// How to compile it:
//   gcc -o ga_find_wcet ga_find_wcet.c -lm
// How to use it:
//   ./ga_find_wcet myconf ./bubblesort
// where
//   bubblesort is the program for which we want to find the WCET.
//   myconfig is a textfile with configuration parameters.
//   Right now, the file myconfig stores the following parameters:
//     0
//     262144
//   The first parmeter (0) indicates the mode; it indicates that we want to find the WCET for a program using default hyperparameters (population size, multation rate).
//   The second parmeter (262144) indicates the input size to the program we want to execute.
//   It assumes that bubblesort reads from stdin.
//   The first parameter can be a number in {0,1,2,3}. 0 means normal GA. 1 means steepest descent. 2 means meta with GA. 3 means meta with steepest descent.

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
#include <time.h>
#include <math.h>
#include <string.h>

int NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED = 4;
int NUMBER_OF_INDIVIDUALS = 4; // this is the size of the population
double MUTATIONRATE = 0.2; // this is the probability that an individual gets a mutation; if so, one bit is flipped
int NGENERATIONS = 4; // this is the number of iterations that the population evolves

char conffilename[200];
int mode = 0;
int inputsizeinnumberofbits; // this must be a multiple of sizeof(int)

struct individual {
  int* inputtoprogram; // this stores an array of bits but it is encoded as an array of int
                       // for example 262144 bits equals 8192 words if one word is 32 bit
  double measuredexecutiontimeofprogram; // in seconds
  struct individual* next;
};

struct individual* listof_individuals;

FILE* mylogfile;

int getinputtoprogram_size_in_number_of_bits() {
  return inputsizeinnumberofbits;
}
int getinputtoprogram_size_in_number_of_bytes() {
  return inputsizeinnumberofbits/8;
}
int getinputtoprogram_size_in_number_of_ints() {
  return inputsizeinnumberofbits/(sizeof(int)*8);
}
int obtain_intindex_from_bitindex(int bitindex) {
  int intindex;
  intindex = bitindex / ((sizeof(int))*8);
  return intindex;
}
int obtain_localbitindex_from_bitindex(int bitindex) {
  int localbitindex;
  localbitindex = bitindex % ((sizeof(int))*8);
  return localbitindex;
}
void flipbit_bitposition_in_integer(int* p_anint, int localbitindex) {
  int mask;
  mask = 1 << localbitindex;
  (*p_anint) = (*p_anint) ^ mask;
}
int isbitonein_bitposition_in_integer(int anint, int localbitindex) {
  int mask; int temp;
  mask = 1 << localbitindex;
  temp = anint & mask;
  if (temp==0) {
    return 0;
  } else {
    return 1;
  }
}
void setbitonein_bitposition_in_integer(int* p_anint, int localbitindex) {
  int mask; int temp;
  mask = 1 << localbitindex;
  (*p_anint) = (*p_anint) | mask; 
}

void fill_int_array_with_random_bits(int* inputtoprogram) {
  int n; int i; int localbitindex;
  n = getinputtoprogram_size_in_number_of_ints();
  for (i=0;i<n;i++) {
    inputtoprogram[i] = 0;
  }  
  for (i=0;i<n;i++) {
    for (localbitindex=0;localbitindex<((sizeof(int))*8);localbitindex++) {
      if (drand48()<=0.5) {
        setbitonein_bitposition_in_integer(&(inputtoprogram[i]), localbitindex);
      }
    }
  }  
}

void openlog() {
  mylogfile = fopen("log.txt", "w+" );
}
void closelog() {
  fclose(mylogfile);
}

void delete_individual_and_deallocate_memory(struct individual* p_anindividual_that_we_want_to_delete) {
  struct individual* oldp;
  struct individual* p;
  p = listof_individuals;
  if (p==p_anindividual_that_we_want_to_delete) {
    listof_individuals = p->next;
    free( p->inputtoprogram);
    free( p);
  } else {
    p = listof_individuals;
    oldp = p;
    p    = p->next;
    while ((p!=NULL) && (p!=p_anindividual_that_we_want_to_delete)) {  
      oldp = p;
      p    = p->next;
    }
    if (p==NULL) { printf("This is an error. We tried to delete an individual that does not exist.\n"); exit(-1); }
    // now, we know that p==p_anindividual_that_we_want_to_delete
    oldp->next = p->next;
    free( p->inputtoprogram);
    free( p);
  }
}

unsigned long long diff_ns_timespec(struct timespec *x, struct timespec *y) {
  unsigned long long abillion = 1000000000;
  unsigned long long u;
  u = x->tv_sec;
  u = u * abillion;
  u = u + x->tv_nsec;
  unsigned long long v;
  v = y->tv_sec;
  v = v * abillion;
  v = v + y->tv_nsec;
  return u-v;
}
double diff_s_timespec (struct timespec *x, struct timespec *y) {
  unsigned long long abillion = 1000000000;
  unsigned long long t;
  unsigned long long tsec;
  unsigned long long tnsec;
  double t_as_double_secondpart;
  double t_as_double_usecondpart;
  double t_as_double;
  t = diff_ns_timespec( x, y);
  tsec = t / abillion;
  tnsec = t % abillion;
  t_as_double_secondpart = tsec;
  t_as_double_usecondpart = tnsec;
  t_as_double_usecondpart = t_as_double_usecondpart / abillion;
  t_as_double = t_as_double_secondpart + t_as_double_usecondpart;
  return t_as_double;
}
double run_program_with_input(int* inputtoprogram, char* commandtorun) {
  struct timespec mybegin;
  struct timespec myend;
  int status_clock_gettime_begin;
  int status_clock_gettime_end;
  int fd; int countwritten; double t;
  fd = open("inputfile.dat", O_RDWR | O_CREAT, S_IRUSR | S_IWUSR );
  if (fd==-1) { printf("Error when opening file\n"); exit(-1); }
  countwritten = write( fd, inputtoprogram, getinputtoprogram_size_in_number_of_bytes() );
  if (countwritten==0) { printf("Error when writing to file\n"); exit(-1); }
  close(fd);
  status_clock_gettime_begin = clock_gettime(CLOCK_MONOTONIC_RAW, &mybegin);
  system(commandtorun);
  status_clock_gettime_end = clock_gettime(CLOCK_MONOTONIC_RAW, &myend);
  t = diff_s_timespec(&myend, &mybegin);
  return t;
}

int create_individual_and_insert_as_head(int* giveninputtoprogram, char* commandtorun) {
  struct individual* p_anindividual;
  if (giveninputtoprogram==NULL) {
    giveninputtoprogram = malloc(getinputtoprogram_size_in_number_of_bytes());
    fill_int_array_with_random_bits(giveninputtoprogram);
  }
  p_anindividual = malloc(sizeof(struct individual));
  p_anindividual->inputtoprogram                 = giveninputtoprogram;
  p_anindividual->measuredexecutiontimeofprogram = run_program_with_input(p_anindividual->inputtoprogram,commandtorun);
  p_anindividual->next                           = listof_individuals;
  listof_individuals                             = p_anindividual;
}

void fill_listof_individuals(int n, char* commandtorun) {
  int i;
  listof_individuals = NULL;
  for (i=0;i<NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED;i++) {
    create_individual_and_insert_as_head(NULL, commandtorun);
    delete_individual_and_deallocate_memory( listof_individuals);
  }
  for (i=0;i<n;i++) {
    create_individual_and_insert_as_head(NULL, commandtorun);
  }
}

void findindividualwithlargestmeasuredexecutiontimeofprogram(struct individual** q) {
  struct individual* p; struct individual* largestexecindividual;
  p = listof_individuals;
  largestexecindividual = NULL;
  while (p!=NULL) {
    if (largestexecindividual==NULL) {
      largestexecindividual = p;
    } else {
      if (largestexecindividual->measuredexecutiontimeofprogram < p->measuredexecutiontimeofprogram) { largestexecindividual = p; }
    }
    p = p->next;
  }
  if (largestexecindividual==NULL) { printf("There was an error. There is no individual with largest execution time.\n"); }
  *q = largestexecindividual;
}
void findindividualwithsmallestmeasuredexecutiontimeofprogram(struct individual** q) {
  struct individual* p; struct individual* smallestexecindividual;
  p = listof_individuals;
  smallestexecindividual = NULL;
  while (p!=NULL) {
    if (smallestexecindividual==NULL) {
      smallestexecindividual = p;
    } else {
      if (smallestexecindividual->measuredexecutiontimeofprogram > p->measuredexecutiontimeofprogram) { smallestexecindividual = p; }
    }
    p = p->next;
  }
  if (smallestexecindividual==NULL) { printf("There was an error. There is no individual with smallest execution time.\n"); }
  *q = smallestexecindividual;
}

double getmaximumexecutiontimeofindividuals() {
  struct individual* p_foundindividual;
  findindividualwithlargestmeasuredexecutiontimeofprogram(&p_foundindividual);
  return p_foundindividual->measuredexecutiontimeofprogram; 
}

void do_mutations_on_inputtoprogram(int* inputtoprogram) {
  int bitindex; int intindex; int localbitindex;
  bitindex      = rand()%inputsizeinnumberofbits;
  intindex      = obtain_intindex_from_bitindex(bitindex);
  localbitindex = obtain_localbitindex_from_bitindex(bitindex);
  flipbit_bitposition_in_integer( &(inputtoprogram[intindex]), localbitindex); 
}

void copy_inputtoprogram(int* inputtoprogram_destination, int* inputtoprogram_source) {
  int i; int n;
  n = getinputtoprogram_size_in_number_of_ints();
  for (i=0;i<n;i++) {
    inputtoprogram_destination[i] = inputtoprogram_source[i];
  }
}

void create_new_inputtoprogram_throughmutations(int* inputtoprogram_destination, int* inputtoprogram_source) {
  copy_inputtoprogram(inputtoprogram_destination,inputtoprogram_source);
  do_mutations_on_inputtoprogram(inputtoprogram_destination);
}

void do_mutations(char* commandtorun) {
  struct individual* p; int* giveninputtoprogram;
  p = listof_individuals;
  while (p!=NULL) {
    if (drand48()<MUTATIONRATE) {
      giveninputtoprogram = malloc(getinputtoprogram_size_in_number_of_bytes());
      create_new_inputtoprogram_throughmutations(giveninputtoprogram,p->inputtoprogram);
      create_individual_and_insert_as_head(giveninputtoprogram, commandtorun);
    }
    p = p->next;
  }
}       

void do_steepest_descent(char* commandtorun) {
  struct individual* p;
  int bitindex; int intindex; int localbitindex;
  double new_measuredexecutiontimeofprogram;
  p = listof_individuals;
  while (p!=NULL) {
    bitindex      = rand()%inputsizeinnumberofbits;
    intindex      = obtain_intindex_from_bitindex(bitindex);
    localbitindex = obtain_localbitindex_from_bitindex(bitindex);
    flipbit_bitposition_in_integer( &((p->inputtoprogram)[intindex]), localbitindex); 
    new_measuredexecutiontimeofprogram = run_program_with_input(p->inputtoprogram, commandtorun);
    if ((p->measuredexecutiontimeofprogram)<new_measuredexecutiontimeofprogram) {
      (p->measuredexecutiontimeofprogram) = new_measuredexecutiontimeofprogram;
    } else {
      flipbit_bitposition_in_integer( &((p->inputtoprogram)[intindex]), localbitindex); 
    }
    p = p->next;
  }
}

void get_statistics_about_population(int* p_n,double* p_averageexecutiontime, double* p_minexecutiontime, double* p_maxexecutiontime) {
  struct individual* p; int n; double sum; double minexecutiontime; double maxexecutiontime;
  if (listof_individuals==NULL) {
    printf("An error has occured in get_statistics_about_population. There are no elements in list.\n"); exit(-1);
  }
  p                = listof_individuals;
  n                = 1;
  sum              = p->measuredexecutiontimeofprogram;
  minexecutiontime = p->measuredexecutiontimeofprogram;
  maxexecutiontime = p->measuredexecutiontimeofprogram; 
  p                = p->next;
  while (p!=NULL) {
    n                  = n   + 1;
    sum                = sum + p->measuredexecutiontimeofprogram;
    if (p->measuredexecutiontimeofprogram<minexecutiontime) { minexecutiontime = p->measuredexecutiontimeofprogram; }
    if (p->measuredexecutiontimeofprogram>maxexecutiontime) { maxexecutiontime = p->measuredexecutiontimeofprogram; }
    p                  = p->next;
  }
  *p_n                    = n;
  *p_averageexecutiontime = sum/n;
  *p_minexecutiontime     = minexecutiontime;
  *p_maxexecutiontime     = maxexecutiontime;
}

int get_numberof_individuals_with_executiontime_greaterthan_or_equal_to(double THR) {
  struct individual* p; int count;
  p = listof_individuals;
  count = 0;
  while (p!=NULL) {
    if (p->measuredexecutiontimeofprogram>=THR) {
      count++;
    }
    p   = p->next;
  }
  return count;
}
struct individual* identify_individual_with_executiontime_greaterthan_or_equal_to(double THR,int orderamongselection) {
  struct individual* p; int count;
  p = listof_individuals;
  count = 0;
  while (p!=NULL) {
    if (p->measuredexecutiontimeofprogram>=THR) {
      if (count==orderamongselection) {
        return p;
      } else {
        count++;
      }
    }
    p   = p->next;
  }
  printf("An error has occured in identify_individual_with_executiontime_greaterthan_or_equal_to. Count not find element.\n"); exit(-1);
}

struct individual* get_an_individual_with_executiontime_greaterthan_or_equal_to(double THR) {
  struct individual* p; int count; int orderamongselection;
  count = get_numberof_individuals_with_executiontime_greaterthan_or_equal_to(THR);
  orderamongselection = random()%count;
  p = identify_individual_with_executiontime_greaterthan_or_equal_to(THR,orderamongselection);
  return p;
}

void create_new_stringthroughcrossover(int* giveninputtoprogram_destination,int* inputtoprogram_source1,int* inputtoprogram_source2) {
  int bitindex; int intindex; int localbitindex; int i;
  bitindex      = rand()%getinputtoprogram_size_in_number_of_bits();
  intindex      = obtain_intindex_from_bitindex(bitindex);
  localbitindex = obtain_localbitindex_from_bitindex(bitindex);
  for (i=0;i<intindex;i++) {
    giveninputtoprogram_destination[i] = inputtoprogram_source1[i];
  }
  for (i=intindex+1;i<getinputtoprogram_size_in_number_of_ints();i++) {
    giveninputtoprogram_destination[i] = inputtoprogram_source2[i];
  } 
  giveninputtoprogram_destination[intindex] = 0;
  for (i=0;i<localbitindex;i++) {
    if (isbitonein_bitposition_in_integer(inputtoprogram_source1[intindex], i)) {
      setbitonein_bitposition_in_integer(&(giveninputtoprogram_destination[intindex]), i);
    }
  }
  for (i=localbitindex;i<(sizeof(int)*8);i++) {
    if (isbitonein_bitposition_in_integer(inputtoprogram_source2[intindex], i)) {
      setbitonein_bitposition_in_integer(&(giveninputtoprogram_destination[intindex]), i);
    }
  }
}

void create_new_individuals_by_doing_crossover(int n_individuals_to_add, int elitism1, int elitism2, char* commandtorun) {
  int i; int n; double averageexecutiontime; double minexecutiontime; double maxexecutiontime; double THR;
  struct individual* p;
  struct individual* p2;
  int* giveninputtoprogram;
  for (i=0;i<n_individuals_to_add;i++) {
    get_statistics_about_population(&n,&averageexecutiontime,&minexecutiontime,&maxexecutiontime);
    THR = (averageexecutiontime+maxexecutiontime)/2.0;
    if (elitism1) {
      p  = get_an_individual_with_executiontime_greaterthan_or_equal_to(THR);
    } else {
      p  = get_an_individual_with_executiontime_greaterthan_or_equal_to(minexecutiontime);
    }
    if (elitism2) {
      p2 = get_an_individual_with_executiontime_greaterthan_or_equal_to(THR);
    } else {
      p2 = get_an_individual_with_executiontime_greaterthan_or_equal_to(minexecutiontime);
    }
    giveninputtoprogram = malloc(getinputtoprogram_size_in_number_of_bytes());
    create_new_stringthroughcrossover(giveninputtoprogram,p->inputtoprogram,p2->inputtoprogram);
    create_individual_and_insert_as_head(giveninputtoprogram, commandtorun);
  }
}

void do_crossover(char* commandtorun) {
  create_new_individuals_by_doing_crossover(NUMBER_OF_INDIVIDUALS,1,1, commandtorun);
  create_new_individuals_by_doing_crossover(NUMBER_OF_INDIVIDUALS,1,0, commandtorun);
  create_new_individuals_by_doing_crossover(NUMBER_OF_INDIVIDUALS,0,1, commandtorun);
  create_new_individuals_by_doing_crossover(NUMBER_OF_INDIVIDUALS,0,0, commandtorun);
}       

void delete_individual_with_lowest_measuredexecutiontimeofprogram() {
  struct individual* individual_with_smallest_executiontime;
  findindividualwithsmallestmeasuredexecutiontimeofprogram(&individual_with_smallest_executiontime);
  delete_individual_and_deallocate_memory(individual_with_smallest_executiontime);
}

