p15.c

#include <stdio.h>
#include <stdlib.h>
#include <strings.h>
#include <string.h>
#include <inttypes.h>
#include <math.h>
#include <gmp.h>

// http://projecteuler.net/problem=15
//
// Starting in the top left corner of a 2×2 grid, and only being able to
// move to the right and down, there are exactly 6 routes to the bottom
// right corner.
//
// How many such routes are there through a 20×20 grid?

void lattice_paths (mpz_ptr v, int64_t size);
void fibonacci_coefficient (mpz_ptr v, int64_t n, int64_t r);
void factorial (mpz_ptr v, int64_t n);

int main () {
  mpz_t paths;
  mpz_init(paths);
  for (int64_t size = 0; size < 21; size++) {
    lattice_paths(paths, size);
    printf("lattice_paths(%" PRId64 ") = ", size);
    mpz_out_str(stdout, 10, paths);
    printf("\n");
  }

  return 0;
}

void lattice_paths (mpz_ptr v, int64_t size) {
  fibonacci_coefficient(v, 2 * size, size);
}

void fibonacci_coefficient (mpz_ptr v, int64_t n, int64_t r) {
  mpz_t a, b, c;
  mpz_init(a);
  mpz_init(b);
  mpz_init(c);

  factorial(a, n);
  factorial(b, r);
  factorial(c, n - r);

  mpz_mul(b, b, c);
  mpz_div(a, a, b);
  mpz_set(v, a);
}

void factorial (mpz_ptr v, int64_t n) {
  mpz_set_si(v, 1);

  for (int64_t i = n; i > 1; i--) {
    mpz_mul_si(v, v, i);
  }
}

sh.sh

fortysix@46mbp:euler ∴ g++ -o p15 p15.c
Undefined symbols for architecture x86_64:
  "___gmpz_fdiv_q", referenced from:
      fibonacci_coefficient(__mpz_struct*, long long, long long)in ccnAfSXb.o
  "___gmpz_init", referenced from:
      _main in ccnAfSXb.o
      fibonacci_coefficient(__mpz_struct*, long long, long long)in ccnAfSXb.o
  "___gmpz_mul", referenced from:
      fibonacci_coefficient(__mpz_struct*, long long, long long)in ccnAfSXb.o
  "___gmpz_mul_si", referenced from:
      factorial(__mpz_struct*, long long)in ccnAfSXb.o
  "___gmpz_out_str", referenced from:
      _main in ccnAfSXb.o
  "___gmpz_set", referenced from:
      fibonacci_coefficient(__mpz_struct*, long long, long long)in ccnAfSXb.o
  "___gmpz_set_si", referenced from:
      factorial(__mpz_struct*, long long)in ccnAfSXb.o
ld: symbol(s) not found for architecture x86_64
collect2: ld returned 1 exit status