We Keep Coding

Selecting set of binary sequences to avoid similarity

I want to be able to programatically generate a set of binary sequences of a given length whilst avoiding similarity between any two sequences.
I'll define 'similar' between two sequences thus:
If sequence A can be converted to sequence B (or B to A) by bit-shifting A (non-circularly) and padding with 0s, A and B are similar (note: bit-shifting is allowed on only one of the sequences otherwise both could always be shifted to a sequence of just 0s)
For example: A = 01010101 B = 10101010 C = 10010010
In this example, A and B are similar because a single left-shift of A results in B (A << 1 = B). A and C are not similar because no bit-shifting of one can result in the other.
A set of sequences is defined is dissimilar if no subset of size 2 is similar.
I believe there could be multiple sets for a given sequence length and presumably the size of the set will be significantly less than the total possibilities (total possibilities = 2 ^ sequence length).
I need a way to generate a set for a given sequence length. Does an algorithm exist that can achieve this? Selecting sequences one at a time and checking against all previously selected sequences is not acceptable for my use case (but may have to be if a better method doesn't exist!).
I've tried generating sets of integers based on primes numbers and also the golden ratio, then converting to binary. This seemed like it might be a viable method, but I have been unable to get it to work as expected.
Update: I have written a function in C# to that uses a prime number modulo to generate the set without success. Also I've tried using the Fibonacci sequence which finds a mostly dissimilar set, but of a size that is very small compared to the number of possibilities:
private List<string> GetSequencesFib(int sequenceLength)
{
var sequences = new List<string>();
long current = 21;
long prev = 13;
long prev2 = 8;
long size = (long)Math.Pow(2, sequenceLength);
while (current < size)
{
current = prev + prev2;
sequences.Add(current.ToBitString(sequenceLength));
prev2 = prev;
prev = current;
}
return sequences;
}
This generates a set of sequences of size 41 that is roughly 60% dissimilar (sequenceLength = 32). It is started at 21 since lower values produce sequences of mostly 0s which are similar to any other sequence.
By relaxing the conditions of similarity to only allowing a small number of successive bit-shifts, the proportion of dissimilar sequences approaches 100%. This may be acceptable in my use case.
Update 2:
I've implemented a function following DCHE's suggestion, by selecting all odd numbers greater than half the maximum value for a given sequence length:
private static List<string> GetSequencesOdd(int length)
{
var sequences = new List<string>();
long max = (long)(Math.Pow(2, length));
long quarterMax = max / 4;
for (long n = quarterMax * 2 + 1; n < max; n += 2)
{
sequences.Add(n.ToBitString(length));
}
return sequences;
}
This produces an entirely dissimilar set as per my requirements. I can see why this works mathematically as well.

I can't prove it, but from my experimenting, I think that your set is the odd integers greater than half of the largest number in binary. E.g. for bit sets of length 3, max integer is 7, so the set is 5 and 7 (101, 111).

Generate unique code from primary key

I have a table of orders and I want to give users a unique code for an order whilst hiding the incrementing identity integer primary key because I don't want to give away how many orders have been made.
One easy way of making sure the codes are unique is to use the primary key to determine the code.
So how can I transform an integer into a friendly, say, eight alpha numeric code such that every code is unique?

The easiest way (if you want an alpha numeric code) is to convert the integer primary key to HEX (like below). And, you can Use `PadLeft()' to make sure the string has 8 characters. But, when the number of orders grow, 8 characters will not be enough.
var uniqueCode = intPrimaryKey.ToString("X").PadLeft(8, '0');
Or, you can create an offset of your primary key, before converting it to HEX, like below:
var uniqueCode = (intPrimaryKey + 999).ToString("X").PadLeft(8, '0');

Assuming the total number of orders being created isn't going to get anywhere near the total number of identifiers in your pool, a reasonably effective technique is to simply generate a random identifier and see if it is used already; continue generating new identifiers until you find one not previously used.

A quick and easy way to do this is to have a guid column that has a default value of
left(newid(),8)
This solution will generally give you a unique value for each row. But if you have extremely large amounts of orders this will not be unique and you should use just the newid() value to generate the guid.

I would just use MD5 for this. MD5 offers enough "uniqueness" for a small subset of integers that represent your customer orders.
For an example see this answer. You will need to adjust input parameter from string to int (or alternatively just call ToString on your number and use the code as-is).