void trim_population(int n_targetpopulationsize) {
  int n; double averageexecutiontime; double minexecutiontime; double maxexecutiontime;
  get_statistics_about_population(&n,&averageexecutiontime,&minexecutiontime,&maxexecutiontime);
  while (n>n_targetpopulationsize) {
    delete_individual_with_lowest_measuredexecutiontimeofprogram();
    n = n - 1;
  }   
}

void delete_all_individuals() {
  trim_population(0);
  listof_individuals = NULL;
}

void readfromconffilename(char* conffilename) {
  FILE* f; int temp;
  f = fopen(conffilename, "r");
  fscanf(f,"%d", &mode);
  fscanf(f,"%d", &inputsizeinnumberofbits);
  fclose(f);
}

void print_to_log_generation(int generationindex) {
  int n; double averageexecutiontime; double minexecutiontime; double maxexecutiontime;
  get_statistics_about_population(&n,&averageexecutiontime,&minexecutiontime,&maxexecutiontime);
  fprintf(mylogfile,"Generation %d. n=%d avg=%lf min=%lf max=%lf\n", generationindex, n, averageexecutiontime, minexecutiontime, maxexecutiontime); fflush(mylogfile);
}
void print_to_log_end(int generationindex) {
  int n; double averageexecutiontime; double minexecutiontime; double maxexecutiontime;
  get_statistics_about_population(&n,&averageexecutiontime,&minexecutiontime,&maxexecutiontime);
  fprintf(mylogfile,"End. n=%d avg=%lf min=%lf max=%lf\n", n, averageexecutiontime, minexecutiontime, maxexecutiontime); fflush(mylogfile); 
}


void get_command_to_run(int argc, char* argv[], char* commandtorun) {
  sprintf(commandtorun,"%s < %s", argv[2], "inputfile.dat");
}

void printallexecutiontimes() {
  struct individual* p;
  p = listof_individuals;
  while (p!=NULL) {
    printf("executiontime: %lf\n", p->measuredexecutiontimeofprogram );
    p = p->next;
  }
}

void printworstcase(char* fn_inputfile,char* fn_measuredexecutiontime) {  
  int fd; int countwritten; FILE* f;
  struct individual* individual_with_largest_executiontime;
  findindividualwithlargestmeasuredexecutiontimeofprogram(&individual_with_largest_executiontime);

  fd = open(fn_inputfile, O_RDWR | O_CREAT, S_IRUSR | S_IWUSR );
  if (fd==-1) { printf("Error when opening file\n"); exit(-1); }
  countwritten = write( fd, individual_with_largest_executiontime->inputtoprogram, getinputtoprogram_size_in_number_of_bytes() );
  if (countwritten==0) { printf("Error when writing to file\n"); exit(-1); }
  close(fd);

  f = fopen(fn_measuredexecutiontime, "w+");
  fprintf(f,"%lf", individual_with_largest_executiontime->measuredexecutiontimeofprogram);
  fclose(f);
}

void produce_results_GA(char* commandtorun) {
  char fn_inputfile[200]; char fn_measuredexecutiontime[200]; 
  int generationindex;
  fill_listof_individuals(NUMBER_OF_INDIVIDUALS, commandtorun);
  for (generationindex=0;generationindex<NGENERATIONS;generationindex++) {
    print_to_log_generation(generationindex);
    do_mutations(commandtorun); // this creates new individuals so it increases the size of the population
    do_crossover(commandtorun); // this creates new individuals so it increases the size of the population
    trim_population(NUMBER_OF_INDIVIDUALS); // this removes the individuals with the lowest execution time
  }  
  print_to_log_end(generationindex);
  printf("%lf\n", getmaximumexecutiontimeofindividuals());
  sprintf(fn_inputfile,"worstcaseinput_GA_inputfile.dat");
  sprintf(fn_measuredexecutiontime,"worstcaseinput_GA_measuredexecutiontime.dat");
  printworstcase(fn_inputfile,fn_measuredexecutiontime);  
}

void produce_results_steepest_descent(char* commandtorun) { 
  char fn_inputfile[200]; char fn_measuredexecutiontime[200]; 
  int generationindex;
  fill_listof_individuals(NUMBER_OF_INDIVIDUALS, commandtorun);
  for (generationindex=0;generationindex<NGENERATIONS;generationindex++) {
    print_to_log_generation(generationindex);
    do_steepest_descent(commandtorun);
  }  
  print_to_log_end(generationindex);
  printf("%lf\n", getmaximumexecutiontimeofindividuals());
  sprintf(fn_inputfile,"worstcaseinput_SD_inputfile.dat");
  sprintf(fn_measuredexecutiontime,"worstcaseinput_SD_measuredexecutiontime.dat");
  printworstcase(fn_inputfile,fn_measuredexecutiontime);  
}

void produce_results_GA_metamode(char* commandtorun) {
  char fn_inputfile[200]; char fn_measuredexecutiontime[200]; 
  int generationindex;
  FILE* metamodeoutputfile;
  metamodeoutputfile = fopen("metamodeoutputfile.txt","w+");
  for (NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED=2;NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED<=64;NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED=NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED*2) {
    for (NUMBER_OF_INDIVIDUALS=2;NUMBER_OF_INDIVIDUALS<=64;NUMBER_OF_INDIVIDUALS=NUMBER_OF_INDIVIDUALS*2) {
      for (MUTATIONRATE=0.001;MUTATIONRATE<=0.064;MUTATIONRATE=MUTATIONRATE*2) {
        for (NGENERATIONS=1;NGENERATIONS<=64;NGENERATIONS=NGENERATIONS*2) {
          fill_listof_individuals(NUMBER_OF_INDIVIDUALS, commandtorun);
          for (generationindex=0;generationindex<NGENERATIONS;generationindex++) {
            print_to_log_generation(generationindex);
            do_mutations(commandtorun); // this creates new individuals so it increases the size of the population
            do_crossover(commandtorun); // this creates new individuals so it increases the size of the population
            trim_population(NUMBER_OF_INDIVIDUALS); // this removes the individuals with the lowest execution time
          }  
          print_to_log_end(generationindex);
          printf("%lf\n", getmaximumexecutiontimeofindividuals());
          fprintf(metamodeoutputfile,"//%8d %8d %9.8lf %8d %12.8lf\n", NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED, NUMBER_OF_INDIVIDUALS, MUTATIONRATE, NGENERATIONS, getmaximumexecutiontimeofindividuals());
          fflush(metamodeoutputfile);
          sprintf(fn_inputfile,"worstcaseinput_GA_%d_%d_%lf_%d_inputfile.dat",NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED,NUMBER_OF_INDIVIDUALS,MUTATIONRATE,NGENERATIONS);
          sprintf(fn_measuredexecutiontime,"worstcaseinput_GA_%d_%d_%lf_%d_measuredexecutiontime.dat",NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED,NUMBER_OF_INDIVIDUALS,MUTATIONRATE,NGENERATIONS);
          printworstcase(fn_inputfile,fn_measuredexecutiontime);  
          delete_all_individuals();
        }
      }
    }
  }
  fclose(metamodeoutputfile);
}

void produce_results_steepest_descent_metamode(char* commandtorun) {
  char fn_inputfile[200]; char fn_measuredexecutiontime[200]; 
  int generationindex;
  FILE* metamodeoutputfile;
  metamodeoutputfile = fopen("metamodeoutputfile.txt","w+");
  for (NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED=2;NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED<=64;NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED=NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED*2) {
    for (NUMBER_OF_INDIVIDUALS=2;NUMBER_OF_INDIVIDUALS<=64;NUMBER_OF_INDIVIDUALS=NUMBER_OF_INDIVIDUALS*2) {
      for (MUTATIONRATE=0.001;MUTATIONRATE<=0.064;MUTATIONRATE=MUTATIONRATE*2) {
        for (NGENERATIONS=1;NGENERATIONS<=64;NGENERATIONS=NGENERATIONS*2) {
          fill_listof_individuals(NUMBER_OF_INDIVIDUALS, commandtorun);
          for (generationindex=0;generationindex<NGENERATIONS;generationindex++) {
            print_to_log_generation(generationindex);
            do_steepest_descent(commandtorun);
          }  
          print_to_log_end(generationindex);
          printf("%lf\n", getmaximumexecutiontimeofindividuals());
          fprintf(metamodeoutputfile,"//%8d %8d %9.8lf %8d %12.8lf\n", NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED, NUMBER_OF_INDIVIDUALS, MUTATIONRATE, NGENERATIONS, getmaximumexecutiontimeofindividuals());
          fflush(metamodeoutputfile);
          sprintf(fn_inputfile,"worstcaseinput_SD_%d_%d_%lf_%d_inputfile.dat",NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED,NUMBER_OF_INDIVIDUALS,MUTATIONRATE,NGENERATIONS);
          sprintf(fn_measuredexecutiontime,"worstcaseinput_SD_%d_%d_%lf_%d_measuredexecutiontime.dat",NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED,NUMBER_OF_INDIVIDUALS,MUTATIONRATE,NGENERATIONS);
          printworstcase(fn_inputfile,fn_measuredexecutiontime);  
          delete_all_individuals();
        }
      }
    }
  }
  fclose(metamodeoutputfile);
}

