values_fc,
+                vars->l_min_values_fc,
+                vars->l_max_values_fc
+              );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  prepareBoundaries(min_k,
+                    max_k,
+                    min_l,
+                    max_l,
+                    bpdist[my_iindx[1] - seq_length],
+                    &vars->k_min_values_fcH,
+                    &vars->k_max_values_fcH,
+                    &vars->l_min_values_fcH,
+                    &vars->l_max_values_fcH
+                    );
+  prepareArray( &vars->E_FcH,
+                vars->k_min_values_fcH,
+                vars->k_max_values_fcH,
+                vars->l_min_values_fcH,
+                vars->l_max_values_fcH
+              );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  prepareBoundaries(min_k,
+                    max_k,
+                    min_l,
+                    max_l,
+                    bpdist[my_iindx[1] - seq_length],
+                    &vars->k_min_values_fcI,
+                    &vars->k_max_values_fcI,
+                    &vars->l_min_values_fcI,
+                    &vars->l_max_values_fcI
+                    );
+  prepareArray( &vars->E_FcI,
+                vars->k_min_values_fcI,
+                vars->k_max_values_fcI,
+                vars->l_min_values_fcI,
+                vars->l_max_values_fcI
+              );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  prepareBoundaries(min_k,
+                    max_k,
+                    min_l,
+                    max_l,
+                    bpdist[my_iindx[1] - seq_length],
+                    &vars->k_min_values_fcM,
+                    &vars->k_max_values_fcM,
+                    &vars->l_min_values_fcM,
+                    &vars->l_max_values_fcM
+                    );
+  prepareArray( &vars->E_FcM,
+                vars->k_min_values_fcM,
+                vars->k_max_values_fcM,
+                vars->l_min_values_fcM,
+                vars->l_max_values_fcM
+              );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  preparePosteriorBoundaries( max_k - min_k + 1,
+                              min_k,
+                              &min_k_real,
+                              &max_k_real,
+                              &min_l_real,
+                              &max_l_real
+                            );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  preparePosteriorBoundaries( max_k - min_k + 1,
+                              min_k,
+                              &min_k_real_fcH,
+                              &max_k_real_fcH,
+                              &min_l_real_fcH,
+                              &max_l_real_fcH
+                            );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  preparePosteriorBoundaries( max_k - min_k + 1,
+                              min_k,
+                              &min_k_real_fcI,
+                              &max_k_real_fcI,
+                              &min_l_real_fcI,
+                              &max_l_real_fcI
+                            );
+
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  preparePosteriorBoundaries( max_k - min_k + 1,
+                              min_k,
+                              &min_k_real_fcM,
+                              &max_k_real_fcM,
+                              &min_l_real_fcM,
+                              &max_l_real_fcM
+                            );
+#ifdef _OPENMP
+  }
+  }
+#endif
+
+  /* begin actual energy calculations */
+#ifdef _OPENMP