If you would like something that would be difficult to trace and you don;t mind it being 16 characters, you could use something like this that includes some random numbers and mixes the byte positions of the original input with them: (EDITED to make a bit more untraceable, by XOR-ing with the generated random numbers).
public static class OrderIdRandomizer
{
private static readonly Random _rnd = new Random();
public static string GenerateFor(int orderId)
{
var rndBytes = new byte[4];
_rnd.NextBytes(rndBytes);
var bytes = new byte[]
{
(byte)rndBytes[0],
(byte)(((byte)(orderId >> 8)) ^ rndBytes[0]),
(byte)(((byte)(orderId >> 24)) ^ rndBytes[1]),
(byte)rndBytes[1],
(byte)(((byte)(orderId >> 16)) ^ rndBytes[2]),
(byte)rndBytes[2],
(byte)(((byte)(orderId)) ^ rndBytes[3]),
(byte)rndBytes[3],
};
return string.Concat(bytes.Select(b => b.ToString("X2")));
}
public static int ReconstructFrom(string generatedId)
{
if (generatedId == null || generatedId.Length != 16)
throw new InvalidDataException("Invalid generated order id");
var bytes = new byte[8];
for (int i = 0; i < 8; i++)
bytes[i] = byte.Parse(generatedId.Substring(i * 2, 2), System.Globalization.NumberStyles.HexNumber);
return (int)(
((bytes[2] ^ bytes[3]) << 24) |
((bytes[4] ^ bytes[5]) << 16) |
((bytes[1] ^ bytes[0]) << 8) |
((bytes[6] ^ bytes[7])));
}
}
Usage:
var obfuscatedId = OrderIdRandomizer.GenerateFor(123456);
Console.WriteLine(obfuscatedId);
Console.WriteLine(OrderIdRandomizer.ReconstructFrom(obfuscatedId));
Disadvantage: If the algorithm is know, it is obviously easy to break.
Advantage: It is completely custom, i.e. not an established algorithm like MD5 that might be easier to guess/crack if you do not know what algorithm is being used.

Fastest way to sum digits in a number

Given a large number, e.g. 9223372036854775807 (Int64.MaxValue), what is the quickest way to sum the digits?
Currently I am ToStringing and reparsing each char into an int:
num.ToString().Sum(c => int.Parse(new String(new char[] { c })));
Which is surely horrifically inefficent. Any suggestions?
And finally, how would you make this work with BigInteger?
Thanks

Well, another option is:
int sum = 0;
while (value != 0)
{
int remainder;
value = Math.DivRem(value, 10, out remainder);
sum += remainder;
}
BigInteger has a DivRem method as well, so you could use the same approach.
Note that I've seen DivRem not be as fast as doing the same arithmetic "manually", so if you're really interested in speed, you might want to consider that.
Also consider a lookup table with (say) 1000 elements precomputed with the sums:
int sum = 0;
while (value != 0)
{
int remainder;
value = Math.DivRem(value, 1000, out remainder);
sum += lookupTable[remainder];
}
That would mean fewer iterations, but each iteration has an added array access...

Nobody has discussed the BigInteger version. For that I'd look at 101, 102, 104, 108 and so on until you find the last 102n that is less than your value. Take your number div and mod 102n to come up with 2 smaller values. Wash, rinse, and repeat recursively. (You should keep your iterated squares of 10 in an array, and in the recursive part pass along the information about the next power to use.)
With a BigInteger with k digits, dividing by 10 is O(k). Therefore finding the sum of the digits with the naive algorithm is O(k2).
I don't know what C# uses internally, but the non-naive algorithms out there for multiplying or dividing a k-bit by a k-bit integer all work in time O(k1.6) or better (most are much, much better, but have an overhead that makes them worse for "small big integers"). In that case preparing your initial list of powers and splitting once takes times O(k1.6). This gives you 2 problems of size O((k/2)1.6) = 2-0.6O(k1.6). At the next level you have 4 problems of size O((k/4)1.6) for another 2-1.2O(k1.6) work. Add up all of the terms and the powers of 2 turn into a geometric series converging to a constant, so the total work is O(k1.6).
This is a definite win, and the win will be very, very evident if you're working with numbers in the many thousands of digits.

Yes, it's probably somewhat inefficient. I'd probably just repeatedly divide by 10, adding together the remainders each time.