int main(int argc, char* argv[]) {
  int generationindex; char commandtorun[200];
  openlog();
  if (argc==1) { printf("You need to give more parameters. You probably forgot to specify the executable file and the size of the input.\n"); exit(-1); }
  if (argc==2) { printf("You need to give more parameters. You probably forgot to specify the executable file or the size of the input.\n");  exit(-1); }
  if (argc>=4) { printf("You gave too many parameters.\n"); exit(-1); }
  sscanf(argv[1],"%s",conffilename);   
  readfromconffilename(conffilename);
  get_command_to_run(argc, argv, commandtorun);
  srand(137); srand48(137.0);
  if (mode==0) {
    produce_results_GA(commandtorun);
  } else {
    if (mode==1) {
      produce_results_steepest_descent(commandtorun);
    } else {
      if (mode==2) {
        produce_results_GA_metamode(commandtorun);
      } else {
        if (mode==3) {
          produce_results_steepest_descent_metamode(commandtorun);
        } else {
          printf("Not yet implemented\n"); exit(-1);
        }
      }
    }
  }
  closelog(); 
  return 0;
}
// Below, we present the following:
//   1. Source code for bubblesort. We have used it to test our WCET analysis tool
//   2. Source code for quicksort. We have used it to test our WCET analysis tool
//   3. Source code for generate_ascending_integers.c We have used it to test bubblesort and quicksort
//   4. Source code for generate_descending_integers.c We have used it to test bubblesort and quicksort
//   5. Experimental results for ascending and descending with bubblesort
//   6. Experimental results for ascending and descending with quicksort
//   7. Miscellaneous experiments
//   8. Experimental results for mode 2 with bubblesort
//   9. Experimental results for mode 3 with bubblesort
//  10. Experimental results for mode 2 with quicksort
//  11. Experimental results for mode 3 with quicksort
//
// ******************** 1. Source code for bubblesort ********************
//
// how to compile it
//   gcc -o bubblesort bubblesort.c
// #include <stdio.h>
// #include <stdlib.h>
// #include <unistd.h>
// #include <sys/types.h>
// #include <sys/stat.h>
// #include <fcntl.h>
// #include <string.h>
// 
// #define ARSIZE 8192
// 
// int ar[ARSIZE];
// 
// void swap(int* p1, int *p2) {
//   int temp;
//   temp = *p1;
//   *p1 = *p2;
//   *p2 = temp;
// }
// 
// void bubblesort() {
//   int n; int i; int swapped;
//   n = ARSIZE;
//   do {
//     swapped = 0;
//     for (i=1;i<=n-1;i++) {
//       if (ar[i-1] > ar[i]) {
//         swap( &(ar[i-1]), &(ar[i]) );
//         swapped = 1;
//       }
//     }
//   } while (swapped);
// }
// 
// int main(int argc, char *argv[]) {
//   int countread;
//   if (argc!=1) { printf("Incorrect number of arguments. argc=%d argv[0]=%s argv[1]=%s\n", argc, argv[0], argv[1]); exit(-1); }
//   countread = read( STDIN_FILENO, ar, ARSIZE*sizeof(int) );
//   if (countread==0) { printf("Error when reading file\n"); exit(-1); }
//   bubblesort();
//   return 0;
// }
//
//
// ******************** 2. Source code for quicksort ********************
//
// how to compile it
//   gcc -o quicksort quicksort.c
//
// #include <stdio.h>
// #include <stdlib.h>
// #include <unistd.h>
// #include <sys/types.h>
// #include <sys/stat.h>
// #include <fcntl.h>
// #include <string.h>
// 
// #define ARSIZE 8192
// 
// int ar[ARSIZE];
// 
// void quicksort(int first, int last) {
//   int i; int j; int pivot; int temp;
//   if (first<last) {
//     pivot = first;
//     i     = first;
//     j     = last;
//     while(i<j) {
//       while ((ar[i]<=ar[pivot]) && (i<last)) {
//         i++;
//       }
//       while (ar[j]>ar[pivot]) {
//         j--;
//       }
//       if(i<j) {
//         temp=ar[i];
//         ar[i]=ar[j];
//         ar[j]=temp;
//       }
//     }
//     temp=ar[pivot];
//     ar[pivot]=ar[j];
//     ar[j]=temp;
//     quicksort(first,j-1);
//     quicksort(j+1,last);
//   }
// }
// 
// int main(int argc, char *argv[]) {
//   int countread;
//   if (argc!=1) { printf("Incorrect number of arguments. argc=%d argv[0]=%s argv[1]=%s\n", argc, argv[0], argv[1]); exit(-1); }
//   countread = read( STDIN_FILENO, ar, ARSIZE*sizeof(int) );
//   if (countread==0) { printf("Error when reading file\n"); exit(-1); }
//   quicksort(0,ARSIZE-1);
//   return 0;
// }
// 
//
// ******************** 3. Source code for generate ascending integers ********************
//
// how to compile it
//   gcc -o generate_ascending_integers generate_ascending_integers.c
//
// #include <stdio.h>
// #include <stdlib.h>
// #include <unistd.h>
// #include <sys/types.h>
// #include <sys/stat.h>
// #include <fcntl.h>
// #include <string.h>
// 
// #define ARSIZE 8192
// 
// int ar[ARSIZE];
// 
// int main(int argc, char *argv[]) {
//   int i; int fd; int countwritten;
//   for (i=0;i<ARSIZE;i++) {
//     ar[i] = i;
//   }
//   fd = open("ascending_integers.dat", O_CREAT|O_WRONLY|O_TRUNC, S_IRWXU );
//   countwritten = write( fd, ar, ARSIZE*sizeof(int) );
//   if (countwritten==0) { printf("Error when writing to file\n"); exit(-1); }
//   close(fd);
//   return 0;
// }
//
//
// ******************** 4. Source code for generate descending integers ********************
//
// Source code for generate descending integers
//
// how to compile it
//   gcc -o generate_descending_integers generate_descending_integers.c
//
// #include <stdio.h>
// #include <stdlib.h>
// #include <unistd.h>
// #include <sys/types.h>
// #include <sys/stat.h>
// #include <fcntl.h>
// #include <string.h>
// 
// #define ARSIZE 8192
//
// int ar[ARSIZE];
//
// int main(int argc, char *argv[]) {
//   int i; int fd; int countwritten;
//   for (i=0;i<ARSIZE;i++) {
//     ar[i] = ARSIZE-i;
//   }
//   fd = open("descending_integers.dat", O_CREAT|O_WRONLY|O_TRUNC, S_IRWXU);
//   countwritten = write( fd, ar, ARSIZE*sizeof(int) );
//   if (countwritten==0) { printf("Error when writing to file\n"); exit(-1); }
//   close(fd);
//   return 0;
// }
//
//
// ******************** 5. Experimental results for ascending and descending with bubblesort ********************
//
//ba@ba-desktop:~/ga_find_wcet$ time ./bubblesort < ascending_integers.dat 
//
// real	0m0.002s
// user	0m0.002s
// sys	0m0.000s
// ba@ba-desktop:~/ga_find_wcet$ time ./bubblesort < descending_integers.dat
//
// real	0m0.275s
// user	0m0.275s
// sys	0m0.000s
//
// ba@ba-desktop:~/ga_find_wcet$ time ./bubblesort < abadinput.dat 
//
// real	0m0.307s
// user	0m0.307s
// sys	0m0.000s
//
//
// ******************** 6. Experimental results for ascending and descending with quicksort ********************
//
// ba@ba-desktop:~/ga_find_wcet$ time ./quicksort < ascending_integers.dat 
//
// real	0m0.068s
// user	0m0.064s
// sys	0m0.004s
// ba@ba-desktop:~/ga_find_wcet$ time ./quicksort < descending_integers.dat 
// 
// real	0m0.085s
// user	0m0.081s
// sys	0m0.004s
// ba@ba-desktop:~/ga_find_wcet$ 
// 
// ******************** 7. Miscellaneous experiments ********************
// 
// 7.a Running quick sort with
//       int NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED = 1024;
//       int NUMBER_OF_INDIVIDUALS = 2048;
//       double MUTATIONRATE = 0.064;
//       int NGENERATIONS = 2048;
//     yields the output
//       ba@ba-desktop:~/ga_find_wcet$ date ; ./apa myconf ./quicksort ; date
//       Tue Aug 11 22:07:08 EDT 2020
//       0.023777
//       Thu Aug 13 10:33:03 EDT 2020
//     Note that this is far from the maximum execution time of quicksort (0.085). See above. 
// 
// 7.b Running quick sort with
//       int NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED = 1024;
//       int NUMBER_OF_INDIVIDUALS = 4096;
//       double MUTATIONRATE = 0.064;
//       int NGENERATIONS = 4096;
//     yields the output
//       ba@ba-desktop:~/ga_find_wcet$ date ; ./apa myconf ./quicksort ; date
//       Thu Aug 13 12:27:27 EDT 2020
//       0.582735
//       Sun Aug 23 20:47:20 EDT 2020
//       ba@ba-desktop:~/ga_find_wcet$
//     Note that this is closer to the maximum execution time of quicksort (0.085) but there is still some way to go. See above. 
// 
// 7.c Running quick sort with
//       int NUMBER_OF_BURNIN_INDIVIDUALS_DISCARDED = 4;
//       int NUMBER_OF_INDIVIDUALS = 4;
//       double MUTATIONRATE = 0.2;
//       int NGENERATIONS = 4;
//     yields the output
//       ba@ba-desktop:~/ga_find_wcet$ date ; ./apa myconf ./quicksort ; date
//       Sun Aug 23 21:35:04 EDT 2020
//       0.029965
//       Mon Sep 14 01:31:03 EDT 2020
//       ba@ba-desktop:~/ga_find_wcet$
//     Note that this is quite low. It seems like we might have had fortunate cross-over in 7.b but this did not happen here.
// 
// ******************** 8. Experimental results for mode 2 with bubblesort ********************
// 
// Consider GA (mode 2). It considers bubblesort. This takes is from metamodefile.txt with up to 16, 16, 0.016, 8 and it takes 3.5 hours to produce it.
// ba@ba-desktop:~/ga_find_wcet$ more metamodeoutputfile.txt 
//       2        2 0.00100000        1   0.30412875
//       2        2 0.00100000        2   0.30589594
//       2        2 0.00100000        4   0.30502948
//       2        2 0.00100000        8   0.30651599
//       2        2 0.00200000        1   0.30923039
//       2        2 0.00200000        2   0.30727135
//       2        2 0.00200000        4   0.30598156
//       2        2 0.00200000        8   0.30884217
//       2        2 0.00400000        1   0.30534299
//       2        2 0.00400000        2   0.30768522
//       2        2 0.00400000        4   0.30603080
//       2        2 0.00400000        8   0.30702602
//       2        2 0.00800000        1   0.30470007
//       2        2 0.00800000        2   0.30576541
//       2        2 0.00800000        4   0.30459529
//       2        2 0.00800000        8   0.30758186
//       2        2 0.01600000        1   0.30532384
//       2        2 0.01600000        2   0.30479958
//       2        2 0.01600000        4   0.30798572
//       2        2 0.01600000        8   0.30719482
//       2        4 0.00100000        1   0.30616913
//       2        4 0.00100000        2   0.30677494
//       2        4 0.00100000        4   0.30644785
//       2        4 0.00100000        8   0.30865749
//       2        4 0.00200000        1   0.30829562
//       2        4 0.00200000        2   0.30791527
//       2        4 0.00200000        4   0.30731806
//       2        4 0.00200000        8   0.30808321
//       2        4 0.00400000        1   0.30690289
//       2        4 0.00400000        2   0.30562548
//       2        4 0.00400000        4   0.30757075
//       2        4 0.00400000        8   0.30606759
//       2        4 0.00800000        1   0.30655543
//       2        4 0.00800000        2   0.30657225
//       2        4 0.00800000        4   0.30725211
//       2        4 0.00800000        8   0.30823170
//       2        4 0.01600000        1   0.30556865
//       2        4 0.01600000        2   0.30799109
//       2        4 0.01600000        4   0.30688531
//       2        4 0.01600000        8   0.30646263
//       2        8 0.00100000        1   0.30743799
//       2        8 0.00100000        2   0.30735159
//       2        8 0.00100000        4   0.30956763
//       2        8 0.00100000        8   0.30750981
//       2        8 0.00200000        1   0.30818581
//       2        8 0.00200000        2   0.30637506
//       2        8 0.00200000        4   0.30744333
//       2        8 0.00200000        8   0.30856986
//       2        8 0.00400000        1   0.30705464
//       2        8 0.00400000        2   0.30719879
//       2        8 0.00400000        4   0.30754933
//       2        8 0.00400000        8   0.31005169
//       2        8 0.00800000        1   0.30691735
//       2        8 0.00800000        2   0.31019131
//       2        8 0.00800000        4   0.30812548
//       2        8 0.00800000        8   0.30816148
//       2        8 0.01600000        1   0.30709450
//       2        8 0.01600000        2   0.30925984
//       2        8 0.01600000        4   0.30873624
//       2        8 0.01600000        8   0.31096368
//       2       16 0.00100000        1   0.30821369
//       2       16 0.00100000        2   0.30905525
//       2       16 0.00100000        4   0.30922332
//       2       16 0.00100000        8   0.30933270
//       2       16 0.00200000        1   0.30811157
//       2       16 0.00200000        2   0.30867358
//       2       16 0.00200000        4   0.30816512
//       2       16 0.00200000        8   0.30856890
//       2       16 0.00400000        1   0.30867330
//       2       16 0.00400000        2   0.30788131
//       2       16 0.00400000        4   0.30901997
//       2       16 0.00400000        8   0.31012777
//       2       16 0.00800000        1   0.30800430
//       2       16 0.00800000        2   0.30880862
//       2       16 0.00800000        4   0.30686352
//       2       16 0.00800000        8   0.30827228
//       2       16 0.01600000        1   0.30707394
//       2       16 0.01600000        2   0.30759025
//       2       16 0.01600000        4   0.30789389
//       2       16 0.01600000        8   0.30993303
//       4        2 0.00100000        1   0.30344570
//       4        2 0.00100000        2   0.30538160
//       4        2 0.00100000        4   0.30734594
//       4        2 0.00100000        8   0.30646114
//       4        2 0.00200000        1   0.30436279
//       4        2 0.00200000        2   0.30369511
//       4        2 0.00200000        4   0.30710410
//       4        2 0.00200000        8   0.30773930
//       4        2 0.00400000        1   0.30621556
//       4        2 0.00400000        2   0.30580190
//       4        2 0.00400000        4   0.30460118
//       4        2 0.00400000        8   0.30607314
//       4        2 0.00800000        1   0.30729189
//       4        2 0.00800000        2   0.30798562
//       4        2 0.00800000        4   0.30655450
//       4        2 0.00800000        8   0.30700433
//       4        2 0.01600000        1   0.30414141
//       4        2 0.01600000        2   0.30504488
//       4        2 0.01600000        4   0.30697315
//       4        2 0.01600000        8   0.30825120
//       4        4 0.00100000        1   0.30694888
//       4        4 0.00100000        2   0.30745969
//       4        4 0.00100000        4   0.30739391
//       4        4 0.00100000        8   0.30719929
//       4        4 0.00200000        1   0.30603718
//       4        4 0.00200000        2   0.30927018
//       4        4 0.00200000        4   0.30780293
//       4        4 0.00200000        8   0.30703257
//       4        4 0.00400000        1   0.30764418
//       4        4 0.00400000        2   0.30722360
//       4        4 0.00400000        4   0.30741158
//       4        4 0.00400000        8   0.30701971
//       4        4 0.00800000        1   0.30664416
//       4        4 0.00800000        2   0.30729998
//       4        4 0.00800000        4   0.30728049
//       4        4 0.00800000        8   0.30796916
//       4        4 0.01600000        1   0.30562819
//       4        4 0.01600000        2   0.30755618
//       4        4 0.01600000        4   0.30543784
//       4        4 0.01600000        8   0.30542132
//       4        8 0.00100000        1   0.30599598
//       4        8 0.00100000        2   0.30816398
//       4        8 0.00100000        4   0.30802756
//       4        8 0.00100000        8   0.30863480
//       4        8 0.00200000        1   0.30790390
//       4        8 0.00200000        2   0.30743048
//       4        8 0.00200000        4   0.30838491
//       4        8 0.00200000        8   0.30847453
//       4        8 0.00400000        1   0.30772218
//       4        8 0.00400000        2   0.30797308
//       4        8 0.00400000        4   0.30741250
//       4        8 0.00400000        8   0.30792793
//       4        8 0.00800000        1   0.30729245
//       4        8 0.00800000        2   0.30854760
//       4        8 0.00800000        4   0.30958634
//       4        8 0.00800000        8   0.30705185
//       4        8 0.01600000        1   0.30734754
//       4        8 0.01600000        2   0.30905435
//       4        8 0.01600000        4   0.30803997
//       4        8 0.01600000        8   0.30811188
//       4       16 0.00100000        1   0.30800607
//       4       16 0.00100000        2   0.30758301
//       4       16 0.00100000        4   0.30840266
//       4       16 0.00100000        8   0.30969864
//       4       16 0.00200000        1   0.30752511
//       4       16 0.00200000        2   0.30985915
//       4       16 0.00200000        4   0.31119621
//       4       16 0.00200000        8   0.30899023
//       4       16 0.00400000        1   0.30653268
//       4       16 0.00400000        2   0.31586329
//       4       16 0.00400000        4   0.30939051
//       4       16 0.00400000        8   0.30885951
//       4       16 0.00800000        1   0.30907351
//       4       16 0.00800000        2   0.30739886
//       4       16 0.00800000        4   0.30846504
//       4       16 0.00800000        8   0.30903572
//       4       16 0.01600000        1   0.31511131
//       4       16 0.01600000        2   0.30767823
//       4       16 0.01600000        4   0.30946299
//       4       16 0.01600000        8   0.30883326
//       8        2 0.00100000        1   0.30479754
//       8        2 0.00100000        2   0.30617823
//       8        2 0.00100000        4   0.30685608
//       8        2 0.00100000        8   0.30584253
//       8        2 0.00200000        1   0.30614637
//       8        2 0.00200000        2   0.30583330
//       8        2 0.00200000        4   0.30653549
//       8        2 0.00200000        8   0.30734478
//       8        2 0.00400000        1   0.30683748
//       8        2 0.00400000        2   0.30542820
//       8        2 0.00400000        4   0.30931987
//       8        2 0.00400000        8   0.30756733
//       8        2 0.00800000        1   0.30843096
//       8        2 0.00800000        2   0.30451502
//       8        2 0.00800000        4   0.30613273
//       8        2 0.00800000        8   0.30605596
//       8        2 0.01600000        1   0.30612091
//       8        2 0.01600000        2   0.30693976
//       8        2 0.01600000        4   0.30637614
//       8        2 0.01600000        8   0.30632202
//       8        4 0.00100000        1   0.30661310
//       8        4 0.00100000        2   0.30615769
//       8        4 0.00100000        4   0.30893048
//       8        4 0.00100000        8   0.30802366
//       8        4 0.00200000        1   0.30615682
//       8        4 0.00200000        2   0.30667284
//       8        4 0.00200000        4   0.30652735
//       8        4 0.00200000        8   0.30737501
//       8        4 0.00400000        1   0.30514128
//       8        4 0.00400000        2   0.30580940
//       8        4 0.00400000        4   0.30776652
//       8        4 0.00400000        8   0.30706687
//       8        4 0.00800000        1   0.30638977
//       8        4 0.00800000        2   0.30751739
//       8        4 0.00800000        4   0.30601585
//       8        4 0.00800000        8   0.30835163
//       8        4 0.01600000        1   0.30428977
//       8        4 0.01600000        2   0.30752941
//       8        4 0.01600000        4   0.30648480
//       8        4 0.01600000        8   0.30784824
//       8        8 0.00100000        1   0.30721987
//       8        8 0.00100000        2   0.30860135
//       8        8 0.00100000        4   0.30893656
//       8        8 0.00100000        8   0.30827163
//       8        8 0.00200000        1   0.30661832
//       8        8 0.00200000        2   0.30799613
//       8        8 0.00200000        4   0.30851991
//       8        8 0.00200000        8   0.30810091
