Calculate e

euler.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gmp.h> // Bignum support

int main(void) {
  long long iteration=0;

  mpq_t current_term; /* Contains 1/n!              */
  mpq_t sum;          /* Contains sum over all 1/n! */

  mpf_t result; /* Contains the denominator first, then e */
  mpf_t divisor;

  mpq_init(current_term);
  mpq_init(sum);


  /*
   * We calculate E using Taylor series expansion. We know from Wikipedia that
   * e can be calculated using the following formula.
   *
   *                              oo
   *                             ____
   *                             \        1
   *                         e =  )     -----
   *                             /___     n!
   *                              i=0
   *
   * Because calculating the fraction every time takes a long time, we just
   * calculate the denominator and the numerator and add them. When we are
   * done summing up all the terms, we finally do the division.
   */

  /* Make sure numerator is always 1 */
  mpz_set_ui(mpq_numref(current_term), 1);

  printf("Starting main summing...");
  for(;iteration<3500;iteration++) {
    mpz_fac_ui(mpq_denref(current_term), iteration); /* set the denominator of current_term
                                           to the factorial of n */
    // Add current term to result.
    mpq_add(sum, sum, current_term);
  }

  printf("done\nStarting division...");

  /* Finally divide integers */
  mpf_init2(result, 100000);
  mpf_init2(divisor, 100000);

  mpf_set_z(result, mpq_numref(sum));
  mpf_set_z(divisor, mpq_denref(sum));
  mpf_div(result, result, divisor);

  printf("done\n");

  printf("Result: ");
  mpf_out_str(stdout, 10, 1000, result);
  printf("\n");
}

Makefile

CC=gcc

euler: euler.o
	$(CC) -lgmp -o euler euler.o

euler.o: euler.c
	$(CC) -O3 -c euler.c -o euler.o

.PHONY: clean
clean:
	rm -f euler.o euler