+  #pragma omp sections private(d, d1,d2,cnt1,cnt2,cnt3,cnt4,j, i, energy)
+  {
+
+  #pragma omp section
+  {
+#endif
+  for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+    for (j = d; j <= seq_length; j++) {
+      unsigned int  u, ij;
+      int           type, no_close;
+      char          loopseq[10];
+      i = j-d+1;
+      ij = my_iindx[i]-j;
+      u = seq_length-j + i-1;
+      if (u<TURN) continue;
+
+      type = ptype[ij];
+
+      no_close = (((type==3)||(type==4))&&no_closingGU);
+
+      type=rtype[type];
+
+      if (!type) continue;
+      if(no_close) continue;
+
+      d1 = base_d1 - referenceBPs1[ij];
+      d2 = base_d2 - referenceBPs2[ij];
+      if (u<7) {
+        strcpy(loopseq , sequence+j-1);
+        strncat(loopseq, sequence, i);
+      }
+      energy = E_Hairpin(u, type, S1[j+1], S1[i-1],  loopseq, P);
+
+      if(E_C_rem[ij] != INF)
+        vars->E_FcH_rem = MIN2(vars->E_FcH_rem, E_C_rem[ij] + energy);
+
+      if (!E_C[ij]) continue;
+      for(cnt1 = k_min_values[ij]; cnt1 <= k_max_values[ij]; cnt1++)
+        for(cnt2 = l_min_values[ij][cnt1]; cnt2 <= l_max_values[ij][cnt1]; cnt2 += 2){
+          if(((cnt1 + d1) <= maxD1) && ((cnt2 + d2) <= maxD2)){
+            vars->E_FcH[cnt1 + d1][(cnt2+d2)/2] = MIN2( vars->E_FcH[cnt1 + d1][(cnt2+d2)/2],
+                                                  energy + E_C[ij][cnt1][cnt2/2]
+                                                );
+            updatePosteriorBoundaries(cnt1 + d1,
+                                      cnt2 + d2,
+                                      &min_k_real_fcH,
+                                      &max_k_real_fcH,
+                                      &min_l_real_fcH,
+                                      &max_l_real_fcH
+                                    );
+          }
+          else
+            vars->E_FcH_rem = MIN2(vars->E_FcH_rem, energy + E_C[ij][cnt1][cnt2/2]);
+        }
+    }
+  /* end of i-j loop */
+
+  /* resize and move memory portions of energy matrix E_FcH */
+  adjustArrayBoundaries(&vars->E_FcH,
+                        &vars->k_min_values_fcH,
+                        &vars->k_max_values_fcH,
+                        &vars->l_min_values_fcH,
+                        &vars->l_max_values_fcH,
+                        min_k_real_fcH,
+                        max_k_real_fcH,
+                        min_l_real_fcH,
+                        max_l_real_fcH
+                      );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
+    for (j = d; j <= seq_length; j++) {
+      unsigned int  u, ij, p, q, pq;
+      int           type, type_2, no_close;
+      i = j-d+1;
+      ij = my_iindx[i]-j;
+      u = seq_length-j + i-1;
+      if (u<TURN) continue;
+
+      type = ptype[ij];
+
+      no_close = (((type==3)||(type==4))&&no_closingGU);
+
+      type=rtype[type];
+
+      if (!type) continue;
+      if(no_close) continue;
+
+      if(E_C_rem[ij] != INF){
+        for(p = j+1; p < seq_length ; p++){
+          unsigned int u1, qmin, ln_pre;
+          u1 = p-j-1;
+          if (u1+i-1>MAXLOOP) break;
+          qmin = p + TURN + 1;
+          ln_pre = u1 + i + seq_length;
+          if(ln_pre > qmin + MAXLOOP) qmin = ln_pre - MAXLOOP - 1;
+          for(q = qmin; q <= seq_length; q++){
+            unsigned int u2;
+            pq = my_iindx[p]-q;
+            type_2 = rtype[(unsigned int)ptype[pq]];
+            if (type_2==0) continue;
+            u2 = i-1 + seq_length-q;
+            if (u1+u2>MAXLOOP) continue;
+            /* get distance to reference if closing the interior loop