//       8        8 0.00400000        1   0.30796109
//       8        8 0.00400000        2   0.30705772
//       8        8 0.00400000        4   0.30674120
//       8        8 0.00400000        8   0.30992664
//       8        8 0.00800000        1   0.30954706
//       8        8 0.00800000        2   0.30743790
//       8        8 0.00800000        4   0.31027582
//       8        8 0.00800000        8   0.30900923
//       8        8 0.01600000        1   0.30624468
//       8        8 0.01600000        2   0.30725454
//       8        8 0.01600000        4   0.30794047
//       8        8 0.01600000        8   0.30757028
//       8       16 0.00100000        1   0.30815649
//       8       16 0.00100000        2   0.31074635
//       8       16 0.00100000        4   0.31020252
//       8       16 0.00100000        8   0.30850720
//       8       16 0.00200000        1   0.30901377
//       8       16 0.00200000        2   0.30886437
//       8       16 0.00200000        4   0.31026282
//       8       16 0.00200000        8   0.30948876
//       8       16 0.00400000        1   0.30617291
//       8       16 0.00400000        2   0.30736306
//       8       16 0.00400000        4   0.30865698
//       8       16 0.00400000        8   0.30962140
//       8       16 0.00800000        1   0.30793606
//       8       16 0.00800000        2   0.30886704
//       8       16 0.00800000        4   0.30912522
//       8       16 0.00800000        8   0.30885985
//       8       16 0.01600000        1   0.30873630
//       8       16 0.01600000        2   0.30949667
//       8       16 0.01600000        4   0.30910486
//       8       16 0.01600000        8   0.30802045
//      16        2 0.00100000        1   0.30592027
//      16        2 0.00100000        2   0.30885222
//      16        2 0.00100000        4   0.30565880
//      16        2 0.00100000        8   0.30693825
//      16        2 0.00200000        1   0.30637045
//      16        2 0.00200000        2   0.30463685
//      16        2 0.00200000        4   0.30572332
//      16        2 0.00200000        8   0.30679280
//      16        2 0.00400000        1   0.30561691
//      16        2 0.00400000        2   0.30626118
//      16        2 0.00400000        4   0.30762080
//      16        2 0.00400000        8   0.30728914
//      16        2 0.00800000        1   0.30503356
//      16        2 0.00800000        2   0.30732687
//      16        2 0.00800000        4   0.30763813
//      16        2 0.00800000        8   0.30756701
//      16        2 0.01600000        1   0.30777433
//      16        2 0.01600000        2   0.30545593
//      16        2 0.01600000        4   0.30883350
//      16        2 0.01600000        8   0.30712259
//      16        4 0.00100000        1   0.30765818
//      16        4 0.00100000        2   0.30767987
//      16        4 0.00100000        4   0.30661930
//      16        4 0.00100000        8   0.30665311
//      16        4 0.00200000        1   0.30450531
//      16        4 0.00200000        2   0.30851622
//      16        4 0.00200000        4   0.30879790
//      16        4 0.00200000        8   0.30715866
//      16        4 0.00400000        1   0.30687047
//      16        4 0.00400000        2   0.30624623
//      16        4 0.00400000        4   0.30826704
//      16        4 0.00400000        8   0.30758071
//      16        4 0.00800000        1   0.30711275
//      16        4 0.00800000        2   0.30885873
//      16        4 0.00800000        4   0.30645386
//      16        4 0.00800000        8   0.30845506
//      16        4 0.01600000        1   0.30908598
//      16        4 0.01600000        2   0.30863445
//      16        4 0.01600000        4   0.30850170
//      16        4 0.01600000        8   0.30794224
//      16        8 0.00100000        1   0.30654051
//      16        8 0.00100000        2   0.30944414
//      16        8 0.00100000        4   0.30678134
//      16        8 0.00100000        8   0.30801705
//      16        8 0.00200000        1   0.30723331
//      16        8 0.00200000        2   0.30724522
//      16        8 0.00200000        4   0.30775196
//      16        8 0.00200000        8   0.30989237
//      16        8 0.00400000        1   0.30830251
//      16        8 0.00400000        2   0.30746086
//      16        8 0.00400000        4   0.30806176
//      16        8 0.00400000        8   0.30764382
//      16        8 0.00800000        1   0.30695519
//      16        8 0.00800000        2   0.30783028
//      16        8 0.00800000        4   0.30742359
//      16        8 0.00800000        8   0.30634387
//      16        8 0.01600000        1   0.30722976
//      16        8 0.01600000        2   0.30675435
//      16        8 0.01600000        4   0.30923172
//      16        8 0.01600000        8   0.30850409
//      16       16 0.00100000        1   0.30749545
//      16       16 0.00100000        2   0.30924334
//      16       16 0.00100000        4   0.30956672
//      16       16 0.00100000        8   0.30911804
//      16       16 0.00200000        1   0.30858373
//      16       16 0.00200000        2   0.30983100
//      16       16 0.00200000        4   0.30768026
//      16       16 0.00200000        8   0.30985545
//      16       16 0.00400000        1   0.30845480
//      16       16 0.00400000        2   0.30843878
//      16       16 0.00400000        4   0.32187353
//      16       16 0.00400000        8   0.30910816
//      16       16 0.00800000        1   0.30738732
//      16       16 0.00800000        2   0.30903120
//      16       16 0.00800000        4   0.30732201
//      16       16 0.00800000        8   0.30912951
//      16       16 0.01600000        1   0.30880358
//      16       16 0.01600000        2   0.30927815
//      16       16 0.01600000        4   0.30825595
//      16       16 0.01600000        8   0.30990672
//
// ******************** 9. Experimental results for mode 3 with bubblesort ********************
//
// Consider steepest descent (mode 3). It considers bubblesort. This takes is from metamodefile.txt with up to 16, 16, 0.016, 8 and it takes 1.1 h to produce it.
// ba@ba-desktop:~/ga_find_wcet$ more metamodeoutputfile.txt 
//       2        2 0.00100000        1   0.30193092
//       2        2 0.00100000        2   0.30234037
//       2        2 0.00100000        4   0.30667764
//       2        2 0.00100000        8   0.30541030
//       2        2 0.00200000        1   0.30506643
//       2        2 0.00200000        2   0.30702089
//       2        2 0.00200000        4   0.30614540
//       2        2 0.00200000        8   0.30183860
//       2        2 0.00400000        1   0.30663534
//       2        2 0.00400000        2   0.30604416
//       2        2 0.00400000        4   0.30710994
//       2        2 0.00400000        8   0.30780543
//       2        2 0.00800000        1   0.30474534
//       2        2 0.00800000        2   0.30804429
//       2        2 0.00800000        4   0.30648634
//       2        2 0.00800000        8   0.30757480
//       2        2 0.01600000        1   0.30358984
//       2        2 0.01600000        2   0.30493461
//       2        2 0.01600000        4   0.30391693
//       2        2 0.01600000        8   0.30547229
//       2        4 0.00100000        1   0.30568902
//       2        4 0.00100000        2   0.30657934
//       2        4 0.00100000        4   0.30780647
//       2        4 0.00100000        8   0.30532463
//       2        4 0.00200000        1   0.30512404
//       2        4 0.00200000        2   0.30746573
//       2        4 0.00200000        4   0.30653408
//       2        4 0.00200000        8   0.30670485
//       2        4 0.00400000        1   0.30644462
//       2        4 0.00400000        2   0.30648749
//       2        4 0.00400000        4   0.30568756
//       2        4 0.00400000        8   0.30666048
//       2        4 0.00800000        1   0.30886587
//       2        4 0.00800000        2   0.30308532
//       2        4 0.00800000        4   0.30411821
//       2        4 0.00800000        8   0.30728565
//       2        4 0.01600000        1   0.30534892
//       2        4 0.01600000        2   0.30706149
//       2        4 0.01600000        4   0.30597574
//       2        4 0.01600000        8   0.30771331
//       2        8 0.00100000        1   0.30639255
//       2        8 0.00100000        2   0.30736381
//       2        8 0.00100000        4   0.30763976
//       2        8 0.00100000        8   0.30827837
//       2        8 0.00200000        1   0.30800685
//       2        8 0.00200000        2   0.30530269
//       2        8 0.00200000        4   0.30801282
//       2        8 0.00200000        8   0.30880063
//       2        8 0.00400000        1   0.30881425
//       2        8 0.00400000        2   0.30772649
//       2        8 0.00400000        4   0.30740465
//       2        8 0.00400000        8   0.30877127
//       2        8 0.00800000        1   0.30792645
//       2        8 0.00800000        2   0.30746293
//       2        8 0.00800000        4   0.30910687
//       2        8 0.00800000        8   0.30856269
//       2        8 0.01600000        1   0.30642474
//       2        8 0.01600000        2   0.30597329
//       2        8 0.01600000        4   0.30570403
//       2        8 0.01600000        8   0.30665671
//       2       16 0.00100000        1   0.30602622
//       2       16 0.00100000        2   0.30601242
//       2       16 0.00100000        4   0.30681815
//       2       16 0.00100000        8   0.30819463
//       2       16 0.00200000        1   0.31971188
//       2       16 0.00200000        2   0.30614434
//       2       16 0.00200000        4   0.30806806
//       2       16 0.00200000        8   0.30693628
//       2       16 0.00400000        1   0.30553097
//       2       16 0.00400000        2   0.30892382
//       2       16 0.00400000        4   0.30736723
//       2       16 0.00400000        8   0.30703865
//       2       16 0.00800000        1   0.30554668
//       2       16 0.00800000        2   0.30606286
//       2       16 0.00800000        4   0.30702683
//       2       16 0.00800000        8   0.30626127
//       2       16 0.01600000        1   0.30675186
//       2       16 0.01600000        2   0.30576909
//       2       16 0.01600000        4   0.30797920
//       2       16 0.01600000        8   0.30835256
//       4        2 0.00100000        1   0.30485766
//       4        2 0.00100000        2   0.30625928
//       4        2 0.00100000        4   0.30744768
//       4        2 0.00100000        8   0.30658727
//       4        2 0.00200000        1   0.30575612
//       4        2 0.00200000        2   0.30613761
//       4        2 0.00200000        4   0.30754865
//       4        2 0.00200000        8   0.30546981
//       4        2 0.00400000        1   0.30613316
//       4        2 0.00400000        2   0.30601195
//       4        2 0.00400000        4   0.30602693
//       4        2 0.00400000        8   0.30400822
//       4        2 0.00800000        1   0.30481317
//       4        2 0.00800000        2   0.30448547
//       4        2 0.00800000        4   0.30711264
//       4        2 0.00800000        8   0.30624385
//       4        2 0.01600000        1   0.30363569
//       4        2 0.01600000        2   0.30539097
//       4        2 0.01600000        4   0.30421263
//       4        2 0.01600000        8   0.30653042
//       4        4 0.00100000        1   0.30634741
//       4        4 0.00100000        2   0.30676659
//       4        4 0.00100000        4   0.30629961
//       4        4 0.00100000        8   0.30598135
//       4        4 0.00200000        1   0.30358331
//       4        4 0.00200000        2   0.30881429
//       4        4 0.00200000        4   0.30668411
//       4        4 0.00200000        8   0.30654563
//       4        4 0.00400000        1   0.30393951
//       4        4 0.00400000        2   0.30511721
//       4        4 0.00400000        4   0.30716269
//       4        4 0.00400000        8   0.30460278
//       4        4 0.00800000        1   0.30675725
//       4        4 0.00800000        2   0.30490640
//       4        4 0.00800000        4   0.30506905
//       4        4 0.00800000        8   0.30805942
//       4        4 0.01600000        1   0.30311713
//       4        4 0.01600000        2   0.30503429
//       4        4 0.01600000        4   0.30566028
//       4        4 0.01600000        8   0.30762550
//       4        8 0.00100000        1   0.30765047
//       4        8 0.00100000        2   0.30768189
//       4        8 0.00100000        4   0.30771520
//       4        8 0.00100000        8   0.30732904
//       4        8 0.00200000        1   0.30468610
//       4        8 0.00200000        2   0.30719279
//       4        8 0.00200000        4   0.30733640
//       4        8 0.00200000        8   0.30590079
//       4        8 0.00400000        1   0.30643222
//       4        8 0.00400000        2   0.30923095
//       4        8 0.00400000        4   0.30560221
//       4        8 0.00400000        8   0.30783989
//       4        8 0.00800000        1   0.30554473
//       4        8 0.00800000        2   0.30585479
//       4        8 0.00800000        4   0.30758661
//       4        8 0.00800000        8   0.30643247
//       4        8 0.01600000        1   0.30585488
//       4        8 0.01600000        2   0.30593014
//       4        8 0.01600000        4   0.30638905
//       4        8 0.01600000        8   0.30605234
//       4       16 0.00100000        1   0.30817760
//       4       16 0.00100000        2   0.30685586
//       4       16 0.00100000        4   0.30808094
//       4       16 0.00100000        8   0.30691639
//       4       16 0.00200000        1   0.30607693
//       4       16 0.00200000        2   0.30626360
//       4       16 0.00200000        4   0.30748872
//       4       16 0.00200000        8   0.30778785
//       4       16 0.00400000        1   0.32136930
//       4       16 0.00400000        2   0.30842450
//       4       16 0.00400000        4   0.30823023
//       4       16 0.00400000        8   0.30713859
//       4       16 0.00800000        1   0.30719273
//       4       16 0.00800000        2   0.30817547
//       4       16 0.00800000        4   0.30796086
//       4       16 0.00800000        8   0.30667553
//       4       16 0.01600000        1   0.30593103
//       4       16 0.01600000        2   0.30690839
//       4       16 0.01600000        4   0.30749547
//       4       16 0.01600000        8   0.30808197
//       8        2 0.00100000        1   0.30905924
//       8        2 0.00100000        2   0.30434693
//       8        2 0.00100000        4   0.30487369
//       8        2 0.00100000        8   0.30542043
//       8        2 0.00200000        1   0.30317746
//       8        2 0.00200000        2   0.30472300
//       8        2 0.00200000        4   0.30489674
//       8        2 0.00200000        8   0.30433573
//       8        2 0.00400000        1   0.30390470
//       8        2 0.00400000        2   0.30660258
//       8        2 0.00400000        4   0.30627679
//       8        2 0.00400000        8   0.30858937
//       8        2 0.00800000        1   0.30541322
//       8        2 0.00800000        2   0.30379159
//       8        2 0.00800000        4   0.30613412
//       8        2 0.00800000        8   0.30549814
//       8        2 0.01600000        1   0.30688101
//       8        2 0.01600000        2   0.30587159
//       8        2 0.01600000        4   0.30541376
//       8        2 0.01600000        8   0.30703216
//       8        4 0.00100000        1   0.30627844
//       8        4 0.00100000        2   0.30723178
//       8        4 0.00100000        4   0.30580957
//       8        4 0.00100000        8   0.30754301
//       8        4 0.00200000        1   0.30829896
//       8        4 0.00200000        2   0.30710040
//       8        4 0.00200000        4   0.30656156
//       8        4 0.00200000        8   0.30626547
//       8        4 0.00400000        1   0.30626900
//       8        4 0.00400000        2   0.30485240
//       8        4 0.00400000        4   0.30674422
//       8        4 0.00400000        8   0.30727552
//       8        4 0.00800000        1   0.30348169
//       8        4 0.00800000        2   0.30736978
//       8        4 0.00800000        4   0.30697551
//       8        4 0.00800000        8   0.30563268
//       8        4 0.01600000        1   0.30504247
//       8        4 0.01600000        2   0.30662770
//       8        4 0.01600000        4   0.30697027
//       8        4 0.01600000        8   0.30718103
//       8        8 0.00100000        1   0.30538433
//       8        8 0.00100000        2   0.30631330
//       8        8 0.00100000        4   0.30595347
//       8        8 0.00100000        8   0.30623128
//       8        8 0.00200000        1   0.30670741
//       8        8 0.00200000        2   0.30738002
//       8        8 0.00200000        4   0.30691601
//       8        8 0.00200000        8   0.30642336
//       8        8 0.00400000        1   0.30446974
//       8        8 0.00400000        2   0.30634758
//       8        8 0.00400000        4   0.30831689
//       8        8 0.00400000        8   0.30972752
//       8        8 0.00800000        1   0.30695941
//       8        8 0.00800000        2   0.30438880
//       8        8 0.00800000        4   0.30665590
//       8        8 0.00800000        8   0.30647919
//       8        8 0.01600000        1   0.30699623
//       8        8 0.01600000        2   0.30807600
//       8        8 0.01600000        4   0.30734973
//       8        8 0.01600000        8   0.30674773
//       8       16 0.00100000        1   0.30619059
//       8       16 0.00100000        2   0.30750818
//       8       16 0.00100000        4   0.30600106
//       8       16 0.00100000        8   0.30709670
//       8       16 0.00200000        1   0.30655760
//       8       16 0.00200000        2   0.30777709
//       8       16 0.00200000        4   0.30708977
//       8       16 0.00200000        8   0.30762015
//       8       16 0.00400000        1   0.30616978
//       8       16 0.00400000        2   0.30726497
//       8       16 0.00400000        4   0.30646498
//       8       16 0.00400000        8   0.30676592
//       8       16 0.00800000        1   0.30649180
//       8       16 0.00800000        2   0.30759802
//       8       16 0.00800000        4   0.30661703
//       8       16 0.00800000        8   0.30856249
//       8       16 0.01600000        1   0.30565913
//       8       16 0.01600000        2   0.30848522
//       8       16 0.01600000        4   0.30803530
//       8       16 0.01600000        8   0.30700630
//      16        2 0.00100000        1   0.30399660
//      16        2 0.00100000        2   0.30748001
//      16        2 0.00100000        4   0.30543056
//      16        2 0.00100000        8   0.30517372
//      16        2 0.00200000        1   0.30609194
//      16        2 0.00200000        2   0.30478101
//      16        2 0.00200000        4   0.30470496
//      16        2 0.00200000        8   0.30716621
//      16        2 0.00400000        1   0.30638671
//      16        2 0.00400000        2   0.30473059
//      16        2 0.00400000        4   0.30478668
//      16        2 0.00400000        8   0.30425046
//      16        2 0.00800000        1   0.30714182
//      16        2 0.00800000        2   0.30287101
//      16        2 0.00800000        4   0.30838712
//      16        2 0.00800000        8   0.30610965
//      16        2 0.01600000        1   0.30594542
//      16        2 0.01600000        2   0.30401467