The first rule of performance optimization: Don't divide when you can multiply instead. The following function will take four digit numbers 0-9999 and do what you ask. The intermediate calculations are larger than 16 bits. We multiple the number by 1/10000 and take the result as a Q16 fixed point number. Digits are then extracted by multiplication by 10 and taking the integer part.
#define TEN_OVER_10000 ((1<<25)/1000 +1) // .001 Q25
int sum_digits(unsigned int n)
{
int c;
int sum = 0;
n = (n * TEN_OVER_10000)>>9; // n*10/10000 Q16
for (c=0;c<4;c++)
{
printf("Digit: %d\n", n>>16);
sum += n>>16;
n = (n & 0xffff) * 10; // next digit
}
return sum;
}
This can be extended to larger sizes but its tricky. You need to ensure that the rounding in the fixed point calculation always works correctly. I also did 4 digit numbers so the intermediate result of the fixed point multiply would not overflow.

Int64 BigNumber = 9223372036854775807;
String BigNumberStr = BigNumber.ToString();
int Sum = 0;
foreach (Char c in BigNumberStr)
Sum += (byte)c;
// 48 is ascii value of zero
// remove in one step rather than in the loop
Sum -= 48 * BigNumberStr.Length;

Instead of int.parse, why not subtract '0' from each digit to get the actual value.
Remember, '9' - '0' = 9, so you should be able to do this in order k (length of the number). The subtraction is just one operation, so that should not slow things down.

How can I best generate a static array of random number on demand?

An application I'm working on requires a matrix of random numbers. The matrix can grow in any direction at any time, and isn't always full. (I'll probably end up re-implementing it with a quad tree or something else, rather than a matrix with a lot of null objects.)
I need a way to generate the same matrix, given the same seed, no matter in which order I calculate the matrix.
LazyRandomMatrix rndMtx1 = new LazyRandomMatrix(1234) // Seed new object
float X = rndMtx1[0,0] // Lazily generate random numbers on demand
float Y = rndMtx1[3,16]
float Z = rndMtx1[23,-5]
Debug.Assert(X == rndMtx1[0,0])
Debug.Assert(Y == rndMtx1[3,16])
Debug.Assert(Z == rndMtx1[23,-5])
LazyRandomMatrix rndMtx2 = new LazyRandomMatrix(1234) // Seed second object
Debug.Assert(Y == rndMtx2[3,16]) // Lazily generate the same random numbers
Debug.Assert(Z == rndMtx2[23,-5]) // on demand in a different order
Debug.Assert(X == rndMtx2[0,0])
Yes, if I knew the dimensions of the array, the best way would be to generate the entire array, and just return values, but they need to be generated independently and on demand.
My first idea was to initialize a new random number generator for each call to a new coordinate, seeding it with some hash of the overall matrix's seed and the coordinates used in calling, but this seems like a terrible hack, as it would require creating a ton of new Random objects.

What you're talking about is typically called "Perlin Noise", here's a link for you: http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
The most important thing in that article is the noise function in 2D:
function Noise1(integer x, integer y)
n = x + y * 57
n = (n<<13) ^ n;
return ( 1.0 - ( (n * (n * n * 15731 + 789221) + 1376312589) & 7fffffff) / 1073741824.0);
end function
It returns a number between -1.0 and +1.0 based on the x and y coordonates alone (and a hard coded seed that you can change randomly at the start of your app or just leave it as it is).
The rest of the article is about interpolating these numbers, but depending on how random you want these numbers, you can just leave them as it is. Note that these numbers will be utterly random. If you instead apply a Cosine Interpolator and use the generated noise every 5-6 indexes, interpolating inbetween, you get heightmap data (which is what I used it for). Skip it for totally random data.

Standart random generator usually is generator of sequence, where each next element is build from previous. So to generate rndMtx1[3,16] you have to generate all previous elements in a sequence.
Actually you need something different from random generator, because you need only one value, but not the sequence. You have to build your own "generator" which uses seed and indexes as input for formula to produce single random value. You can invent many ways to do so. One of the simplest way is to take random value asm hash(seed + index) (I guess idea of hashes used in passwords and signing is to produce some stable "random" value out of input data).
P.S. You can improve your approach with independent generators (Random(seed + index)) by making lazy blocks of matrix.

