How can I convert seconds since the epoch to hours/minutes/seconds in Java?

I’ve figured out how to deal with leap years in integer arithmetic and implemented a converter from seconds since Epoch to date/time (it never gives you more than 59 seconds, though). The below C code should be very easy to port to Java.

#include <string.h>
#include <time.h>

typedef unsigned uint;
typedef unsigned long long uint64;

struct tm* SecondsSinceEpochToDateTime(struct tm* pTm, uint64 SecondsSinceEpoch)
{
  uint64 sec;
  uint quadricentennials, centennials, quadrennials, annuals/*1-ennial?*/;
  uint year, leap;
  uint yday, hour, min;
  uint month, mday, wday;
  static const uint daysSinceJan1st[2][13]=
  {
    {0,31,59,90,120,151,181,212,243,273,304,334,365}, // 365 days, non-leap
    {0,31,60,91,121,152,182,213,244,274,305,335,366}  // 366 days, leap
  };
/*
  400 years:

  1st hundred, starting immediately after a leap year that's a multiple of 400:
  n n n l  \
  n n n l   } 24 times
  ...      /
  n n n l /
  n n n n

  2nd hundred:
  n n n l  \
  n n n l   } 24 times
  ...      /
  n n n l /
  n n n n

  3rd hundred:
  n n n l  \
  n n n l   } 24 times
  ...      /
  n n n l /
  n n n n

  4th hundred:
  n n n l  \
  n n n l   } 24 times
  ...      /
  n n n l /
  n n n L <- 97'th leap year every 400 years
*/

  // Re-bias from 1970 to 1601:
  // 1970 - 1601 = 369 = 3*100 + 17*4 + 1 years (incl. 89 leap days) =
  // (3*100*(365+24/100) + 17*4*(365+1/4) + 1*365)*24*3600 seconds
  sec = SecondsSinceEpoch + 11644473600LL;

  wday = (uint)((sec / 86400 + 1) % 7); // day of week

  // Remove multiples of 400 years (incl. 97 leap days)
  quadricentennials = (uint)(sec / 12622780800ULL); // 400*365.2425*24*3600
  sec %= 12622780800ULL;

  // Remove multiples of 100 years (incl. 24 leap days), can't be more than 3
  // (because multiples of 4*100=400 years (incl. leap days) have been removed)
  centennials = (uint)(sec / 3155673600ULL); // 100*(365+24/100)*24*3600
  if (centennials > 3)
  {
    centennials = 3;
  }
  sec -= centennials * 3155673600ULL;

  // Remove multiples of 4 years (incl. 1 leap day), can't be more than 24
  // (because multiples of 25*4=100 years (incl. leap days) have been removed)
  quadrennials = (uint)(sec / 126230400); // 4*(365+1/4)*24*3600
  if (quadrennials > 24)
  {
    quadrennials = 24;
  }
  sec -= quadrennials * 126230400ULL;

  // Remove multiples of years (incl. 0 leap days), can't be more than 3
  // (because multiples of 4 years (incl. leap days) have been removed)
  annuals = (uint)(sec / 31536000); // 365*24*3600
  if (annuals > 3)
  {
    annuals = 3;
  }
  sec -= annuals * 31536000ULL;

  // Calculate the year and find out if it's leap
  year = 1601 + quadricentennials * 400 + centennials * 100 + quadrennials * 4 + annuals;
  leap = !(year % 4) && (year % 100 || !(year % 400));

  // Calculate the day of the year and the time
  yday = sec / 86400;
  sec %= 86400;
  hour = sec / 3600;
  sec %= 3600;
  min = sec / 60;
  sec %= 60;

  // Calculate the month
  for (mday = month = 1; month < 13; month++)
  {
    if (yday < daysSinceJan1st[leap][month])
    {
      mday += yday - daysSinceJan1st[leap][month - 1];
      break;
    }
  }

  // Fill in C's "struct tm"
  memset(pTm, 0, sizeof(*pTm));
  pTm->tm_sec = sec;          // [0,59]
  pTm->tm_min = min;          // [0,59]
  pTm->tm_hour = hour;        // [0,23]
  pTm->tm_mday = mday;        // [1,31]  (day of month)
  pTm->tm_mon = month - 1;    // [0,11]  (month)
  pTm->tm_year = year - 1900; // 70+     (year since 1900)
  pTm->tm_wday = wday;        // [0,6]   (day since Sunday AKA day of week)
  pTm->tm_yday = yday;        // [0,365] (day since January 1st AKA day of year)
  pTm->tm_isdst = -1;         // daylight saving time flag

  return pTm;
}

See a test run at ideone.