//      16        2 0.01600000        4   0.30557774
//      16        2 0.01600000        8   0.30619044
//      16        4 0.00100000        1   0.30601600
//      16        4 0.00100000        2   0.30517251
//      16        4 0.00100000        4   0.30594442
//      16        4 0.00100000        8   0.30772783
//      16        4 0.00200000        1   0.30527421
//      16        4 0.00200000        2   0.30563527
//      16        4 0.00200000        4   0.30569833
//      16        4 0.00200000        8   0.30698574
//      16        4 0.00400000        1   0.30619417
//      16        4 0.00400000        2   0.30637760
//      16        4 0.00400000        4   0.30493781
//      16        4 0.00400000        8   0.30638924
//      16        4 0.00800000        1   0.30589033
//      16        4 0.00800000        2   0.30479321
//      16        4 0.00800000        4   0.30722374
//      16        4 0.00800000        8   0.30920584
//      16        4 0.01600000        1   0.30563628
//      16        4 0.01600000        2   0.30666519
//      16        4 0.01600000        4   0.30636806
//      16        4 0.01600000        8   0.30575172
//      16        8 0.00100000        1   0.30438919
//      16        8 0.00100000        2   0.30596149
//      16        8 0.00100000        4   0.30563998
//      16        8 0.00100000        8   0.30883443
//      16        8 0.00200000        1   0.30731821
//      16        8 0.00200000        2   0.30610393
//      16        8 0.00200000        4   0.30715610
//      16        8 0.00200000        8   0.30664494
//      16        8 0.00400000        1   0.30535997
//      16        8 0.00400000        2   0.30598466
//      16        8 0.00400000        4   0.30732914
//      16        8 0.00400000        8   0.30772756
//      16        8 0.00800000        1   0.30548815
//      16        8 0.00800000        2   0.30821543
//      16        8 0.00800000        4   0.30621405
//      16        8 0.00800000        8   0.30597916
//      16        8 0.01600000        1   0.30546341
//      16        8 0.01600000        2   0.30715990
//      16        8 0.01600000        4   0.30694659
//      16        8 0.01600000        8   0.31864633
//      16       16 0.00100000        1   0.30870846
//      16       16 0.00100000        2   0.30678462
//      16       16 0.00100000        4   0.30773288
//      16       16 0.00100000        8   0.30739919
//      16       16 0.00200000        1   0.30688516
//      16       16 0.00200000        2   0.30751406
//      16       16 0.00200000        4   0.30685624
//      16       16 0.00200000        8   0.30660050
//      16       16 0.00400000        1   0.30617820
//      16       16 0.00400000        2   0.30934514
//      16       16 0.00400000        4   0.30822297
//      16       16 0.00400000        8   0.30696525
//      16       16 0.00800000        1   0.30743368
//      16       16 0.00800000        2   0.30637560
//      16       16 0.00800000        4   0.30736320
//      16       16 0.00800000        8   0.30665255
//      16       16 0.01600000        1   0.30555218
//      16       16 0.01600000        2   0.30616334
//      16       16 0.01600000        4   0.30763246
//      16       16 0.01600000        8   0.30708502
//
// ******************** 10. Experimental results for mode 2 with quicksort ********************
//
// Consider GA (mode 2). It considers quicksort. This takes is from metamodefile.txt with up to 64 64 0.064 64 and it takes 3.5 hours to produce it.
// ba@ba-desktop:~/ga_find_wcet$ more metamodeoutputfile.txt 
//       2        2 0.00100000        1   0.00255059
//       2        2 0.00100000        2   0.00338877
//       2        2 0.00100000        4   0.00448021
//       2        2 0.00100000        8   0.00451370
//       2        2 0.00100000       16   0.00450854
//       2        2 0.00100000       32   0.00478489
//       2        2 0.00100000       64   0.00525816
//       2        2 0.00200000        1   0.00221690
//       2        2 0.00200000        2   0.00286286
//       2        2 0.00200000        4   0.00385217
//       2        2 0.00200000        8   0.00450088
//       2        2 0.00200000       16   0.00457986
//       2        2 0.00200000       32   0.00462157
//       2        2 0.00200000       64   0.00456151
//       2        2 0.00400000        1   0.00219313
//       2        2 0.00400000        2   0.00385078
//       2        2 0.00400000        4   0.00387668
//       2        2 0.00400000        8   0.00457311
//       2        2 0.00400000       16   0.00461084
//       2        2 0.00400000       32   0.00459301
//       2        2 0.00400000       64   0.00524003
//       2        2 0.00800000        1   0.00209159
//       2        2 0.00800000        2   0.00354509
//       2        2 0.00800000        4   0.00448530
//       2        2 0.00800000        8   0.00447070
//       2        2 0.00800000       16   0.00459087
//       2        2 0.00800000       32   0.00592198
//       2        2 0.00800000       64   0.00671969
//       2        2 0.01600000        1   0.00209786
//       2        2 0.01600000        2   0.00322593
//       2        2 0.01600000        4   0.00457001
//       2        2 0.01600000        8   0.00461356
//       2        2 0.01600000       16   0.00472940
//       2        2 0.01600000       32   0.00462682
//       2        2 0.01600000       64   0.00573826
//       2        2 0.03200000        1   0.00263891
//       2        2 0.03200000        2   0.00251713
//       2        2 0.03200000        4   0.00328865
//       2        2 0.03200000        8   0.00401267
//       2        2 0.03200000       16   0.00456106
//       2        2 0.03200000       32   0.00453399
//       2        2 0.03200000       64   0.00531267
//       2        2 0.06400000        1   0.00199571
//       2        2 0.06400000        2   0.00228773
//       2        2 0.06400000        4   0.00454218
//       2        2 0.06400000        8   0.00396886
//       2        2 0.06400000       16   0.00449934
//       2        2 0.06400000       32   0.00452268
//       2        2 0.06400000       64   0.00454185
//       2        4 0.00100000        1   0.00443182
//       2        4 0.00100000        2   0.00458761
//       2        4 0.00100000        4   0.00466226
//       2        4 0.00100000        8   0.00450936
//       2        4 0.00100000       16   0.00455465
//       2        4 0.00100000       32   0.00479157
//       2        4 0.00100000       64   0.00562469
//       2        4 0.00200000        1   0.00245691
//       2        4 0.00200000        2   0.00453111
//       2        4 0.00200000        4   0.00389282
//       2        4 0.00200000        8   0.00465674
//       2        4 0.00200000       16   0.00543234
//       2        4 0.00200000       32   0.00513480
//       2        4 0.00200000       64   0.00473742
//       2        4 0.00400000        1   0.00242735
//       2        4 0.00400000        2   0.00459091
//       2        4 0.00400000        4   0.00440010
//       2        4 0.00400000        8   0.00461169
//       2        4 0.00400000       16   0.00515901
//       2        4 0.00400000       32   0.00523260
//       2        4 0.00400000       64   0.00515066
//       2        4 0.00800000        1   0.00272570
//       2        4 0.00800000        2   0.00391983
//       2        4 0.00800000        4   0.00445856
//       2        4 0.00800000        8   0.00465216
//       2        4 0.00800000       16   0.00542902
//       2        4 0.00800000       32   0.00652628
//       2        4 0.00800000       64   0.00522578
//       2        4 0.01600000        1   0.00335433
//       2        4 0.01600000        2   0.00443409
//       2        4 0.01600000        4   0.00449984
//       2        4 0.01600000        8   0.00465256
//       2        4 0.01600000       16   0.00622425
//       2        4 0.01600000       32   0.00651635
//       2        4 0.01600000       64   0.00523544
//       2        4 0.03200000        1   0.00446227
//       2        4 0.03200000        2   0.00460426
//       2        4 0.03200000        4   0.00453778
//       2        4 0.03200000        8   0.00463144
//       2        4 0.03200000       16   0.00462513
//       2        4 0.03200000       32   0.00510660
//       2        4 0.03200000       64   0.00537913
//       2        4 0.06400000        1   0.00228758
//       2        4 0.06400000        2   0.00451714
//       2        4 0.06400000        4   0.00452826
//       2        4 0.06400000        8   0.00449288
//       2        4 0.06400000       16   0.00462435
//       2        4 0.06400000       32   0.00569947
//       2        4 0.06400000       64   0.00666270
//       2        8 0.00100000        1   0.00399537
//       2        8 0.00100000        2   0.00455398
//       2        8 0.00100000        4   0.00465930
//       2        8 0.00100000        8   0.00468376
//       2        8 0.00100000       16   0.00470697
//       2        8 0.00100000       32   0.00513821
//       2        8 0.00100000       64   0.00499152
//       2        8 0.00200000        1   0.00453013
//       2        8 0.00200000        2   0.00459564
//       2        8 0.00200000        4   0.00459552
//       2        8 0.00200000        8   0.00463746
//       2        8 0.00200000       16   0.00463933
//       2        8 0.00200000       32   0.00532013
//       2        8 0.00200000       64   0.00668136
//       2        8 0.00400000        1   0.00508149
//       2        8 0.00400000        2   0.00459670
//       2        8 0.00400000        4   0.00466632
//       2        8 0.00400000        8   0.00468087
//       2        8 0.00400000       16   0.00534710
//       2        8 0.00400000       32   0.00481825
//       2        8 0.00400000       64   0.00475441
//       2        8 0.00800000        1   0.00449430
//       2        8 0.00800000        2   0.00464274
//       2        8 0.00800000        4   0.00457682
//       2        8 0.00800000        8   0.00470587
//       2        8 0.00800000       16   0.00466876
//       2        8 0.00800000       32   0.00583917
//       2        8 0.00800000       64   0.00562556
//       2        8 0.01600000        1   0.00447109
//       2        8 0.01600000        2   0.00455331
//       2        8 0.01600000        4   0.00468793
//       2        8 0.01600000        8   0.00466774
//       2        8 0.01600000       16   0.00464825
//       2        8 0.01600000       32   0.00468775
//       2        8 0.01600000       64   0.00667081
//       2        8 0.03200000        1   0.00448279
//       2        8 0.03200000        2   0.00453780
//       2        8 0.03200000        4   0.00463465
//       2        8 0.03200000        8   0.00461309
//       2        8 0.03200000       16   0.00464250
//       2        8 0.03200000       32   0.00664137
//       2        8 0.03200000       64   0.00530633
//       2        8 0.06400000        1   0.00446327
//       2        8 0.06400000        2   0.00464466
//       2        8 0.06400000        4   0.00462049
//       2        8 0.06400000        8   0.00462852
//       2        8 0.06400000       16   0.00488766
//       2        8 0.06400000       32   0.00670022
//       2        8 0.06400000       64   0.00532094
//       2       16 0.00100000        1   0.00465971
//       2       16 0.00100000        2   0.00464042
//       2       16 0.00100000        4   0.00630195
//       2       16 0.00100000        8   0.00666089
//       2       16 0.00100000       16   0.00503531
//       2       16 0.00100000       32   0.00611669
//       2       16 0.00100000       64   0.00651205
//       2       16 0.00200000        1   0.00465825
//       2       16 0.00200000        2   0.00531977
//       2       16 0.00200000        4   0.00470196
//       2       16 0.00200000        8   0.00473362
//       2       16 0.00200000       16   0.00521879
//       2       16 0.00200000       32   0.00658318
//       2       16 0.00200000       64   0.00667149
//       2       16 0.00400000        1   0.00465255
//       2       16 0.00400000        2   0.00478693
//       2       16 0.00400000        4   0.00466923
//       2       16 0.00400000        8   0.00476006
//       2       16 0.00400000       16   0.00514773
//       2       16 0.00400000       32   0.00534095
//       2       16 0.00400000       64   0.01012563
//       2       16 0.00800000        1   0.00457383
//       2       16 0.00800000        2   0.00461090
//       2       16 0.00800000        4   0.00462909
//       2       16 0.00800000        8   0.00484383
//       2       16 0.00800000       16   0.00527767
//       2       16 0.00800000       32   0.00479646
//       2       16 0.00800000       64   0.00664317
//       2       16 0.01600000        1   0.00460260
//       2       16 0.01600000        2   0.00467245
//       2       16 0.01600000        4   0.00467480
//       2       16 0.01600000        8   0.00497189
//       2       16 0.01600000       16   0.00681228
//       2       16 0.01600000       32   0.00517095
//       2       16 0.01600000       64   0.00681140
//       2       16 0.03200000        1   0.00452301
//       2       16 0.03200000        2   0.00466759
//       2       16 0.03200000        4   0.00489454
//       2       16 0.03200000        8   0.00474058
//       2       16 0.03200000       16   0.00675432
//       2       16 0.03200000       32   0.00657519
//       2       16 0.03200000       64   0.00675159
//       2       16 0.06400000        1   0.00454503
//       2       16 0.06400000        2   0.00516401
//       2       16 0.06400000        4   0.00652040
//       2       16 0.06400000        8   0.00522938
//       2       16 0.06400000       16   0.00531023
//       2       16 0.06400000       32   0.00473002
//       2       16 0.06400000       64   0.00666362
//       2       32 0.00100000        1   0.00467298
//       2       32 0.00100000        2   0.00640891
//       2       32 0.00100000        4   0.00526492
//       2       32 0.00100000        8   0.00671728
//       2       32 0.00100000       16   0.00670215
//       2       32 0.00100000       32   0.00669573
//       2       32 0.00100000       64   0.00675066
//       2       32 0.00200000        1   0.00664719
//       2       32 0.00200000        2   0.00486440
//       2       32 0.00200000        4   0.00686654
//       2       32 0.00200000        8   0.00536899
//       2       32 0.00200000       16   0.00642619
//       2       32 0.00200000       32   0.00538060
//       2       32 0.00200000       64   0.00670886
//       2       32 0.00400000        1   0.00472746
//       2       32 0.00400000        2   0.00478196
//       2       32 0.00400000        4   0.00670956
//       2       32 0.00400000        8   0.00663055
//       2       32 0.00400000       16   0.00666399
//       2       32 0.00400000       32   0.00676835
//       2       32 0.00400000       64   0.00620767
//       2       32 0.00800000        1   0.00471454
//       2       32 0.00800000        2   0.00670901
//       2       32 0.00800000        4   0.00490280
//       2       32 0.00800000        8   0.00543071
//       2       32 0.00800000       16   0.00670354
//       2       32 0.00800000       32   0.00686869
//       2       32 0.00800000       64   0.00664496
//       2       32 0.01600000        1   0.00472804
//       2       32 0.01600000        2   0.00494906
//       2       32 0.01600000        4   0.00668745
//       2       32 0.01600000        8   0.00545191
//       2       32 0.01600000       16   0.00493920
//       2       32 0.01600000       32   0.00674449
//       2       32 0.01600000       64   0.00671076
//       2       32 0.03200000        1   0.00510136
//       2       32 0.03200000        2   0.00656135
//       2       32 0.03200000        4   0.00502796
//       2       32 0.03200000        8   0.00546822
//       2       32 0.03200000       16   0.00643071
//       2       32 0.03200000       32   0.00665715
//       2       32 0.03200000       64   0.00676793
//       2       32 0.06400000        1   0.00471561
//       2       32 0.06400000        2   0.00673286
//       2       32 0.06400000        4   0.00683291
//       2       32 0.06400000        8   0.00518200
//       2       32 0.06400000       16   0.00643821
//       2       32 0.06400000       32   0.00653825
//       2       32 0.06400000       64   0.00674770
//       2       64 0.00100000        1   0.00658393
//       2       64 0.00100000        2   0.00668959
//       2       64 0.00100000        4   0.00529445
//       2       64 0.00100000        8   0.00515654
//       2       64 0.00100000       16   0.00670107
//       2       64 0.00100000       32   0.00684106
//       2       64 0.00100000       64   0.00690369
//       2       64 0.00200000        1   0.00481743
//       2       64 0.00200000        2   0.00503064
//       2       64 0.00200000        4   0.00529521
//       2       64 0.00200000        8   0.00495861
//       2       64 0.00200000       16   0.00694448
//       2       64 0.00200000       32   0.00684541
//       2       64 0.00200000       64   0.00692876
//       2       64 0.00400000        1   0.00525869
//       2       64 0.00400000        2   0.00497031
//       2       64 0.00400000        4   0.00505255
//       2       64 0.00400000        8   0.00677624
//       2       64 0.00400000       16   0.00669253
//       2       64 0.00400000       32   0.00688936
//       2       64 0.00400000       64   0.00686360
//       2       64 0.00800000        1   0.00487876
//       2       64 0.00800000        2   0.00580238
//       2       64 0.00800000        4   0.00677429
//       2       64 0.00800000        8   0.00609299
//       2       64 0.00800000       16   0.00678607
//       2       64 0.00800000       32   0.00689863
//       2       64 0.00800000       64   0.00691471
//       2       64 0.01600000        1   0.00674561
//       2       64 0.01600000        2   0.00683153
//       2       64 0.01600000        4   0.00561670
//       2       64 0.01600000        8   0.00521967
//       2       64 0.01600000       16   0.00662613
//       2       64 0.01600000       32   0.00704440
//       2       64 0.01600000       64   0.00678432
//       2       64 0.03200000        1   0.00511774
//       2       64 0.03200000        2   0.00488829
//       2       64 0.03200000        4   0.00523302
//       2       64 0.03200000        8   0.00510200
//       2       64 0.03200000       16   0.00692662
//       2       64 0.03200000       32   0.00694930
//       2       64 0.03200000       64   0.00696019
//       2       64 0.06400000        1   0.00552402
//       2       64 0.06400000        2   0.00524349
//       2       64 0.06400000        4   0.00690667
//       2       64 0.06400000        8   0.00533032
//       2       64 0.06400000       16   0.00691451
//       2       64 0.06400000       32   0.00676358
//       2       64 0.06400000       64   0.00700758
//       4        2 0.00100000        1   0.00255512
//       4        2 0.00100000        2   0.00218905
//       4        2 0.00100000        4   0.00446881
//       4        2 0.00100000        8   0.00452412
//       4        2 0.00100000       16   0.00497121
//       4        2 0.00100000       32   0.00456672
//       4        2 0.00100000       64   0.00458439
//       4        2 0.00200000        1   0.00222265
//       4        2 0.00200000        2   0.00220072
//       4        2 0.00200000        4   0.00440102
//       4        2 0.00200000        8   0.00459751
//       4        2 0.00200000       16   0.00442434
//       4        2 0.00200000       32   0.00478417
//       4        2 0.00200000       64   0.00463543
//       4        2 0.00400000        1   0.00204671
