I developed a solution similar to Insta's approach, but with some differences. In effect, it looks a lot like his chunked array solution. However, instead of just simply splitting the data, my approach builds an index of chunks and directs the search only to the appropriate chunk.
The way the index is built is very similar to a hashtable, with each bucket being an sorted array that can be search with a binary search. However, I figured that there's little point in computing a hash of an SHA256 hash, so instead I simply take a prefix of the value.
The interesting thing about this technique is that you can tune it by extending the length of the index keys. A longer key means a larger index and smaller buckets. My test case of 8 bits is probably on the small side; 10-12 bits would probably be more effective.
I attempted to benchmark this approach, but it quickly ran out of memory so I wasn't able to see anything interesting in terms of performance.
I also wrote a C implementation. The C implementation wasn't able to deal with a data set of the specified size either (the test machine has only 4GB of RAM), but it did manage somewhat more. (The target data set actually wasn't so much of a problem in that case, it was the test data that filled up the RAM.) I wasn't able to figure out a good way to throw data at it fast enough to really see its performance tested.
While I enjoyed writing this, I'd say overall it mostly provides evidence in favor of the argument that you shouldn't be trying to do this in memory with C#.
public interface IKeyed
{
int ExtractKey();
}
struct Sha256_Long : IComparable<Sha256_Long>, IKeyed
{
private UInt64 _piece1;
private UInt64 _piece2;
private UInt64 _piece3;
private UInt64 _piece4;
public Sha256_Long(string hex)
{
if (hex.Length != 64)
{
throw new ArgumentException("Hex string must contain exactly 64 digits.");
}
UInt64[] pieces = new UInt64[4];
for (int i = 0; i < 4; i++)
{
pieces[i] = UInt64.Parse(hex.Substring(i * 8, 1), NumberStyles.HexNumber);
}
_piece1 = pieces[0];
_piece2 = pieces[1];
_piece3 = pieces[2];
_piece4 = pieces[3];
}
public Sha256_Long(byte[] bytes)
{
if (bytes.Length != 32)
{
throw new ArgumentException("Sha256 values must be exactly 32 bytes.");
}
_piece1 = BitConverter.ToUInt64(bytes, 0);
_piece2 = BitConverter.ToUInt64(bytes, 8);
_piece3 = BitConverter.ToUInt64(bytes, 16);
_piece4 = BitConverter.ToUInt64(bytes, 24);
}
public override string ToString()
{
return String.Format("{0:X}{0:X}{0:X}{0:X}", _piece1, _piece2, _piece3, _piece4);
}
public int CompareTo(Sha256_Long other)
{
if (this._piece1 < other._piece1) return -1;
if (this._piece1 > other._piece1) return 1;
if (this._piece2 < other._piece2) return -1;
if (this._piece2 > other._piece2) return 1;
if (this._piece3 < other._piece3) return -1;
if (this._piece3 > other._piece3) return 1;
if (this._piece4 < other._piece4) return -1;
if (this._piece4 > other._piece4) return 1;
return 0;
}
//-------------------------------------------------------------------
// Implementation of key extraction
public const int KeyBits = 8;
private static UInt64 _keyMask;
private static int _shiftBits;
static Sha256_Long()
{
_keyMask = 0;
for (int i = 0; i < KeyBits; i++)
{
_keyMask |= (UInt64)1 << i;
}
_shiftBits = 64 - KeyBits;
}
public int ExtractKey()
{
UInt64 keyRaw = _piece1 & _keyMask;
return (int)(keyRaw >> _shiftBits);
}
}
class IndexedSet<T> where T : IComparable<T>, IKeyed
{
private T[][] _keyedSets;
public IndexedSet(IEnumerable<T> source, int keyBits)
{
// Arrange elements into groups by key
var keyedSetsInit = new Dictionary<int, List<T>>();
foreach (T item in source)
{
int key = item.ExtractKey();
List<T> vals;
if (!keyedSetsInit.TryGetValue(key, out vals))
{
vals = new List<T>();
keyedSetsInit.Add(key, vals);
}
vals.Add(item);
}
// Transform the above structure into a more efficient array-based structure
int nKeys = 1 << keyBits;
_keyedSets = new T[nKeys][];
for (int key = 0; key < nKeys; key++)
{
List<T> vals;
if (keyedSetsInit.TryGetValue(key, out vals))
{
_keyedSets[key] = vals.OrderBy(x => x).ToArray();
}
}
}
public bool Contains(T item)
{
int key = item.ExtractKey();
if (_keyedSets[key] == null)
{
return false;
}
else
{
return Search(item, _keyedSets[key]);
}
}
private bool Search(T item, T[] set)
{
int first = 0;
int last = set.Length - 1;
while (first <= last)
{
int midpoint = (first + last) / 2;
int cmp = item.CompareTo(set[midpoint]);
if (cmp == 0)
{
return true;
}
else if (cmp < 0)
{
last = midpoint - 1;
}
else
{
first = midpoint + 1;
}
}
return false;
}
}
class Program
{
//private const int NTestItems = 100 * 1000 * 1000;
private const int NTestItems = 1 * 1000 * 1000;
private static Sha256_Long RandomHash(Random rand)
{
var bytes = new byte[32];
rand.NextBytes(bytes);
return new Sha256_Long(bytes);
}
static IEnumerable<Sha256_Long> GenerateRandomHashes(
Random rand, int nToGenerate)
{
for (int i = 0; i < nToGenerate; i++)
{
yield return RandomHash(rand);
}
}
static void Main(string[] args)
{
Console.WriteLine("Generating test set.");
var rand = new Random();
IndexedSet<Sha256_Long> set =
new IndexedSet<Sha256_Long>(
GenerateRandomHashes(rand, NTestItems),
Sha256_Long.KeyBits);
Console.WriteLine("Testing with random input.");
int nFound = 0;
int nItems = NTestItems;
int waypointDistance = 100000;
int waypoint = 0;
for (int i = 0; i < nItems; i++)
{
if (++waypoint == waypointDistance)
{
Console.WriteLine("Test lookups complete: " + (i + 1));
waypoint = 0;
}
var item = RandomHash(rand);
nFound += set.Contains(item) ? 1 : 0;
}
Console.WriteLine("Testing complete.");
Console.WriteLine(String.Format("Found: {0} / {0}", nFound, nItems));
Console.ReadKey();
}
}
