/* It is well known that if the square root of a natural number is not an integer, then it is irrational.
 * The decimal expansion of such square roots is infinite without any repeating pattern at all.
 *
 * The square root of two is 1.41421356237309504880..., and the digital sum of the first one hundred decimal digits is 475.
 *
 * For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits
 * for all the irrational square roots*/

#define _POSIX_C_SOURCE 199309L

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

int is_square(int n);

int main(int argc, char **argv)
{
    int i, j, sum = 0;
    char sqrt_digits[104];
    double elapsed;
    struct timespec start, end;
    mpf_t sqrt;

    clock_gettime(CLOCK_MONOTONIC, &start);

    /* Set the precision to 333 bits (should be enough for 100 decimal digits.*/
    mpf_set_default_prec(333);
    mpf_init(sqrt);

    for(i = 2; i < 100; i++)
    {
        if(is_square(i))
        {
            continue;
        }

        /* Calculate the square root of the current number with the given precision
         * and sum the digits to the total.*/
        mpf_sqrt_ui(sqrt, i);
        gmp_sprintf(sqrt_digits, "%.101Ff\n", sqrt);
        sum += (sqrt_digits[0] - '0');

        for(j = 2; j < 101; j++)
        {
            sum += (sqrt_digits[j] - '0');
        }
    }

    mpf_clear(sqrt);

    clock_gettime(CLOCK_MONOTONIC, &end);

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

    printf("Project Euler, Problem 80\n");
    printf("Answer: %d\n", sum);

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

    return 0;
}

int is_square(int n)
{
    int m;
    double p;

    p = sqrt(n);
    m = p;

    if(p == m)
    {
        return 1;
    }
    else
    {
        return 0;
    }
}