+            *  d2a = dbp(T1_[1,n}, T1_{p,q} + T1_{i,j})
+            *  d2b = dbp(T2_[1,n}, T2_{p,q} + T2_{i,j})
+            */
+            d1 = base_d1 - referenceBPs1[ij] - referenceBPs1[pq];
+            d2 = base_d2 - referenceBPs2[ij] - referenceBPs2[pq];
+            energy = E_IntLoop(u1, u2, type, type_2, S1[j+1], S1[i-1], S1[p-1], S1[q+1], P);
+
+            if(E_C_rem[pq] != INF)
+              vars->E_FcI_rem = MIN2(vars->E_FcI_rem, E_C_rem[ij] + E_C_rem[pq] + energy);
+
+            if(E_C[pq])
+              for(cnt1 = k_min_values[pq];
+                  cnt1 <= k_max_values[pq];
+                  cnt1++)
+                for(cnt2 = l_min_values[pq][cnt1];
+                    cnt2 <= l_max_values[pq][cnt1];
+                    cnt2 += 2)
+                  vars->E_FcI_rem = MIN2(vars->E_FcI_rem, E_C_rem[ij] + E_C[pq][cnt1][cnt2/2] + energy);
+          }
+        }
+      }
+
+      if(E_C[ij]){
+        for(p = j+1; p < seq_length ; p++){
+          unsigned int u1, qmin, ln_pre;
+          u1 = p-j-1;
+          if (u1+i-1>MAXLOOP) break;
+          qmin = p + TURN + 1;
+          ln_pre = u1 + i + seq_length;
+          if(ln_pre > qmin + MAXLOOP) qmin = ln_pre - MAXLOOP - 1;
+          for(q = qmin; q <= seq_length; q++){
+            unsigned int u2;
+            pq = my_iindx[p]-q;
+            type_2 = rtype[(unsigned int)ptype[pq]];
+            if (type_2==0) continue;
+            u2 = i-1 + seq_length-q;
+            if (u1+u2>MAXLOOP) continue;
+            /* get distance to reference if closing the interior loop
+            *  d2a = dbp(T1_[1,n}, T1_{p,q} + T1_{i,j})
+            *  d2b = dbp(T2_[1,n}, T2_{p,q} + T2_{i,j})
+            */
+            d1 = base_d1 - referenceBPs1[ij] - referenceBPs1[pq];
+            d2 = base_d2 - referenceBPs2[ij] - referenceBPs2[pq];
+            energy = E_IntLoop(u1, u2, type, type_2, S1[j+1], S1[i-1], S1[p-1], S1[q+1], P);
+            if(E_C_rem[pq] != INF){
+              for(cnt1 = k_min_values[ij];
+                  cnt1 <= k_max_values[ij];
+                  cnt1++)
+                for(cnt2 = l_min_values[ij][cnt1];
+                    cnt2 <= l_max_values[ij][cnt1];
+                    cnt2 += 2)
+                  vars->E_FcI_rem = MIN2(vars->E_FcI_rem, E_C[ij][cnt1][cnt2/2] + E_C_rem[pq] + energy);
+            }
+
+            if(E_C[pq])
+              for(cnt1 = k_min_values[ij];
+                  cnt1 <= k_max_values[ij];
+                  cnt1++)
+                for(cnt2 = l_min_values[ij][cnt1];
+                    cnt2 <= l_max_values[ij][cnt1];
+                    cnt2 += 2)
+                  for(cnt3 = k_min_values[pq];
+                      cnt3 <= k_max_values[pq];
+                      cnt3++)
+                    for(cnt4 = l_min_values[pq][cnt3];
+                        cnt4 <= l_max_values[pq][cnt3];
+                        cnt4 += 2){
+                      if(((cnt1 + cnt3 + d1) <= maxD1) && ((cnt2 + cnt4 + d2) <= maxD2)){
+                        vars->E_FcI[cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2] = MIN2(
+                                                                          vars->E_FcI[cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2],
+                                                                          E_C[ij][cnt1][cnt2/2]
+                                                                        + E_C[pq][cnt3][cnt4/2]
+                                                                        + energy
