#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>

mpz_t *mpz_array(int number_of_elements);
void mpz_init_array(mpz_t *array,int number_of_elements);
void fraction_expansion(mpz_t *fraction,unsigned int expansions,unsigned int expansion);
mpz_t *e(unsigned int expansions);
int main()
{
      char numerator[60];
      int index=0,sum=0;
      mpz_t *fraction;

      fraction=e(100);
      gmp_sprintf(numerator,"%Zd",fraction[0]);
      for(;numerator[index]!='\0';index++)
            sum+=numerator[index]-48;                       // sum+=numerator[index]-'0';
      printf("\n\t%i\n\n",sum);

      return 0;
}
mpz_t *mpz_array(int number_of_elements)
{
      mpz_t *array;

      array=malloc(number_of_elements*sizeof(mpz_t));
      mpz_init_array(array,number_of_elements);

      return array;
}
void mpz_init_array(mpz_t *array,int number_of_elements)
{
      int element=0;

      for(;element<number_of_elements;element++)
            mpz_init(array[element]);
}
void fraction_expansion(mpz_t *fraction,unsigned int expansions,unsigned int expansion)
{
      if(expansions-expansion<0)
            return;
      unsigned int den=!(expansion%2),num=expansion%2,k=2*((expansion%3)%2)*expansion/3;

      if(!k)
            k=1;
      if(expansions-expansion==0)
      {
            if(!expansion)
            {
                  mpz_set_ui(fraction[0],0);
                  mpz_set_ui(fraction[1],1);
            }
            else
            {
                  mpz_set_ui(fraction[den],1);
                  mpz_set_ui(fraction[num],k);
            }
            return;
      }
      if(!expansion)
      {
            if(expansions==1)
            {
                  mpz_set_ui(fraction[0],1);
                  mpz_set_ui(fraction[1],1);
                  return;
            }
            else
            {
                  den=0;
                  num=1;
                  expansion+=3;
                  expansions+=2;
            }
      }
      fraction_expansion(fraction,expansions,expansion+1);
      mpz_t product;

      mpz_init_set_ui(product,k);
      mpz_mul(product,product,fraction[den]);
      mpz_add(fraction[num],fraction[num],product);
}
mpz_t *e(unsigned int expansions)
{
      mpz_t auxiliary,*fraction=mpz_array(2);
      mpz_init(auxiliary);

      expansions--;
      fraction_expansion(fraction,expansions,0);// The function  returns the numerator
      if(mpz_cmp(fraction[0],fraction[1])>0)    // and the denominator(not necessarily
      {                                         // in this order) of the fraction that
                                                // approximates  the  decimal  part of 
                                                // 'e' with  the  specified  number of
                                                // iterations.
            mpz_set(auxiliary,fraction[0]);     // Must be  checked  the  order of the
            mpz_set(fraction[0],fraction[1]);   // returned  elements   (the  fraction
            mpz_set(fraction[1],auxiliary);     // have to be lesser of one).
      }
      mpz_mul_si(auxiliary,fraction[1],2);
      mpz_add(fraction[0],fraction[0],auxiliary);

      return fraction;
}