static void Main(string[] args)
{
N = int.Parse(args[0]);
for (long m = 0; m <= Math.Sqrt(N); m++)
{
long nmax = (long)Math.Ceiling(Math.Sqrt(N - m * m));
for (long n = 0; n <= nmax; n++)
{
long pmax = (long)Math.Ceiling(Math.Sqrt(N - m * m - n * n));
for (long p = 0; p <= pmax; p++)
{
long qmax = (long)Math.Ceiling(Math.Sqrt(N - m * m - n * n - p * p));
for (long q = 0; q <= qmax; q++)
{
if (((m + n + p + q) % 2) == 1)
{
mnpq it = new mnpq(m, n, p, q);
try
{
process_mnpq(it);
}
catch (InvalidOperationException e)
{
throw new InvalidOperationException($"{e.Message} while processing {it}");
}
}
}
}
}
}
Console.Out.WriteLine($"S = {S}");
}
private static vectortriple get_triple(abcd baseAbcd, mnpq item)
{
var itemArray = new[] { item.m, item.n, item.p, item.q };
Array.Sort(itemArray);
long[][] perms = Permutations.Of(itemArray, 4, false, false);
vector[] allVectors = perms.SelectMany(p => new mnpq(p[0], p[1], p[2], p[3]).get_abcd().get_vectors()).ToArray();
var u = new vector(baseAbcd.a, baseAbcd.b, baseAbcd.c);
foreach (var v in allVectors)
{
if (v.is_orthogonal_to(u))
{
var n = v.cross_product(u);
return(new vectortriple(u, v, n));
}
}
throw new InvalidOperationException("No triple found!");
}
private static void process_mnpq(mnpq item)
{
abcd baseAbcd = item.get_abcd();
if (new[] { baseAbcd.a, baseAbcd.b, baseAbcd.c /*NOT d (although doesn't seem to make much difference in C++*/ }.gcd() == 1)
{
HashSet <cube> thisCubes = new HashSet <cube>();
vectortriple baseTriple = get_triple(baseAbcd, item);
long sumgcd = baseTriple.u.gcd() + baseTriple.v.gcd() + baseTriple.n.gcd();
long l = baseTriple.u.length;
var abcds = baseAbcd.get_permutations();
foreach (var abcd in abcds)
{
var triple = get_triple(abcd, item);
for (int f = 0; f < 8; f++)
{
bool flipX = (f & 1) != 0,
flipY = (f & 2) != 0,
flipZ = (f & 4) != 0;
int [] order = { 0, 1, 2 };
foreach (var orderPermutation in Permutations.Of(order, 3, false, false))
{
var cube = new cube(triple.u, triple.v, triple.n, flipX, flipY, flipZ, orderPermutation);
thisCubes.Add(cube);
}
}
}
massiveinteger thisS = new massiveinteger();
foreach (var thisCube in thisCubes)
{
if (!thisCube.is_oversize() && cubesDone.Add(thisCube))
{
long maxSize = new[] { thisCube.width, thisCube.height, thisCube.depth }.Max();
long tmax = N / maxSize;
if (tmax * maxSize > N)
{
throw new InvalidOperationException("tmax is too lenient - would produce oversize cubes!");
}
if ((tmax + 1) * maxSize <= N)
{
throw new InvalidOperationException("tmax is not lenient enough - could squeeze another one out!");
}
if (tmax <= 0)
{
throw new InvalidOperationException("tmax <= 0");
}
for (long t = 1; t <= tmax; t++)
{
long repeatability = (N + 1L - thisCube.width * t) *
(N + 1L - thisCube.height * t) *
(N + 1L - thisCube.depth * t);
if (repeatability <= 0)
{
throw new InvalidOperationException("Repeatability <= 0");
}
massiveinteger ehp = new massiveinteger(l * l * l) * new massiveinteger(t * t * t) +
new massiveinteger(l * sumgcd) * new massiveinteger(t * t) + new massiveinteger(sumgcd * t + 1);
massiveinteger contributionS = ehp * new massiveinteger(repeatability);
// var line = $"{item},{t},{thisS},{contributionS},";
thisS += contributionS;
// line += thisS;
// File.AppendAllLines("s5_verbose_csh.csv", new [] {line});
}
}
}
S += thisS;
S.truncate(9);
}
}