//       4        2 0.00400000        2   0.00243284
//       4        2 0.00400000        4   0.00294143
//       4        2 0.00400000        8   0.00426517
//       4        2 0.00400000       16   0.00458618
//       4        2 0.00400000       32   0.00468360
//       4        2 0.00400000       64   0.00462449
//       4        2 0.00800000        1   0.00238901
//       4        2 0.00800000        2   0.00324504
//       4        2 0.00800000        4   0.00450214
//       4        2 0.00800000        8   0.00357020
//       4        2 0.00800000       16   0.00459791
//       4        2 0.00800000       32   0.00476063
//       4        2 0.00800000       64   0.00472676
//       4        2 0.01600000        1   0.00230496
//       4        2 0.01600000        2   0.00338562
//       4        2 0.01600000        4   0.00423003
//       4        2 0.01600000        8   0.00447124
//       4        2 0.01600000       16   0.00471399
//       4        2 0.01600000       32   0.00457075
//       4        2 0.01600000       64   0.00655064
//       4        2 0.03200000        1   0.00203468
//       4        2 0.03200000        2   0.00219654
//       4        2 0.03200000        4   0.00353052
//       4        2 0.03200000        8   0.00461902
//       4        2 0.03200000       16   0.00459032
//       4        2 0.03200000       32   0.00466103
//       4        2 0.03200000       64   0.00458297
//       4        2 0.06400000        1   0.00262108
//       4        2 0.06400000        2   0.00243286
//       4        2 0.06400000        4   0.00415942
//       4        2 0.06400000        8   0.00446059
//       4        2 0.06400000       16   0.00464502
//       4        2 0.06400000       32   0.00459914
//       4        2 0.06400000       64   0.00532712
//       4        4 0.00100000        1   0.00232095
//       4        4 0.00100000        2   0.00462402
//       4        4 0.00100000        4   0.00446387
//       4        4 0.00100000        8   0.00511857
//       4        4 0.00100000       16   0.00459918
//       4        4 0.00100000       32   0.00472407
//       4        4 0.00100000       64   0.00533786
//       4        4 0.00200000        1   0.00234139
//       4        4 0.00200000        2   0.00447930
//       4        4 0.00200000        4   0.00452057
//       4        4 0.00200000        8   0.00465463
//       4        4 0.00200000       16   0.00519532
//       4        4 0.00200000       32   0.00465052
//       4        4 0.00200000       64   0.00654514
//       4        4 0.00400000        1   0.00321174
//       4        4 0.00400000        2   0.00391079
//       4        4 0.00400000        4   0.00464473
//       4        4 0.00400000        8   0.00456508
//       4        4 0.00400000       16   0.00469119
//       4        4 0.00400000       32   0.00656665
//       4        4 0.00400000       64   0.00658350
//       4        4 0.00800000        1   0.00278529
//       4        4 0.00800000        2   0.00325371
//       4        4 0.00800000        4   0.00462844
//       4        4 0.00800000        8   0.00457683
//       4        4 0.00800000       16   0.00461300
//       4        4 0.00800000       32   0.00660904
//       4        4 0.00800000       64   0.00655558
//       4        4 0.01600000        1   0.00201659
//       4        4 0.01600000        2   0.00453786
//       4        4 0.01600000        4   0.00450475
//       4        4 0.01600000        8   0.00454516
//       4        4 0.01600000       16   0.00461445
//       4        4 0.01600000       32   0.00651890
//       4        4 0.01600000       64   0.00649307
//       4        4 0.03200000        1   0.00312938
//       4        4 0.03200000        2   0.00449395
//       4        4 0.03200000        4   0.00457697
//       4        4 0.03200000        8   0.00461345
//       4        4 0.03200000       16   0.00470629
//       4        4 0.03200000       32   0.00519005
//       4        4 0.03200000       64   0.00536659
//       4        4 0.06400000        1   0.00322297
//       4        4 0.06400000        2   0.00444543
//       4        4 0.06400000        4   0.00465250
//       4        4 0.06400000        8   0.00460410
//       4        4 0.06400000       16   0.00457993
//       4        4 0.06400000       32   0.00471911
//       4        4 0.06400000       64   0.00476817
//       4        8 0.00100000        1   0.00450871
//       4        8 0.00100000        2   0.00449295
//       4        8 0.00100000        4   0.00462602
//       4        8 0.00100000        8   0.00515166
//       4        8 0.00100000       16   0.00677552
//       4        8 0.00100000       32   0.00644630
//       4        8 0.00100000       64   0.00602691
//       4        8 0.00200000        1   0.00326353
//       4        8 0.00200000        2   0.00446377
//       4        8 0.00200000        4   0.00466257
//       4        8 0.00200000        8   0.00460179
//       4        8 0.00200000       16   0.00598555
//       4        8 0.00200000       32   0.00495672
//       4        8 0.00200000       64   0.00476021
//       4        8 0.00400000        1   0.00453680
//       4        8 0.00400000        2   0.00459784
//       4        8 0.00400000        4   0.00479246
//       4        8 0.00400000        8   0.00520622
//       4        8 0.00400000       16   0.00463919
//       4        8 0.00400000       32   0.00536320
//       4        8 0.00400000       64   0.00656780
//       4        8 0.00800000        1   0.00452563
//       4        8 0.00800000        2   0.00450807
//       4        8 0.00800000        4   0.00456819
//       4        8 0.00800000        8   0.00458920
//       4        8 0.00800000       16   0.00517325
//       4        8 0.00800000       32   0.00521777
//       4        8 0.00800000       64   0.00650002
//       4        8 0.01600000        1   0.00458081
//       4        8 0.01600000        2   0.00459026
//       4        8 0.01600000        4   0.00469840
//       4        8 0.01600000        8   0.00465847
//       4        8 0.01600000       16   0.00504559
//       4        8 0.01600000       32   0.00532180
//       4        8 0.01600000       64   0.00528791
//       4        8 0.03200000        1   0.00449537
//       4        8 0.03200000        2   0.00454823
//       4        8 0.03200000        4   0.00463965
//       4        8 0.03200000        8   0.00460074
//       4        8 0.03200000       16   0.00540389
//       4        8 0.03200000       32   0.00499470
//       4        8 0.03200000       64   0.00657361
//       4        8 0.06400000        1   0.00457741
//       4        8 0.06400000        2   0.00454476
//       4        8 0.06400000        4   0.00463198
//       4        8 0.06400000        8   0.00651739
//       4        8 0.06400000       16   0.00536665
//       4        8 0.06400000       32   0.00659238
//       4        8 0.06400000       64   0.00507434
//       4       16 0.00100000        1   0.00455225
//       4       16 0.00100000        2   0.00659556
//       4       16 0.00100000        4   0.00485356
//       4       16 0.00100000        8   0.00519789
//       4       16 0.00100000       16   0.00512545
//       4       16 0.00100000       32   0.00658348
//       4       16 0.00100000       64   0.00656271
//       4       16 0.00200000        1   0.00470879
//       4       16 0.00200000        2   0.00469333
//       4       16 0.00200000        4   0.00469203
//       4       16 0.00200000        8   0.00520013
//       4       16 0.00200000       16   0.00667788
//       4       16 0.00200000       32   0.00654945
//       4       16 0.00200000       64   0.00677709
//       4       16 0.00400000        1   0.00464843
//       4       16 0.00400000        2   0.00460010
//       4       16 0.00400000        4   0.00467281
//       4       16 0.00400000        8   0.00516035
//       4       16 0.00400000       16   0.00497050
//       4       16 0.00400000       32   0.00468229
//       4       16 0.00400000       64   0.00594442
//       4       16 0.00800000        1   0.00464037
//       4       16 0.00800000        2   0.00465066
//       4       16 0.00800000        4   0.00493007
//       4       16 0.00800000        8   0.00467485
//       4       16 0.00800000       16   0.00661143
//       4       16 0.00800000       32   0.00496262
//       4       16 0.00800000       64   0.00671288
//       4       16 0.01600000        1   0.00464493
//       4       16 0.01600000        2   0.00462213
//       4       16 0.01600000        4   0.00507796
//       4       16 0.01600000        8   0.00658680
//       4       16 0.01600000       16   0.00660024
//       4       16 0.01600000       32   0.00656906
//       4       16 0.01600000       64   0.00525453
//       4       16 0.03200000        1   0.00458107
//       4       16 0.03200000        2   0.00463674
//       4       16 0.03200000        4   0.00469698
//       4       16 0.03200000        8   0.00472512
//       4       16 0.03200000       16   0.00657209
//       4       16 0.03200000       32   0.00477036
//       4       16 0.03200000       64   0.00660230
//       4       16 0.06400000        1   0.00466262
//       4       16 0.06400000        2   0.00467951
//       4       16 0.06400000        4   0.00465403
//       4       16 0.06400000        8   0.00660999
//       4       16 0.06400000       16   0.00598521
//       4       16 0.06400000       32   0.00635063
//       4       16 0.06400000       64   0.00665473
//       4       32 0.00100000        1   0.00484929
//       4       32 0.00100000        2   0.00485377
//       4       32 0.00100000        4   0.00499927
//       4       32 0.00100000        8   0.00667457
//       4       32 0.00100000       16   0.00665693
//       4       32 0.00100000       32   0.00540657
//       4       32 0.00100000       64   0.00683338
//       4       32 0.00200000        1   0.00472062
//       4       32 0.00200000        2   0.00493478
//       4       32 0.00200000        4   0.00510205
//       4       32 0.00200000        8   0.00672839
//       4       32 0.00200000       16   0.00483979
//       4       32 0.00200000       32   0.00686220
//       4       32 0.00200000       64   0.00690489
//       4       32 0.00400000        1   0.00470686
//       4       32 0.00400000        2   0.00476787
//       4       32 0.00400000        4   0.00692052
//       4       32 0.00400000        8   0.00585628
//       4       32 0.00400000       16   0.00526631
//       4       32 0.00400000       32   0.00682134
//       4       32 0.00400000       64   0.00595345
//       4       32 0.00800000        1   0.00471351
//       4       32 0.00800000        2   0.00660800
//       4       32 0.00800000        4   0.00659679
//       4       32 0.00800000        8   0.00678174
//       4       32 0.00800000       16   0.00683293
//       4       32 0.00800000       32   0.00674129
//       4       32 0.00800000       64   0.00681859
//       4       32 0.01600000        1   0.00507461
//       4       32 0.01600000        2   0.00510582
//       4       32 0.01600000        4   0.00537019
//       4       32 0.01600000        8   0.00672090
//       4       32 0.01600000       16   0.00663310
//       4       32 0.01600000       32   0.00666753
//       4       32 0.01600000       64   0.00672030
//       4       32 0.03200000        1   0.00476831
//       4       32 0.03200000        2   0.00496308
//       4       32 0.03200000        4   0.00495512
//       4       32 0.03200000        8   0.00667906
//       4       32 0.03200000       16   0.00667942
//       4       32 0.03200000       32   0.00675949
//       4       32 0.03200000       64   0.00675143
//       4       32 0.06400000        1   0.00479083
//       4       32 0.06400000        2   0.00530655
//       4       32 0.06400000        4   0.00682292
//       4       32 0.06400000        8   0.00532942
//       4       32 0.06400000       16   0.00641762
//       4       32 0.06400000       32   0.00677346
//       4       32 0.06400000       64   0.00675632
//       4       64 0.00100000        1   0.00682500
//       4       64 0.00100000        2   0.00686559
//       4       64 0.00100000        4   0.00683700
//       4       64 0.00100000        8   0.00516976
//       4       64 0.00100000       16   0.00684731
//       4       64 0.00100000       32   0.00813438
//       4       64 0.00100000       64   0.00691709
//       4       64 0.00200000        1   0.00487454
//       4       64 0.00200000        2   0.00491411
//       4       64 0.00200000        4   0.00700178
//       4       64 0.00200000        8   0.00501889
//       4       64 0.00200000       16   0.00688877
//       4       64 0.00200000       32   0.00695830
//       4       64 0.00200000       64   0.00684761
//       4       64 0.00400000        1   0.00485469
//       4       64 0.00400000        2   0.00567910
//       4       64 0.00400000        4   0.00554594
//       4       64 0.00400000        8   0.00498424
//       4       64 0.00400000       16   0.00685097
//       4       64 0.00400000       32   0.00679573
//       4       64 0.00400000       64   0.00689852
//       4       64 0.00800000        1   0.00667844
//       4       64 0.00800000        2   0.00659463
//       4       64 0.00800000        4   0.00695488
//       4       64 0.00800000        8   0.00681177
//       4       64 0.00800000       16   0.00696768
//       4       64 0.00800000       32   0.00692432
//       4       64 0.00800000       64   0.00683779
//       4       64 0.01600000        1   0.00484731
//       4       64 0.01600000        2   0.00498839
//       4       64 0.01600000        4   0.00492200
//       4       64 0.01600000        8   0.00518550
//       4       64 0.01600000       16   0.00688087
//       4       64 0.01600000       32   0.00705132
//       4       64 0.01600000       64   0.00701493
//       4       64 0.03200000        1   0.00501309
//       4       64 0.03200000        2   0.00681362
//       4       64 0.03200000        4   0.00699709
//       4       64 0.03200000        8   0.00691833
//       4       64 0.03200000       16   0.00597879
//       4       64 0.03200000       32   0.00695778
//       4       64 0.03200000       64   0.00693062
//       4       64 0.06400000        1   0.00489928
//       4       64 0.06400000        2   0.00539500
//       4       64 0.06400000        4   0.00571639
//       4       64 0.06400000        8   0.00698587
//       4       64 0.06400000       16   0.00711649
//       4       64 0.06400000       32   0.00685332
//       4       64 0.06400000       64   0.00670192
//       8        2 0.00100000        1   0.00204896
//       8        2 0.00100000        2   0.00298825
//       8        2 0.00100000        4   0.00446235
//       8        2 0.00100000        8   0.00389062
//       8        2 0.00100000       16   0.00464258
//       8        2 0.00100000       32   0.00465250
//       8        2 0.00100000       64   0.00464383
//       8        2 0.00200000        1   0.00199854
//       8        2 0.00200000        2   0.00221560
//       8        2 0.00200000        4   0.00448879
//       8        2 0.00200000        8   0.00443978
//       8        2 0.00200000       16   0.00458385
//       8        2 0.00200000       32   0.00453975
//       8        2 0.00200000       64   0.00600695
//       8        2 0.00400000        1   0.00201524
//       8        2 0.00400000        2   0.00219892
//       8        2 0.00400000        4   0.00390032
//       8        2 0.00400000        8   0.00387710
//       8        2 0.00400000       16   0.00482571
//       8        2 0.00400000       32   0.00484450
//       8        2 0.00400000       64   0.00497199
//       8        2 0.00800000        1   0.00206562
//       8        2 0.00800000        2   0.00237288
//       8        2 0.00800000        4   0.00452598
//       8        2 0.00800000        8   0.00453460
//       8        2 0.00800000       16   0.00667950
//       8        2 0.00800000       32   0.00469962
//       8        2 0.00800000       64   0.00615388
//       8        2 0.01600000        1   0.00207015
//       8        2 0.01600000        2   0.00299796
//       8        2 0.01600000        4   0.00452178
//       8        2 0.01600000        8   0.00459363
//       8        2 0.01600000       16   0.00461936
//       8        2 0.01600000       32   0.00462818
//       8        2 0.01600000       64   0.00482118
//       8        2 0.03200000        1   0.00200807
//       8        2 0.03200000        2   0.00217429
//       8        2 0.03200000        4   0.00447754
//       8        2 0.03200000        8   0.00458497
//       8        2 0.03200000       16   0.00460798
//       8        2 0.03200000       32   0.00653958
//       8        2 0.03200000       64   0.00665217
//       8        2 0.06400000        1   0.00200673
//       8        2 0.06400000        2   0.00218602
//       8        2 0.06400000        4   0.00383756
//       8        2 0.06400000        8   0.00453902
//       8        2 0.06400000       16   0.00492502
//       8        2 0.06400000       32   0.00510183
//       8        2 0.06400000       64   0.00562573
//       8        4 0.00100000        1   0.00216807
//       8        4 0.00100000        2   0.00448892
//       8        4 0.00100000        4   0.00469602
//       8        4 0.00100000        8   0.00488904
//       8        4 0.00100000       16   0.00513215
//       8        4 0.00100000       32   0.00483865
//       8        4 0.00100000       64   0.00551040
//       8        4 0.00200000        1   0.00225971
//       8        4 0.00200000        2   0.00453894
//       8        4 0.00200000        4   0.00465461
//       8        4 0.00200000        8   0.00507826
//       8        4 0.00200000       16   0.00456451
//       8        4 0.00200000       32   0.00475663
//       8        4 0.00200000       64   0.00677229
//       8        4 0.00400000        1   0.00226223
//       8        4 0.00400000        2   0.00518305
//       8        4 0.00400000        4   0.00472843
//       8        4 0.00400000        8   0.00452829
//       8        4 0.00400000       16   0.00458365
//       8        4 0.00400000       32   0.00499675
//       8        4 0.00400000       64   0.00664046
//       8        4 0.00800000        1   0.00447202
//       8        4 0.00800000        2   0.00460205
//       8        4 0.00800000        4   0.00456966
//       8        4 0.00800000        8   0.00458916
//       8        4 0.00800000       16   0.00457211
//       8        4 0.00800000       32   0.00461508
//       8        4 0.00800000       64   0.00651038
//       8        4 0.01600000        1   0.00217337
//       8        4 0.01600000        2   0.00442749
//       8        4 0.01600000        4   0.00452920
//       8        4 0.01600000        8   0.00461923
//       8        4 0.01600000       16   0.00491328
//       8        4 0.01600000       32   0.00464302
//       8        4 0.01600000       64   0.00655489
//       8        4 0.03200000        1   0.00202305
//       8        4 0.03200000        2   0.00450392
//       8        4 0.03200000        4   0.00450213
//       8        4 0.03200000        8   0.00465332
//       8        4 0.03200000       16   0.00504496
//       8        4 0.03200000       32   0.00635709
//       8        4 0.03200000       64   0.00515443
//       8        4 0.06400000        1   0.00199740
//       8        4 0.06400000        2   0.00443732
//       8        4 0.06400000        4   0.00638853
//       8        4 0.06400000        8   0.00460827
//       8        4 0.06400000       16   0.00464863
//       8        4 0.06400000       32   0.00665213
