#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>


int k;
double * tau; 
long int *binom;

long int _binom(k, i) {
	if (i == 0) return 1;
	else return ((k-i+1)*_binom(k, i-1))/i;
}

double f(double x) {
	double y;
	int i;

	y = 0;
	for (i=0; i<=k; i++) {
		y += tau[i] * binom[i]*pow(x,i)*pow(1-x, k-i);
	}
	return y;
}

int main() {
	int i;
	double x, h;
  double J, W;

  srand48(time(NULL));

  k=20;
  W = 10;
  tau = (double *) calloc(k+1, sizeof(double));
  
  binom=(long int *) calloc(k+1, sizeof(long int));
  /* precalcolo i coeff. binomiali */
  for (i=0; i<=k; i++) {
    binom[i] = _binom(k,i);
  }
 for (J=0; J>=-10; J-=0.01) {
    /* calcolo le prob. di transizione */
    for (i=0; i<=k; i++) {
      h = (double) (2*i-k)/k;
      tau[i] = 1/(1+exp(-2*(J*h + W*h*h*h)));
    }

    x = drand48(); // initial value
 
    for (i=0; i<2000+100; i++) {
      x = f(x);
      if (i>2000){
        printf("%f %f\n", J, x);
      }
    }
  }
}