+                                                                            );
+                        updatePosteriorBoundaries(cnt1 + cnt3 + d1,
+                                                  cnt2 + cnt4 + d2,
+                                                  &min_k_real_fcI,
+                                                  &max_k_real_fcI,
+                                                  &min_l_real_fcI,
+                                                  &max_l_real_fcI
+                                                );
+                      }
+                      else{
+                        vars->E_FcI_rem = MIN2(
+                                      vars->E_FcI_rem,
+                                      E_C[ij][cnt1][cnt2/2]
+                                    + E_C[pq][cnt3][cnt4/2]
+                                    + energy
+                                          );
+                      }
+                    }
+          }
+        }
+      }
+    }
+  /* end of i-j loop */
+
+  /* resize and move memory portions of energy matrix E_FcI */
+  adjustArrayBoundaries(&vars->E_FcI,
+                        &vars->k_min_values_fcI,
+                        &vars->k_max_values_fcI,
+                        &vars->l_min_values_fcI,
+                        &vars->l_max_values_fcI,
+                        min_k_real_fcI,
+                        max_k_real_fcI,
+                        min_l_real_fcI,
+                        max_l_real_fcI
+                      );
+#ifdef _OPENMP
+  }
+  #pragma omp section
+  {
+#endif
+  if(seq_length > 2*TURN){
+    for (i=TURN+1; i<seq_length-2*TURN; i++) {
+      /* get distancies to references
+      * d3a = dbp(T1_[1,n}, T1_{1,k} + T1_{k+1, n})
+      * d3b = dbp(T2_[1,n}, T2_{1,k} + T2_{k+1, n})
+      */
+      d1 = base_d1 - referenceBPs1[my_iindx[1]-i] - referenceBPs1[my_iindx[i+1]-seq_length];
+      d2 = base_d2 - referenceBPs2[my_iindx[1]-i] - referenceBPs2[my_iindx[i+1]-seq_length];
+
+      if(E_M_rem[my_iindx[1]-i] != INF){
+        if(vars->E_M2[i+1])
+          for(cnt1 = vars->k_min_values_m2[i+1];
+              cnt1 <= vars->k_max_values_m2[i+1];
+              cnt1++)
+            for(cnt2 = vars->l_min_values_m2[i+1][cnt1];
+                cnt2 <= vars->l_max_values_m2[i+1][cnt1];
+                cnt2 += 2)
+              vars->E_FcM_rem = MIN2(vars->E_FcM_rem, E_M_rem[my_iindx[1]-i] + vars->E_M2[i+1][cnt1][cnt2/2] + P->MLclosing);
+        if(vars->E_M2_rem[i+1] != INF)
+          vars->E_FcM_rem = MIN2(vars->E_FcM_rem, E_M_rem[my_iindx[1]-i] + vars->E_M2_rem[i+1] + P->MLclosing);
+      }
+      if(vars->E_M2_rem[i+1] != INF){
+        if(E_M[my_iindx[1]-i])
+          for(cnt1 = k_min_values_m[my_iindx[1]-i];
+              cnt1 <= k_max_values_m[my_iindx[1]-i];
+              cnt1++)
+            for(cnt2 = l_min_values_m[my_iindx[1]-i][cnt1];
+                cnt2 <= l_max_values_m[my_iindx[1]-i][cnt1];
+                cnt2 += 2)
+              vars->E_FcM_rem = MIN2(vars->E_FcM_rem, E_M[my_iindx[1]-i][cnt1][cnt2/2] + vars->E_M2_rem[i+1] + P->MLclosing);
+      }
+
+      if(!E_M[my_iindx[1]-i]) continue;
+      if(!vars->E_M2[i+1]) continue;
+      for(cnt1 = k_min_values_m[my_iindx[1]-i]; cnt1 <= k_max_values_m[my_iindx[1]-i]; cnt1++)
+        for(cnt2 = l_min_values_m[my_iindx[1]-i][cnt1]; cnt2 <= l_max_values_m[my_iindx[1]-i][cnt1]; cnt2 += 2)
+          for(cnt3 = vars->k_min_values_m2[i+1]; cnt3 <= vars->k_max_values_m2[i+1]; cnt3++)
+            for(cnt4 = vars->l_min_values_m2[i+1][cnt3]; cnt4 <= vars->l_max_values_m2[i+1][cnt3]; cnt4 += 2){
