#include <iostream>
#include <sstream>
#include <stdexcept>

// Gregorian Calendar started on Julian Day 2299161

const long gregorianEpoch = 2299161L;

const int nMonths = 12;

static int monthDays[nMonths + 1] = {
  0,
  31, 28, 31, 30, 31, 30,
  31, 31, 30, 31, 30, 31
};

void jul2greg(
  long  jul,
  int & day,
  int & month,
  int & year
) {
  // From "Software, Practice and Experience", Vol. 23 (1993),
  // pag. 384

  if (jul < gregorianEpoch) {
    std::ostringstream s;
    s << "Julian Day " << jul << " comes before Gregorian Calendar";
    throw std::domain_error(s.str());
  }

  // JD 1721425 corresponds to a (virtual) January 1, year 1 of the
  // Gregorian Calendar.  n400 is the number of completed 400 year
  // cycles; n100 the number of completed 100 year cycles not included
  // in n400; n4 the number of completed 4 year cycles not included in
  // n400 and n100; n1 the number of years not included in n400, n100
  // or n4.

  jul       -= 1721426;
  long n400  = jul / 146097;
  jul       %= 146097;
  long n100  = jul / 36524;
  jul       %= 36524;
  long n4    = jul / 1461;
  jul       %= 1461;
  long n1    = jul / 365;
  jul       %= 365;

  year = 400 * n400 + 100 * n100 + 4 * n4 + n1;

  if (n100 == 4   ||   n1 == 4) {
    // Day 366 of year "year"

    day   = 31;
    month = 12;

  } else {
    // Day "jul+1" of year "year+1"

    if (isLeap(++year)) monthDays[2] = 29;
    else                monthDays[2] = 28;

    ++jul;

    for (int i = 1;   i <= nMonths;   ++i) {
      if (jul <= monthDays[i]) {
        day   = jul;
        month = i;
        return;
      }
      jul -= monthDays[i];
    }
    std::cerr << "Can't happen\n";
  }
}