I think your first idea of instantiating a new Random object seeded by some deterministic hash of (x-coordinate, y-coordinate, LazyRandomMatrix seed) is probably reasonable for most situations. In general, creating lots of small objects on the managed heap is something the CLR is very good at handling efficiently. And I don't think Random.ctor() is terribly expensive. You can easily measure the performance if it's a concern.
A very similar solution which may be easier than creating a good deterministic hash is to use two Random objects each time. Something like:
public int this[int x, int y]
{
get
{
Random r1 = new Random(_seed * x);
Random r2 = new Random(y);
return (r1.Next() ^ r2.Next());
}
}

Here is a solution based on a SHA1 hash. Basically this takes the bytes for the X, Y and Seed values and packs this into a byte array. Then a hash for the byte array and the first 4 bytes of the hash used to generate an int. This should be pretty random.
public class LazyRandomMatrix
{
private int _seed;
private SHA1 _hashProvider = new SHA1CryptoServiceProvider();
public LazyRandomMatrix(int seed)
{
_seed = seed;
}
public int this[int x, int y]
{
get
{
byte[] data = new byte[12];
Buffer.BlockCopy(BitConverter.GetBytes(x), 0, data, 0, 4);
Buffer.BlockCopy(BitConverter.GetBytes(y), 0, data, 4, 4);
Buffer.BlockCopy(BitConverter.GetBytes(_seed), 0, data, 8, 4);
byte[] hash = _hashProvider.ComputeHash(data);
return BitConverter.ToInt32(hash, 0);
}
}
}

PRNGs can be built out of hash functions.
This is what e.g. MS Research did with parallelizing random number generation with MD5 or others with TEA on a GPU.
(In fact, PRNGs can be thought of as a hash function from (seed, state) => nextnumber.)
Generating massive amounts of random numbers on a GPU brings up similar problems.
(E.g., to make it parallel, there should not be a single shared state.)
Although it is more common in the crypto world, using a crypto hash, I have taken the liberty to use MurmurHash 2.0 for sake of speed and simplicity. It has very good statistical properties as a hash function. A related, but not identical test shows that it gives good results as a PRNG. (unless I have fsc#kd up something in the C# code, that is.:) Feel free to use any other suitable hash function; crypto ones (MD5, TEA, SHA) as well - though crypto hashes tend to be much slower.
public class LazyRandomMatrix
{
private uint seed;
public LazyRandomMatrix(int seed)
{
this.seed = (uint)seed;
}
public int this[int x, int y]
{
get
{
return MurmurHash2((uint)x, (uint)y, seed);
}
}
static int MurmurHash2(uint key1, uint key2, uint seed)
{
// 'm' and 'r' are mixing constants generated offline.
// They're not really 'magic', they just happen to work well.
const uint m = 0x5bd1e995;
const int r = 24;
// Initialize the hash to a 'random' value
uint h = seed ^ 8;
// Mix 4 bytes at a time into the hash
key1 *= m;
key1 ^= key1 >> r;
key1 *= m;
h *= m;
h ^= key1;
key2 *= m;
key2 ^= key2 >> r;
key2 *= m;
h *= m;
h ^= key2;
// Do a few final mixes of the hash to ensure the last few
// bytes are well-incorporated.
h ^= h >> 13;
h *= m;
h ^= h >> 15;
return (int)h;
}
}

A pseudo-random number generator is essentially a function that deterministically calculates a successor for a given value.
You could invent a simple algorithm that calculates a value from its neighbours. If a neighbour doesn't have a value yet, calculate its value from its respective neighbours first.
Something like this:
value(0,0) = seed
value(x+1,0) = successor(value(x,0))
value(x,y+1) = successor(value(x,y))
Example with successor(n) = n+1 to calculate value(2,4):
\ x 0 1 2
y +-------------------
0 | 627 628 629
1 | 630
2 | 631
3 | 632
4 | 633
This example algorithm is obviously not very good, but you get the idea.