+              if(((cnt1 + cnt3 + d1) <= maxD1) && ((cnt2 + cnt4 + d2) <= maxD2)){
+                vars->E_FcM[cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2] = MIN2(
+                                                                  vars->E_FcM[cnt1 + cnt3 + d1][(cnt2 + cnt4 + d2)/2],
+                                                                  E_M[my_iindx[1]-i][cnt1][cnt2/2]
+                                                                + vars->E_M2[i+1][cnt3][cnt4/2]
+                                                                + P->MLclosing
+                                                                    );
+                updatePosteriorBoundaries(cnt1 + cnt3 + d1,
+                                          cnt2 + cnt4 + d2,
+                                          &min_k_real_fcM,
+                                          &max_k_real_fcM,
+                                          &min_l_real_fcM,
+                                          &max_l_real_fcM
+                                        );
+              }
+              else{
+                vars->E_FcM_rem = MIN2(
+                              vars->E_FcM_rem,
+                              E_M[my_iindx[1]-i][cnt1][cnt2/2]
+                            + vars->E_M2[i+1][cnt3][cnt4/2]
+                            + P->MLclosing
+                                  );
+              }
+            }
+    }
+  }
+  /* resize and move memory portions of energy matrix E_FcM */
+  adjustArrayBoundaries(&vars->E_FcM,
+                        &vars->k_min_values_fcM,
+                        &vars->k_max_values_fcM,
+                        &vars->l_min_values_fcM,
+                        &vars->l_max_values_fcM,
+                        min_k_real_fcM,
+                        max_k_real_fcM,
+                        min_l_real_fcM,
+                        max_l_real_fcM
+                      );
+#ifdef _OPENMP
+  }
+  }
+#endif
+
+
+
+  /* compute E_Fc_rem */
+  vars->E_Fc_rem = MIN2(vars->E_FcH_rem, vars->E_FcI_rem);
+  vars->E_Fc_rem = MIN2(vars->E_Fc_rem, vars->E_FcM_rem);
+  /* add the case were structure is unfolded chain */
+  if((referenceBPs1[my_iindx[1]-seq_length] > maxD1) || (referenceBPs2[my_iindx[1]-seq_length] > maxD2))
+    vars->E_Fc_rem = MIN2(vars->E_Fc_rem, 0);
+
+
+  /* compute all E_Fc */
+  for(cnt1 = vars->k_min_values_fcH; cnt1 <= vars->k_max_values_fcH; cnt1++)
+    for(cnt2 = vars->l_min_values_fcH[cnt1]; cnt2 <= vars->l_max_values_fcH[cnt1]; cnt2 += 2){
+      vars->E_Fc[cnt1][cnt2/2] = MIN2(vars->E_Fc[cnt1][cnt2/2],
+                                      vars->E_FcH[cnt1][cnt2/2]
+                                      );
+      updatePosteriorBoundaries(cnt1,
+                                cnt2,
+                                &min_k_real,
+                                &max_k_real,
+                                &min_l_real,
+                                &max_l_real
+                                );
+    }
+  for(cnt1 = vars->k_min_values_fcI; cnt1 <= vars->k_max_values_fcI; cnt1++)
+    for(cnt2 = vars->l_min_values_fcI[cnt1]; cnt2 <= vars->l_max_values_fcI[cnt1]; cnt2 += 2){
+      vars->E_Fc[cnt1][cnt2/2] = MIN2(vars->E_Fc[cnt1][cnt2/2],
+                                      vars->E_FcI[cnt1][cnt2/2]
+                                      );
+      updatePosteriorBoundaries(cnt1,
+                                cnt2,
+                                &min_k_real,
+                                &max_k_real,
+                                &min_l_real,
