Examples

• Compute 10000 iterates of the logistic map:

#include "iRRAM.h"
using namespace iRRAM;
using std::setw;

/* Compute logistic map 
 *    x_n+1 =c * x_n * (1-x_n)
 * for c=3.75 and x_0 = 0.5
 */

void compute(){
       REAL x = 0.5;
       REAL c = 3.75;
       cout << setRwidth(40) << setw(6);

       for ( int i=0; i <= 9999; i++ ) {
              cout << x  << " : " << i << "\n";
             x = c * x * (1 -x);
       }
}

Comparison to evaluation using double precision:

 

• Compute many decimals of the Euler’s number e = 2.7172… as the limit of a sequence

#include "iRRAM.h"
using namespace iRRAM;

/* Compute an approximation to e=2.71... 
 * up to an error of 2^p */
REAL e_approx (int p)
{
  REAL y = 1, sum = 2;
  for (int i=2; !bound(y,p-1); i++ ) {
    y = y / i;
    sum = sum + y;
  }
  return sum;
}

/* Compute e=2.71... */
void compute(){
  REAL euler_number = limit( e_approx ); 
  auto widths= {50, 100, 1000, 10000};
  for (int w: widths) {
    cout << setRwidth(w) << euler_number << "\n\n"; 
  }
}