gauss_easter.c

#include <stdio.h>

char *computus(int year, int servois, char *out, size_t out_size) {
    // Year's position on the 19 year metonic cycle
    int a = year % 19;

    // Century index
    int k = year / 100;

    //Shift of metonic cycle, add a day offset every 300 years
    int p = (13 + 8 * k) / 25;

    // Correction for non-observed leap days
    int q = k / 4;

    // Correction to starting point of calculation each century
    int M = (15 - p + k - q) % 30;

    // Number of days from March 21st until the full moon
    int d = (19 * a + M) % 30;

    // Returning if user wants value for Servois' table
    if (servois) {
        snprintf(out, out_size, "%d",(21 + d) % 31);
        return out;
    }

    // Finding the next Sunday
    // Century-based offset in weekly calculation
    int N = (4 + k - q) % 7;

    // Correction for leap days
    int b = year % 4;
    int c = year % 7;

    // Days from d to next Sunday
    int e = (2 * b + 4 * c + 6 * d + N) % 7;

    // Historical corrections for April 26 and 25
    if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {
        e = -1;
    }

    if ((22 + d + e) > 31) {
        snprintf(out, out_size, "April %d", d + e - 9);
    } else {
        snprintf(out, out_size, "March %d", 22 + d + e);
    }

    return out;
}

int main() {
    char tmp1[9], tmp2[9];

    printf("The following are the dates of the Paschal full moon (using "
           "Servois notation) and the date of Easter for 2020-2030 AD:\n");

    printf("Year\tServois number\tEaster\n");

    for (int year = 2020; year <= 2030; year++) {
        printf("%d\t\t%s\t%s\n", year, computus(year, 1, tmp1, 9),
               computus(year, 0, tmp2, 9));
    }

    return 0;
}