//       8        4 0.06400000       64   0.00533462
//       8        8 0.00100000        1   0.00395752
//       8        8 0.00100000        2   0.00457364
//       8        8 0.00100000        4   0.00500242
//       8        8 0.00100000        8   0.00497468
//       8        8 0.00100000       16   0.00465159
//       8        8 0.00100000       32   0.00483976
//       8        8 0.00100000       64   0.00572916
//       8        8 0.00200000        1   0.00327943
//       8        8 0.00200000        2   0.00456700
//       8        8 0.00200000        4   0.00467004
//       8        8 0.00200000        8   0.00469203
//       8        8 0.00200000       16   0.00468628
//       8        8 0.00200000       32   0.00493693
//       8        8 0.00200000       64   0.00659455
//       8        8 0.00400000        1   0.00468505
//       8        8 0.00400000        2   0.00455431
//       8        8 0.00400000        4   0.00471536
//       8        8 0.00400000        8   0.00462729
//       8        8 0.00400000       16   0.00463732
//       8        8 0.00400000       32   0.00514002
//       8        8 0.00400000       64   0.00471453
//       8        8 0.00800000        1   0.00451197
//       8        8 0.00800000        2   0.00542681
//       8        8 0.00800000        4   0.00468285
//       8        8 0.00800000        8   0.00484646
//       8        8 0.00800000       16   0.00665904
//       8        8 0.00800000       32   0.00468923
//       8        8 0.00800000       64   0.00667524
//       8        8 0.01600000        1   0.00391415
//       8        8 0.01600000        2   0.00404090
//       8        8 0.01600000        4   0.00391102
//       8        8 0.01600000        8   0.00659251
//       8        8 0.01600000       16   0.00568783
//       8        8 0.01600000       32   0.00671935
//       8        8 0.01600000       64   0.00537061
//       8        8 0.03200000        1   0.00454001
//       8        8 0.03200000        2   0.00454547
//       8        8 0.03200000        4   0.00454255
//       8        8 0.03200000        8   0.00488007
//       8        8 0.03200000       16   0.00469872
//       8        8 0.03200000       32   0.00495783
//       8        8 0.03200000       64   0.00660300
//       8        8 0.06400000        1   0.00391650
//       8        8 0.06400000        2   0.00451557
//       8        8 0.06400000        4   0.00663884
//       8        8 0.06400000        8   0.00455551
//       8        8 0.06400000       16   0.00467039
//       8        8 0.06400000       32   0.00524637
//       8        8 0.06400000       64   0.00660846
//       8       16 0.00100000        1   0.00402865
//       8       16 0.00100000        2   0.00469824
//       8       16 0.00100000        4   0.00470716
//       8       16 0.00100000        8   0.00673497
//       8       16 0.00100000       16   0.00682753
//       8       16 0.00100000       32   0.00516798
//       8       16 0.00100000       64   0.00662876
//       8       16 0.00200000        1   0.00456174
//       8       16 0.00200000        2   0.00463383
//       8       16 0.00200000        4   0.00600497
//       8       16 0.00200000        8   0.00499315
//       8       16 0.00200000       16   0.00721836
//       8       16 0.00200000       32   0.00469381
//       8       16 0.00200000       64   0.00678859
//       8       16 0.00400000        1   0.00462850
//       8       16 0.00400000        2   0.00460975
//       8       16 0.00400000        4   0.00523000
//       8       16 0.00400000        8   0.00552502
//       8       16 0.00400000       16   0.00530069
//       8       16 0.00400000       32   0.00633390
//       8       16 0.00400000       64   0.00677422
//       8       16 0.00800000        1   0.00396022
//       8       16 0.00800000        2   0.00513555
//       8       16 0.00800000        4   0.00521343
//       8       16 0.00800000        8   0.00514526
//       8       16 0.00800000       16   0.00489014
//       8       16 0.00800000       32   0.00475860
//       8       16 0.00800000       64   0.00666753
//       8       16 0.01600000        1   0.00400214
//       8       16 0.01600000        2   0.00512993
//       8       16 0.01600000        4   0.00490106
//       8       16 0.01600000        8   0.00661840
//       8       16 0.01600000       16   0.00659898
//       8       16 0.01600000       32   0.00571394
//       8       16 0.01600000       64   0.01081489
//       8       16 0.03200000        1   0.00456993
//       8       16 0.03200000        2   0.00467209
//       8       16 0.03200000        4   0.00477854
//       8       16 0.03200000        8   0.00509429
//       8       16 0.03200000       16   0.00655605
//       8       16 0.03200000       32   0.00672988
//       8       16 0.03200000       64   0.00576508
//       8       16 0.06400000        1   0.00407451
//       8       16 0.06400000        2   0.00466233
//       8       16 0.06400000        4   0.00663160
//       8       16 0.06400000        8   0.00484974
//       8       16 0.06400000       16   0.00651439
//       8       16 0.06400000       32   0.00659863
//       8       16 0.06400000       64   0.00652298
//       8       32 0.00100000        1   0.00471751
//       8       32 0.00100000        2   0.00478197
//       8       32 0.00100000        4   0.00508586
//       8       32 0.00100000        8   0.00664256
//       8       32 0.00100000       16   0.00540962
//       8       32 0.00100000       32   0.00553161
//       8       32 0.00100000       64   0.00679918
//       8       32 0.00200000        1   0.00468310
//       8       32 0.00200000        2   0.00489452
//       8       32 0.00200000        4   0.00476601
//       8       32 0.00200000        8   0.00580185
//       8       32 0.00200000       16   0.00522707
//       8       32 0.00200000       32   0.00668074
//       8       32 0.00200000       64   0.00679683
//       8       32 0.00400000        1   0.00482662
//       8       32 0.00400000        2   0.00491834
//       8       32 0.00400000        4   0.00668616
//       8       32 0.00400000        8   0.00593636
//       8       32 0.00400000       16   0.00533402
//       8       32 0.00400000       32   0.00571808
//       8       32 0.00400000       64   0.00670179
//       8       32 0.00800000        1   0.00469857
//       8       32 0.00800000        2   0.00476549
//       8       32 0.00800000        4   0.00486256
//       8       32 0.00800000        8   0.00502309
//       8       32 0.00800000       16   0.00919219
//       8       32 0.00800000       32   0.00675284
//       8       32 0.00800000       64   0.00667576
//       8       32 0.01600000        1   0.00477690
//       8       32 0.01600000        2   0.00664319
//       8       32 0.01600000        4   0.00517969
//       8       32 0.01600000        8   0.01010537
//       8       32 0.01600000       16   0.00530515
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//       8       64 0.06400000       64   0.00691481
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//      16       16 0.00200000        8   0.00501807
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//      64       16 0.03200000        2   0.00478067
//      64       16 0.03200000        4   0.00516496
//      64       16 0.03200000        8   0.00471051
//      64       16 0.03200000       16   0.00473864
//      64       16 0.03200000       32   0.00517122
//      64       16 0.03200000       64   0.00637724
//      64       16 0.06400000        1   0.00460178
//      64       16 0.06400000        2   0.00523095
//      64       16 0.06400000        4   0.00467963
//      64       16 0.06400000        8   0.00502293
//      64       16 0.06400000       16   0.00657868
//      64       16 0.06400000       32   0.00529447
//      64       16 0.06400000       64   0.00669725
//      64       32 0.00100000        1   0.00478202
//      64       32 0.00100000        2   0.00473414
//      64       32 0.00100000        4   0.00661515
//      64       32 0.00100000        8   0.00511701
//      64       32 0.00100000       16   0.00684349
//      64       32 0.00100000       32   0.00985903
//      64       32 0.00100000       64   0.00688047
//      64       32 0.00200000        1   0.00470837
//      64       32 0.00200000        2   0.00500165
//      64       32 0.00200000        4   0.00481476
//      64       32 0.00200000        8   0.00673159
//      64       32 0.00200000       16   0.00673028
//      64       32 0.00200000       32   0.00666727
//      64       32 0.00200000       64   0.00671965
//      64       32 0.00400000        1   0.00470335
//      64       32 0.00400000        2   0.00476107
//      64       32 0.00400000        4   0.00477488
//      64       32 0.00400000        8   0.00546071
//      64       32 0.00400000       16   0.00535475
//      64       32 0.00400000       32   0.00667772
//      64       32 0.00400000       64   0.00681260
//      64       32 0.00800000        1   0.00472900
//      64       32 0.00800000        2   0.00467442
//      64       32 0.00800000        4   0.00538075
//      64       32 0.00800000        8   0.00499564
//      64       32 0.00800000       16   0.00530394
//      64       32 0.00800000       32   0.01207198
//      64       32 0.00800000       64   0.00642438
//      64       32 0.01600000        1   0.00470527
//      64       32 0.01600000        2   0.00545013
//      64       32 0.01600000        4   0.00669783
//      64       32 0.01600000        8   0.00678505
//      64       32 0.01600000       16   0.00671182
//      64       32 0.01600000       32   0.00495601
//      64       32 0.01600000       64   0.00663906
//      64       32 0.03200000        1   0.00479442
//      64       32 0.03200000        2   0.00527709
//      64       32 0.03200000        4   0.00496121
//      64       32 0.03200000        8   0.00528842
//      64       32 0.03200000       16   0.00673406
//      64       32 0.03200000       32   0.00679529
//      64       32 0.03200000       64   0.00671536
//      64       32 0.06400000        1   0.00470844
//      64       32 0.06400000        2   0.00477278
//      64       32 0.06400000        4   0.00665257
//      64       32 0.06400000        8   0.00505180
//      64       32 0.06400000       16   0.00690544
//      64       32 0.06400000       32   0.00668865
//      64       32 0.06400000       64   0.00646176
//      64       64 0.00100000        1   0.00549224
//      64       64 0.00100000        2   0.00522224
//      64       64 0.00100000        4   0.00700088
//      64       64 0.00100000        8   0.00685606
//      64       64 0.00100000       16   0.00691712
//      64       64 0.00100000       32   0.00665009
//      64       64 0.00100000       64   0.00687129
//      64       64 0.00200000        1   0.00507963
//      64       64 0.00200000        2   0.00501091
//      64       64 0.00200000        4   0.00569114
//      64       64 0.00200000        8   0.00709159
//      64       64 0.00200000       16   0.00688686
//      64       64 0.00200000       32   0.00683761
//      64       64 0.00200000       64   0.00697305
//      64       64 0.00400000        1   0.00491007
//      64       64 0.00400000        2   0.00497487
//      64       64 0.00400000        4   0.00699121
//      64       64 0.00400000        8   0.00699518
//      64       64 0.00400000       16   0.00703111
//      64       64 0.00400000       32   0.00687793
//      64       64 0.00400000       64   0.00689121
//      64       64 0.00800000        1   0.00498374
//      64       64 0.00800000        2   0.00526829
//      64       64 0.00800000        4   0.00669988
//      64       64 0.00800000        8   0.00528479
//      64       64 0.00800000       16   0.00682291
//      64       64 0.00800000       32   0.00695859
//      64       64 0.00800000       64   0.00694374
//      64       64 0.01600000        1   0.00679563
//      64       64 0.01600000        2   0.00497139
//      64       64 0.01600000        4   0.00531115
//      64       64 0.01600000        8   0.00954769
//      64       64 0.01600000       16   0.00716585
//      64       64 0.01600000       32   0.00700514
//      64       64 0.01600000       64   0.00706118
//      64       64 0.03200000        1   0.00527333
//      64       64 0.03200000        2   0.00522648
//      64       64 0.03200000        4   0.00694870
//      64       64 0.03200000        8   0.00523875
//      64       64 0.03200000       16   0.00547611
//      64       64 0.03200000       32   0.00588605
//      64       64 0.03200000       64   0.00693446
//      64       64 0.06400000        1   0.00512733
//      64       64 0.06400000        2   0.00674935
//      64       64 0.06400000        4   0.00557267
//      64       64 0.06400000        8   0.00692544
//      64       64 0.06400000       16   0.00662856
//      64       64 0.06400000       32   0.00685234
//      64       64 0.06400000       64   0.00689606
//
// ******************** 11. Experimental results for mode 3 with quicksort ********************
//
// Consider steepest descent (mode 3). It considers quicksort. This takes is from metamodefile.txt with up to 64 64 0.064 64 and it takes 56 minutes to produce it.
// ba@ba-desktop:~/ga_find_wcet$ more metamodeoutputfile.txt 
//       2        2 0.00100000        1   0.00197434
//       2        2 0.00100000        2   0.00198849
//       2        2 0.00100000        4   0.00200040
//       2        2 0.00100000        8   0.00277107
//       2        2 0.00100000       16   0.00452214
//       2        2 0.00100000       32   0.00585160
//       2        2 0.00100000       64   0.00657907
//       2        2 0.00200000        1   0.00198546
//       2        2 0.00200000        2   0.00199354
//       2        2 0.00200000        4   0.00200557
//       2        2 0.00200000        8   0.00220683
//       2        2 0.00200000       16   0.00446931
//       2        2 0.00200000       32   0.00455976
//       2        2 0.00200000       64   0.00458568
//       2        2 0.00400000        1   0.00354577
//       2        2 0.00400000        2   0.00206229
//       2        2 0.00400000        4   0.00199756
//       2        2 0.00400000        8   0.00278158
//       2        2 0.00400000       16   0.00452968
//       2        2 0.00400000       32   0.00496071
//       2        2 0.00400000       64   0.00424461
//       2        2 0.00800000        1   0.00198173
//       2        2 0.00800000        2   0.00201628
//       2        2 0.00800000        4   0.00200305
//       2        2 0.00800000        8   0.00220056
//       2        2 0.00800000       16   0.00453567
//       2        2 0.00800000       32   0.00454796
//       2        2 0.00800000       64   0.00535985
//       2        2 0.01600000        1   0.00447195
//       2        2 0.01600000        2   0.00231478
//       2        2 0.01600000        4   0.00200331
//       2        2 0.01600000        8   0.00295667
//       2        2 0.01600000       16   0.00243591
//       2        2 0.01600000       32   0.00463755
//       2        2 0.01600000       64   0.00513686
//       2        2 0.03200000        1   0.00219473
//       2        2 0.03200000        2   0.00220800
//       2        2 0.03200000        4   0.00217235
//       2        2 0.03200000        8   0.00223825
//       2        2 0.03200000       16   0.00451377
//       2        2 0.03200000       32   0.00457790
//       2        2 0.03200000       64   0.00468754
//       2        2 0.06400000        1   0.00247254
//       2        2 0.06400000        2   0.00243366
//       2        2 0.06400000        4   0.00211784
//       2        2 0.06400000        8   0.00264596
//       2        2 0.06400000       16   0.00456274
//       2        2 0.06400000       32   0.00453619
//       2        2 0.06400000       64   0.00518985
//       2        4 0.00100000        1   0.00312168
//       2        4 0.00100000        2   0.00199942
//       2        4 0.00100000        4   0.00217234
//       2        4 0.00100000        8   0.00451641
//       2        4 0.00100000       16   0.00451261
//       2        4 0.00100000       32   0.00672278
//       2        4 0.00100000       64   0.00459777
//       2        4 0.00200000        1   0.00218914
//       2        4 0.00200000        2   0.00217255
//       2        4 0.00200000        4   0.00221695
//       2        4 0.00200000        8   0.00458377
//       2        4 0.00200000       16   0.00455008
//       2        4 0.00200000       32   0.00493835
//       2        4 0.00200000       64   0.00460408
//       2        4 0.00400000        1   0.00207679
//       2        4 0.00400000        2   0.00198820
//       2        4 0.00400000        4   0.00241473
//       2        4 0.00400000        8   0.00341818
//       2        4 0.00400000       16   0.00453749
//       2        4 0.00400000       32   0.00497014
//       2        4 0.00400000       64   0.00463258
//       2        4 0.00800000        1   0.00316059
//       2        4 0.00800000        2   0.00227702
//       2        4 0.00800000        4   0.00243335
//       2        4 0.00800000        8   0.00446877
//       2        4 0.00800000       16   0.00658888
//       2        4 0.00800000       32   0.00439746
//       2        4 0.00800000       64   0.00459768
//       2        4 0.01600000        1   0.00286866
//       2        4 0.01600000        2   0.00220656
//       2        4 0.01600000        4   0.00208533
//       2        4 0.01600000        8   0.00450085
//       2        4 0.01600000       16   0.00460583
//       2        4 0.01600000       32   0.00449487
//       2        4 0.01600000       64   0.00484579
//       2        4 0.03200000        1   0.00449778
//       2        4 0.03200000        2   0.00291587
//       2        4 0.03200000        4   0.00218183
//       2        4 0.03200000        8   0.00619578
//       2        4 0.03200000       16   0.00508614
//       2        4 0.03200000       32   0.00498974
//       2        4 0.03200000       64   0.00660437
//       2        4 0.06400000        1   0.00523104
//       2        4 0.06400000        2   0.00219979
//       2        4 0.06400000        4   0.00224580
//       2        4 0.06400000        8   0.00453562
//       2        4 0.06400000       16   0.00475927
//       2        4 0.06400000       32   0.00457957
//       2        4 0.06400000       64   0.00455425
//       2        8 0.00100000        1   0.00439072
//       2        8 0.00100000        2   0.00246940
//       2        8 0.00100000        4   0.00389322
//       2        8 0.00100000        8   0.00451172
//       2        8 0.00100000       16   0.00459329
//       2        8 0.00100000       32   0.00463846
//       2        8 0.00100000       64   0.00459710
//       2        8 0.00200000        1   0.00444436
//       2        8 0.00200000        2   0.00217990
//       2        8 0.00200000        4   0.00443428
//       2        8 0.00200000        8   0.00450756
//       2        8 0.00200000       16   0.00459702
//       2        8 0.00200000       32   0.00459397
//       2        8 0.00200000       64   0.00473211
//       2        8 0.00400000        1   0.00441365
//       2        8 0.00400000        2   0.00203705
//       2        8 0.00400000        4   0.00223624
//       2        8 0.00400000        8   0.00325792
//       2        8 0.00400000       16   0.00451815
//       2        8 0.00400000       32   0.00512944
//       2        8 0.00400000       64   0.00496506
//       2        8 0.00800000        1   0.00200416
//       2        8 0.00800000        2   0.00216254
//       2        8 0.00800000        4   0.00445964