+                                &max_l_real
+                                );
+    }
+  for(cnt1 = vars->k_min_values_fcM; cnt1 <= vars->k_max_values_fcM; cnt1++)
+    for(cnt2 = vars->l_min_values_fcM[cnt1]; cnt2 <= vars->l_max_values_fcM[cnt1]; cnt2 += 2){
+      vars->E_Fc[cnt1][cnt2/2] = MIN2(vars->E_Fc[cnt1][cnt2/2],
+                                      vars->E_FcM[cnt1][cnt2/2]
+                                      );
+      updatePosteriorBoundaries(cnt1,
+                                cnt2,
+                                &min_k_real,
+                                &max_k_real,
+                                &min_l_real,
+                                &max_l_real
+                                );
+    }
+  /* add the case were structure is unfolded chain */
+  vars->E_Fc[referenceBPs1[my_iindx[1]-seq_length]][referenceBPs2[my_iindx[1]-seq_length]/2] = MIN2(vars->E_Fc[referenceBPs1[my_iindx[1]-seq_length]][referenceBPs2[my_iindx[1]-seq_length]/2],
+                                                                                                    0);
+  updatePosteriorBoundaries(referenceBPs1[my_iindx[1]-seq_length],
+                            referenceBPs2[my_iindx[1]-seq_length],
+                            &min_k_real,
+                            &max_k_real,
+                            &min_l_real,
+                            &max_l_real
+                            );
+
+
+  adjustArrayBoundaries(&vars->E_Fc,
+                        &vars->k_min_values_fc,
+                        &vars->k_max_values_fc,
+                        &vars->l_min_values_fc,
+                        &vars->l_max_values_fc,
+                        min_k_real,
+                        max_k_real,
+                        min_l_real,
+                        max_l_real
+                      );
+
+}
+
+
+
+
+PRIVATE void adjustArrayBoundaries(int ***array, int *k_min, int *k_max, int **l_min, int **l_max, int k_min_post, int k_max_post, int *l_min_post, int *l_max_post){
+  int cnt1;
+  int k_diff_pre  = k_min_post - *k_min;
+  int mem_size    = k_max_post - k_min_post + 1;
+
+  if(k_min_post < INF){
+    /* free all the unused memory behind actual data */
+    for(cnt1 = k_max_post + 1; cnt1 <= *k_max; cnt1++){
+      (*array)[cnt1] += (*l_min)[cnt1]/2;
+      free((*array)[cnt1]);
+    }
+
+    /* free unused memory before actual data */
+    for(cnt1 = *k_min; cnt1 < k_min_post; cnt1++){
+      (*array)[cnt1] += (*l_min)[cnt1]/2;
+      free((*array)[cnt1]);
+    }
+    /* move data to front and thereby eliminating unused memory in front of actual data */
+    if(k_diff_pre > 0){
+      memmove((int **)(*array),((int **)(*array)) + k_diff_pre, sizeof(int *) * mem_size);
+      memmove((int *) (*l_min),((int *) (*l_min)) + k_diff_pre, sizeof(int)   * mem_size);
+      memmove((int *) (*l_max),((int *) (*l_max)) + k_diff_pre, sizeof(int)   * mem_size);
+    }
+
+    /* reallocating memory to actual size used */
+    *array  += *k_min;
+    *array = (int **)realloc(*array, sizeof(int *) * mem_size);
+    *array -= k_min_post;
+
+    *l_min  += *k_min;
+    *l_min = (int *)realloc(*l_min, sizeof(int) * mem_size);
+    *l_min -= k_min_post;
+
+    *l_max  += *k_min;
+    *l_max = (int *)realloc(*l_max, sizeof(int) * mem_size);
+    *l_max -= k_min_post;
+
+    /* adjust l dimension of array */
+    for(cnt1 = k_min_post; cnt1 <= k_max_post; cnt1++){
+      if(l_min_post[cnt1] < INF){
+        /* new memsize */
+        mem_size        = (l_max_post[cnt1] - l_min_post[cnt1] + 1)/2 + 1;
