/* The Fibonacci sequence is defined by the recurrence relation:
 *
 * Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
 * Hence the first 12 terms will be:
 * F1 = 1
 * F2 = 1
 * F3 = 2
 * F4 = 3
 * F5 = 5
 * F6 = 8
 * F7 = 13
 * F8 = 21
 * F9 = 34
 * F10 = 55
 * F11 = 89
 * F12 = 144
 *
 * The 12th term, F12, is the first term to contain three digits.
 *
 * What is the index of the first term in the Fibonacci sequence to contain 1000 digits?*/

#define _POSIX_C_SOURCE 199309L

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

int main(int argc, char **argv)
{
    int i;
    double elapsed;
    struct timespec start, end;
    mpz_t f1, f2, fn;
    char *num;
    size_t size;

    clock_gettime(CLOCK_MONOTONIC, &start);

    mpz_init_set_ui(f1, 1);
    mpz_init_set_ui(f2, 1);
    mpz_init(fn);

    i = 2;

    while(1)
    {
        /* Use the GMP Library to calculate the Fibonacci numbers.*/
        mpz_add(fn, f1, f2);
        i++;

        /* The function mpz_sizeinbase gives the number of digits of
         * the number in the given base, but the result is either exact
         * or one too big. To check the exact size, the number is
         * converted to string and the strlen function is used.*/
        if((size = mpz_sizeinbase(fn, 10)) >= 1000)
        {
            if((num = (char *)malloc((2+size)*sizeof(char))) == NULL)
            {
                fprintf(stderr, "Error while allocating memory\n");
                return 1;
            }
            gmp_sprintf(num, "%Zd", fn);
            size = strlen(num);
            free(num);
            if(size == 1000)
            {
                break;
            }
        }

        mpz_set(f1, f2);
        mpz_set(f2, fn);
    }

    mpz_clears(f1, f2, fn, NULL);

    clock_gettime(CLOCK_MONOTONIC, &end);

    elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;

    printf("Project Euler, Problem 25\n");
    printf("Answer: %d\n", i);

    printf("Elapsed time: %.9lf seconds\n", elapsed);

    return 0;
}