//       2        8 0.00800000        8   0.00456319
//       2        8 0.00800000       16   0.00461354
//       2        8 0.00800000       32   0.00485067
//       2        8 0.00800000       64   0.00649656
//       2        8 0.01600000        1   0.00218582
//       2        8 0.01600000        2   0.00216502
//       2        8 0.01600000        4   0.00445855
//       2        8 0.01600000        8   0.00451201
//       2        8 0.01600000       16   0.00588631
//       2        8 0.01600000       32   0.00624141
//       2        8 0.01600000       64   0.00480492
//       2        8 0.03200000        1   0.00219070
//       2        8 0.03200000        2   0.00218106
//       2        8 0.03200000        4   0.00449512
//       2        8 0.03200000        8   0.00468822
//       2        8 0.03200000       16   0.00464014
//       2        8 0.03200000       32   0.00467877
//       2        8 0.03200000       64   0.00460443
//       2        8 0.06400000        1   0.00438154
//       2        8 0.06400000        2   0.00216856
//       2        8 0.06400000        4   0.00448317
//       2        8 0.06400000        8   0.00455336
//       2        8 0.06400000       16   0.00451369
//       2        8 0.06400000       32   0.00500922
//       2        8 0.06400000       64   0.00468127
//       2       16 0.00100000        1   0.00339612
//       2       16 0.00100000        2   0.00448256
//       2       16 0.00100000        4   0.00679341
//       2       16 0.00100000        8   0.00529957
//       2       16 0.00100000       16   0.00463858
//       2       16 0.00100000       32   0.00645843
//       2       16 0.00100000       64   0.00542198
//       2       16 0.00200000        1   0.00217238
//       2       16 0.00200000        2   0.00453218
//       2       16 0.00200000        4   0.00456965
//       2       16 0.00200000        8   0.00457783
//       2       16 0.00200000       16   0.00469348
//       2       16 0.00200000       32   0.00461009
//       2       16 0.00200000       64   0.00519426
//       2       16 0.00400000        1   0.00236698
//       2       16 0.00400000        2   0.00449362
//       2       16 0.00400000        4   0.00466327
//       2       16 0.00400000        8   0.00655734
//       2       16 0.00400000       16   0.00464898
//       2       16 0.00400000       32   0.00533609
//       2       16 0.00400000       64   0.00674633
//       2       16 0.00800000        1   0.00452102
//       2       16 0.00800000        2   0.00449952
//       2       16 0.00800000        4   0.00454056
//       2       16 0.00800000        8   0.00458754
//       2       16 0.00800000       16   0.00649478
//       2       16 0.00800000       32   0.00471535
//       2       16 0.00800000       64   0.00464829
//       2       16 0.01600000        1   0.00225472
//       2       16 0.01600000        2   0.00448777
//       2       16 0.01600000        4   0.00462560
//       2       16 0.01600000        8   0.00465242
//       2       16 0.01600000       16   0.00515400
//       2       16 0.01600000       32   0.00660549
//       2       16 0.01600000       64   0.00581320
//       2       16 0.03200000        1   0.00218863
//       2       16 0.03200000        2   0.00452549
//       2       16 0.03200000        4   0.00456968
//       2       16 0.03200000        8   0.00459194
//       2       16 0.03200000       16   0.00466011
//       2       16 0.03200000       32   0.00540447
//       2       16 0.03200000       64   0.00565974
//       2       16 0.06400000        1   0.00224589
//       2       16 0.06400000        2   0.00444820
//       2       16 0.06400000        4   0.00467812
//       2       16 0.06400000        8   0.00506098
//       2       16 0.06400000       16   0.00533810
//       2       16 0.06400000       32   0.00480219
//       2       16 0.06400000       64   0.00517690
//       2       32 0.00100000        1   0.00448533
//       2       32 0.00100000        2   0.00446236
//       2       32 0.00100000        4   0.00463592
//       2       32 0.00100000        8   0.00465690
//       2       32 0.00100000       16   0.00501607
//       2       32 0.00100000       32   0.00655484
//       2       32 0.00100000       64   0.00660583
//       2       32 0.00200000        1   0.00523053
//       2       32 0.00200000        2   0.00452593
//       2       32 0.00200000        4   0.00461631
//       2       32 0.00200000        8   0.00512600
//       2       32 0.00200000       16   0.00639264
//       2       32 0.00200000       32   0.00516461
//       2       32 0.00200000       64   0.00492534
//       2       32 0.00400000        1   0.00447876
//       2       32 0.00400000        2   0.00451608
//       2       32 0.00400000        4   0.00456031
//       2       32 0.00400000        8   0.00461745
//       2       32 0.00400000       16   0.00476447
//       2       32 0.00400000       32   0.00675083
//       2       32 0.00400000       64   0.00658713
//       2       32 0.00800000        1   0.00443362
//       2       32 0.00800000        2   0.00453588
//       2       32 0.00800000        4   0.00445970
//       2       32 0.00800000        8   0.00593541
//       2       32 0.00800000       16   0.00542001
//       2       32 0.00800000       32   0.00514752
//       2       32 0.00800000       64   0.00529019
//       2       32 0.01600000        1   0.00449232
//       2       32 0.01600000        2   0.00452210
//       2       32 0.01600000        4   0.00462453
//       2       32 0.01600000        8   0.00482475
//       2       32 0.01600000       16   0.00463946
//       2       32 0.01600000       32   0.00467611
//       2       32 0.01600000       64   0.00500415
//       2       32 0.03200000        1   0.00450750
//       2       32 0.03200000        2   0.00451571
//       2       32 0.03200000        4   0.00467049
//       2       32 0.03200000        8   0.00469869
//       2       32 0.03200000       16   0.00510355
//       2       32 0.03200000       32   0.00671654
//       2       32 0.03200000       64   0.00624476
//       2       32 0.06400000        1   0.00451571
//       2       32 0.06400000        2   0.00452477
//       2       32 0.06400000        4   0.00455541
//       2       32 0.06400000        8   0.00700791
//       2       32 0.06400000       16   0.00670048
//       2       32 0.06400000       32   0.00522917
//       2       32 0.06400000       64   0.00651304
//       2       64 0.00100000        1   0.00458432
//       2       64 0.00100000        2   0.00463228
//       2       64 0.00100000        4   0.00466611
//       2       64 0.00100000        8   0.00525261
//       2       64 0.00100000       16   0.00577314
//       2       64 0.00100000       32   0.00657284
//       2       64 0.00100000       64   0.00664213
//       2       64 0.00200000        1   0.00630193
//       2       64 0.00200000        2   0.00463622
//       2       64 0.00200000        4   0.00468850
//       2       64 0.00200000        8   0.00467568
//       2       64 0.00200000       16   0.00630920
//       2       64 0.00200000       32   0.00664527
//       2       64 0.00200000       64   0.00624848
//       2       64 0.00400000        1   0.00469018
//       2       64 0.00400000        2   0.00460593
//       2       64 0.00400000        4   0.00562860
//       2       64 0.00400000        8   0.00570470
//       2       64 0.00400000       16   0.00668479
//       2       64 0.00400000       32   0.00520075
//       2       64 0.00400000       64   0.01148287
//       2       64 0.00800000        1   0.00462026
//       2       64 0.00800000        2   0.00466664
//       2       64 0.00800000        4   0.00644199
//       2       64 0.00800000        8   0.00491129
//       2       64 0.00800000       16   0.00670611
//       2       64 0.00800000       32   0.00659643
//       2       64 0.00800000       64   0.00657502
//       2       64 0.01600000        1   0.00434794
//       2       64 0.01600000        2   0.00465779
//       2       64 0.01600000        4   0.00660314
//       2       64 0.01600000        8   0.00523301
//       2       64 0.01600000       16   0.00497592
//       2       64 0.01600000       32   0.00680527
//       2       64 0.01600000       64   0.00658608
//       2       64 0.03200000        1   0.00404997
//       2       64 0.03200000        2   0.00468063
//       2       64 0.03200000        4   0.00490328
//       2       64 0.03200000        8   0.00663271
//       2       64 0.03200000       16   0.00677222
//       2       64 0.03200000       32   0.00647534
//       2       64 0.03200000       64   0.00658953
//       2       64 0.06400000        1   0.00657780
//       2       64 0.06400000        2   0.00462073
//       2       64 0.06400000        4   0.00468399
//       2       64 0.06400000        8   0.00514770
//       2       64 0.06400000       16   0.00675000
//       2       64 0.06400000       32   0.00467273
//       2       64 0.06400000       64   0.00672934
//       4        2 0.00100000        1   0.00201227
//       4        2 0.00100000        2   0.00202900
//       4        2 0.00100000        4   0.00201961
//       4        2 0.00100000        8   0.00247490
//       4        2 0.00100000       16   0.00450690
//       4        2 0.00100000       32   0.00441098
//       4        2 0.00100000       64   0.00462613
//       4        2 0.00200000        1   0.00202490
//       4        2 0.00200000        2   0.00225805
//       4        2 0.00200000        4   0.00209154
//       4        2 0.00200000        8   0.00222894
//       4        2 0.00200000       16   0.00466155
//       4        2 0.00200000       32   0.00462252
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//      64        8 0.00100000       32   0.00465111
//      64        8 0.00100000       64   0.00624776
//      64        8 0.00200000        1   0.00209621
//      64        8 0.00200000        2   0.00238156
//      64        8 0.00200000        4   0.00454761
//      64        8 0.00200000        8   0.00468501
//      64        8 0.00200000       16   0.00466242
//      64        8 0.00200000       32   0.00518700
//      64        8 0.00200000       64   0.00487155
//      64        8 0.00400000        1   0.00201550
//      64        8 0.00400000        2   0.00240777
//      64        8 0.00400000        4   0.00457207
//      64        8 0.00400000        8   0.00459867
//      64        8 0.00400000       16   0.00465677
//      64        8 0.00400000       32   0.00470678
//      64        8 0.00400000       64   0.00666006
//      64        8 0.00800000        1   0.00202454
//      64        8 0.00800000        2   0.00222520
//      64        8 0.00800000        4   0.00391023
//      64        8 0.00800000        8   0.00667096
//      64        8 0.00800000       16   0.00458655
//      64        8 0.00800000       32   0.00652026
//      64        8 0.00800000       64   0.00467384
//      64        8 0.01600000        1   0.00205190
//      64        8 0.01600000        2   0.00215807
//      64        8 0.01600000        4   0.00453659
//      64        8 0.01600000        8   0.00460748
//      64        8 0.01600000       16   0.00458425
//      64        8 0.01600000       32   0.00463613
//      64        8 0.01600000       64   0.00467970
//      64        8 0.03200000        1   0.00203095
//      64        8 0.03200000        2   0.00222034
//      64        8 0.03200000        4   0.00452808
//      64        8 0.03200000        8   0.00454611
//      64        8 0.03200000       16   0.00466659
//      64        8 0.03200000       32   0.00466829
//      64        8 0.03200000       64   0.00565758
//      64        8 0.06400000        1   0.00206161
//      64        8 0.06400000        2   0.00217170
//      64        8 0.06400000        4   0.00370396
//      64        8 0.06400000        8   0.00452939
//      64        8 0.06400000       16   0.00609140
//      64        8 0.06400000       32   0.00464775
//      64        8 0.06400000       64   0.00466952
//      64       16 0.00100000        1   0.00218156
//      64       16 0.00100000        2   0.00388122
//      64       16 0.00100000        4   0.00491253
//      64       16 0.00100000        8   0.00457862
//      64       16 0.00100000       16   0.00489976
//      64       16 0.00100000       32   0.00532814
//      64       16 0.00100000       64   0.00544565
//      64       16 0.00200000        1   0.00223085
//      64       16 0.00200000        2   0.00443994
//      64       16 0.00200000        4   0.00449524
//      64       16 0.00200000        8   0.00457299
//      64       16 0.00200000       16   0.00459583
//      64       16 0.00200000       32   0.00472716
//      64       16 0.00200000       64   0.00488508
//      64       16 0.00400000        1   0.00240027
//      64       16 0.00400000        2   0.00391078
//      64       16 0.00400000        4   0.00450307
//      64       16 0.00400000        8   0.00517111
//      64       16 0.00400000       16   0.00656970
//      64       16 0.00400000       32   0.00462007
//      64       16 0.00400000       64   0.00528963
//      64       16 0.00800000        1   0.00220438
//      64       16 0.00800000        2   0.00446460
//      64       16 0.00800000        4   0.00453815
//      64       16 0.00800000        8   0.00462642
//      64       16 0.00800000       16   0.00456262
//      64       16 0.00800000       32   0.00648256
//      64       16 0.00800000       64   0.00466500
//      64       16 0.01600000        1   0.00241103
//      64       16 0.01600000        2   0.00626589
//      64       16 0.01600000        4   0.00462332
//      64       16 0.01600000        8   0.00456363
//      64       16 0.01600000       16   0.00453668
//      64       16 0.01600000       32   0.00464542
//      64       16 0.01600000       64   0.00619369
//      64       16 0.03200000        1   0.00222793
//      64       16 0.03200000        2   0.00651482
//      64       16 0.03200000        4   0.00461076
//      64       16 0.03200000        8   0.00637105
//      64       16 0.03200000       16   0.00521997
//      64       16 0.03200000       32   0.00488134
//      64       16 0.03200000       64   0.00477299
//      64       16 0.06400000        1   0.00219310
//      64       16 0.06400000        2   0.00205867
//      64       16 0.06400000        4   0.00448819
//      64       16 0.06400000        8   0.00496202
//      64       16 0.06400000       16   0.00459863
//      64       16 0.06400000       32   0.00463012
//      64       16 0.06400000       64   0.00492550
//      64       32 0.00100000        1   0.00454232
//      64       32 0.00100000        2   0.00451917
//      64       32 0.00100000        4   0.00462821
//      64       32 0.00100000        8   0.00461349
//      64       32 0.00100000       16   0.00515737
//      64       32 0.00100000       32   0.00518576
//      64       32 0.00100000       64   0.00662234
//      64       32 0.00200000        1   0.00452296
//      64       32 0.00200000        2   0.00459985
//      64       32 0.00200000        4   0.00467069
//      64       32 0.00200000        8   0.00650226
//      64       32 0.00200000       16   0.00467673
//      64       32 0.00200000       32   0.00677949
//      64       32 0.00200000       64   0.00575604
//      64       32 0.00400000        1   0.00467478
//      64       32 0.00400000        2   0.00327033
//      64       32 0.00400000        4   0.00570491
//      64       32 0.00400000        8   0.00518798
//      64       32 0.00400000       16   0.00544094
//      64       32 0.00400000       32   0.00657092
//      64       32 0.00400000       64   0.00667666
//      64       32 0.00800000        1   0.00448654
//      64       32 0.00800000        2   0.00395789
//      64       32 0.00800000        4   0.00482171
//      64       32 0.00800000        8   0.00671800
//      64       32 0.00800000       16   0.00588857
//      64       32 0.00800000       32   0.00640279
//      64       32 0.00800000       64   0.00469992
//      64       32 0.01600000        1   0.00449455
//      64       32 0.01600000        2   0.00452858
//      64       32 0.01600000        4   0.00463444
//      64       32 0.01600000        8   0.00594257
//      64       32 0.01600000       16   0.00527270
//      64       32 0.01600000       32   0.00479246
//      64       32 0.01600000       64   0.00617601
//      64       32 0.03200000        1   0.00391341
//      64       32 0.03200000        2   0.00459308
//      64       32 0.03200000        4   0.00461036
//      64       32 0.03200000        8   0.00503672
//      64       32 0.03200000       16   0.00467773
//      64       32 0.03200000       32   0.00501924
//      64       32 0.03200000       64   0.00507411
//      64       32 0.06400000        1   0.00449402
//      64       32 0.06400000        2   0.00461587
//      64       32 0.06400000        4   0.00465161
//      64       32 0.06400000        8   0.00465226
//      64       32 0.06400000       16   0.00481118
//      64       32 0.06400000       32   0.00484021
//      64       32 0.06400000       64   0.00466314
//      64       64 0.00100000        1   0.00455532
//      64       64 0.00100000        2   0.00526280
//      64       64 0.00100000        4   0.00532427
//      64       64 0.00100000        8   0.00523911
//      64       64 0.00100000       16   0.00683607
//      64       64 0.00100000       32   0.00660385
//      64       64 0.00100000       64   0.00654410
//      64       64 0.00200000        1   0.00464753
//      64       64 0.00200000        2   0.00457326
//      64       64 0.00200000        4   0.00460300
//      64       64 0.00200000        8   0.00469599
//      64       64 0.00200000       16   0.00489096
//      64       64 0.00200000       32   0.00631690
//      64       64 0.00200000       64   0.00546414
//      64       64 0.00400000        1   0.00454948
//      64       64 0.00400000        2   0.00654105
//      64       64 0.00400000        4   0.00472782
//      64       64 0.00400000        8   0.00528966
//      64       64 0.00400000       16   0.00523026
//      64       64 0.00400000       32   0.00660729
//      64       64 0.00400000       64   0.00654014
//      64       64 0.00800000        1   0.00458248
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//      64       64 0.00800000        4   0.00463402
//      64       64 0.00800000        8   0.00627488
//      64       64 0.00800000       16   0.00648207
//      64       64 0.00800000       32   0.00656963
//      64       64 0.00800000       64   0.00640736
//      64       64 0.01600000        1   0.00460551
//      64       64 0.01600000        2   0.00538523
//      64       64 0.01600000        4   0.00473476
//      64       64 0.01600000        8   0.00652703
//      64       64 0.01600000       16   0.00653435
//      64       64 0.01600000       32   0.00658923
//      64       64 0.01600000       64   0.00665922
//      64       64 0.03200000        1   0.00451953
//      64       64 0.03200000        2   0.00465613
//      64       64 0.03200000        4   0.00603257
//      64       64 0.03200000        8   0.00506186
//      64       64 0.03200000       16   0.00519696
//      64       64 0.03200000       32   0.00518831
//      64       64 0.03200000       64   0.00661620
//      64       64 0.06400000        1   0.00455253
//      64       64 0.06400000        2   0.00465434
//      64       64 0.06400000        4   0.00472795
//      64       64 0.06400000        8   0.00656600
//      64       64 0.06400000       16   0.00671513
//      64       64 0.06400000       32   0.00660573
//      64       64 0.06400000       64   0.00653944