+        /* reshift the pointer */
+        (*array)[cnt1]  += (*l_min)[cnt1]/2;
+
+        int shift       = (l_min_post[cnt1]%2 == (*l_min)[cnt1]%2) ? 0 : 1;
+        /* eliminate unused memory in front of actual data */
+        unsigned int    start = (l_min_post[cnt1] - (*l_min)[cnt1])/2 + shift;
+        if(start > 0)
+          memmove((int *)((*array)[cnt1]), (int *)((*array)[cnt1])+start, sizeof(int) * mem_size);
+        (*array)[cnt1]  = (int *) realloc((*array)[cnt1], sizeof(int) * mem_size);
+
+        (*array)[cnt1]  -= l_min_post[cnt1]/2;
+      }
+      else{
+        /* free according memory */
+        (*array)[cnt1] += (*l_min)[cnt1]/2;
+        free((*array)[cnt1]);
+      }
+
+      (*l_min)[cnt1] = l_min_post[cnt1];
+      (*l_max)[cnt1] = l_max_post[cnt1];
+    }
+  }
+  else{
+    /* we have to free all unused memory */
+    for(cnt1 = *k_min; cnt1 <= *k_max; cnt1++){
+      (*array)[cnt1] += (*l_min)[cnt1]/2;
+      free((*array)[cnt1]);
+    }
+    (*l_min) += *k_min;
+    (*l_max) += *k_min;
+    free(*l_min);
+    free(*l_max);
+    (*array) += *k_min;
+    free(*array);
+    *array = NULL;
+  }
+
+  l_min_post  += *k_min;
+  l_max_post  += *k_min;
+  free(l_min_post);
+  free(l_max_post);
+  *k_min      = k_min_post;
+  *k_max      = k_max_post;
+}
+
+INLINE PRIVATE void preparePosteriorBoundaries(int size, int shift, int *min_k, int *max_k, int **min_l, int **max_l){
+  int i;
+  *min_k  = INF;
+  *max_k  = 0;
+
+  *min_l  = (int *)space(sizeof(int) * size);
+  *max_l  = (int *)space(sizeof(int) * size);
+
+  for(i = 0; i < size; i++){
+    (*min_l)[i] = INF;
+    (*max_l)[i] = 0;
+  }
+
+  *min_l  -= shift;
+  *max_l  -= shift;
+}
+
+INLINE PRIVATE void updatePosteriorBoundaries(int d1, int d2, int *min_k, int *max_k, int **min_l, int **max_l){
+  (*min_l)[d1]  = MIN2((*min_l)[d1], d2);
+  (*max_l)[d1]  = MAX2((*max_l)[d1], d2);
+  *min_k        = MIN2(*min_k, d1);
+  *max_k        = MAX2(*max_k, d1);
+}
+
+INLINE  PRIVATE void  prepareBoundaries(int min_k_pre, int max_k_pre, int min_l_pre, int max_l_pre, int bpdist, int *min_k, int *max_k, int **min_l, int **max_l){
+  int cnt;
+  int mem = max_k_pre - min_k_pre + 1;
+
+  *min_k  = min_k_pre;
+  *max_k  = max_k_pre;
+  *min_l  = (int *) space(sizeof(int) * mem);
+  *max_l  = (int *) space(sizeof(int) * mem);
+
+  *min_l  -= min_k_pre;
+  *max_l  -= min_k_pre;
+
+  /* for each k guess the according minimum l*/
+  for(cnt = min_k_pre; cnt <= max_k_pre; cnt++){
+    (*min_l)[cnt] = min_l_pre;
+    (*max_l)[cnt] = max_l_pre;
+    while((*min_l)[cnt] + cnt < bpdist) (*min_l)[cnt]++;
+    if((bpdist % 2) != (((*min_l)[cnt] + cnt) % 2)) (*min_l)[cnt]++;
+  }
+}
+
+INLINE  PRIVATE void  prepareArray(int ***array, int min_k, int max_k, int *min_l, int *max_l){
+  int i, j, mem;
+  *array  = (int **)space(sizeof(int *) * (max_k - min_k + 1));
+  *array  -= min_k;
+
+  for(i = min_k; i <= max_k; i++){
+    mem = (max_l[i] - min_l[i] + 1)/2 + 1;
+    (*array)[i] = (int *)space(sizeof(int) * mem);
+    for(j = 0; j < mem; j++)
+      (*array)[i][j] = INF;
+    (*array)[i]  -= min_l[i]/2;
+  }
+}
+
+INLINE  PRIVATE void  prepareArray2(unsigned long ***array, int min_k, int max_k, int *min_l, int *max_l){
+  int i, mem;
+  *array  = (unsigned long **)space(sizeof(unsigned long *) * (max_k - min_k + 1));
+  *array  -= min_k;
+
+  for(i = min_k; i <= max_k; i++){
+    mem = (max_l[i] - min_l[i] + 1)/2 + 1;
+    (*array)[i] = (unsigned long *)space(sizeof(unsigned long) * mem);
+    (*array)[i] -= min_l[i]/2;
+  }
+}
+