You want a random number generator with random access to the elements, instead of sequential access. (Note that you can reduce your two coordinates into a single index i.e. by computing i = x + (y << 16).)
A cool example of such a generator is Blum Blum Shub, which is a cryptographically secure PRNG with easy random-access. Unfortunately, it is very slow.
A more practical example is the well-known linear congruential generator. You can easily modify one to allow random access. Consider the definition:
X(0) = S
X(n) = B + X(n-1)*A (mod M)
Evaluating this directly would take O(n) time (that's pseudo linear, not linear), but you can convert to a non-recursive form:
//Expand a few times to see the pattern:
X(n) = B + X(n-1)*A (mod M)
X(n) = B + (B + X(n-2)*A)*A (mod M)
X(n) = B + (B + (B + X(n-3)*A)*A)*A (mod M)
//Aha! I see it now, and I can reduce it to a closed form:
X(n) = B + B*A + B*A*A + ... + B*A^(N-1) + S*A^N (mod M)
X(n) = S*A^N + B*SUM[i:0..n-1](A^i) (mod M)
X(n) = S*A^N + B*(A^N-1)/(A-1) (mod M)
That last equation can be computed relatively quickly, although the second part of it is a bit tricky to get right (because division doesn't distribute over mod the same way addition and multiplication do).

As far as I see, there are 2 basic algorithms possible here:
Generate a new random number based on func(seed, coord) for each coord
Generate a single random number from seed, and then transform it for the coord (something like rotate(x) + translate(y) or whatever)
In the first case, you have the problem of always generating new random numbers, although this may not be as expensive as you fear.
In the second case, the problem is that you may lose randomness during your transformation operations. However, in either case the result is reproducible.

Quick and Simple Hash Code Combinations

Can people recommend quick and simple ways to combine the hash codes of two objects. I am not too worried about collisions since I have a Hash Table which will handle that efficiently I just want something that generates a code quickly as possible.
Reading around SO and the web there seem to be a few main candidates:
XORing
XORing with Prime Multiplication
Simple numeric operations like multiplication/division (with overflow checking or wrapping around)
Building a String and then using the String classes Hash Code method
What would people recommend and why?

I would personally avoid XOR - it means that any two equal values will result in 0 - so hash(1, 1) == hash(2, 2) == hash(3, 3) etc. Also hash(5, 0) == hash(0, 5) etc which may come up occasionally. I have deliberately used it for set hashing - if you want to hash a sequence of items and you don't care about the ordering, it's nice.
I usually use:
unchecked
{
int hash = 17;
hash = hash * 31 + firstField.GetHashCode();
hash = hash * 31 + secondField.GetHashCode();
return hash;
}
That's the form that Josh Bloch suggests in Effective Java. Last time I answered a similar question I managed to find an article where this was discussed in detail - IIRC, no-one really knows why it works well, but it does. It's also easy to remember, easy to implement, and easy to extend to any number of fields.

If you are using .NET Core 2.1 or later or .NET Framework 4.6.1 or later, consider using the System.HashCode struct to help with producing composite hash codes. It has two modes of operation: Add and Combine.
An example using Combine, which is usually simpler and works for up to eight items:
public override int GetHashCode()
{
return HashCode.Combine(object1, object2);
}
An example of using Add:
public override int GetHashCode()
{
var hash = new HashCode();
hash.Add(this.object1);
hash.Add(this.object2);
return hash.ToHashCode();
}
Pros:
Part of .NET itself, as of .NET Core 2.1/.NET Standard 2.1 (though, see con below)
For .NET Framework 4.6.1 and later, the Microsoft.Bcl.HashCode NuGet package can be used to backport this type.
Looks to have good performance and mixing characteristics, based on the work the author and the reviewers did before merging this into the corefx repo
Handles nulls automatically
Overloads that take IEqualityComparer instances
Cons:
Not available on .NET Framework before .NET 4.6.1. HashCode is part of .NET Standard 2.1. As of September 2019, the .NET team has no plans to support .NET Standard 2.1 on the .NET Framework, as .NET Core/.NET 5 is the future of .NET.
General purpose, so it won't handle super-specific cases as well as hand-crafted code

While the template outlined in Jon Skeet's answer works well in general as a hash function family, the choice of the constants is important and the seed of 17 and factor of 31 as noted in the answer do not work well at all for common use cases. In most use cases, the hashed values are much closer to zero than int.MaxValue, and the number of items being jointly hashed are a few dozen or less.
For hashing an integer tuple {x, y} where -1000 <= x <= 1000 and -1000 <= y <= 1000, it has an abysmal collision rate of almost 98.5%. For example, {1, 0} -> {0, 31}, {1, 1} -> {0, 32}, etc. If we expand the coverage to also include n-tuples where 3 <= n <= 25, it does less terrible with a collision rate of about 38%. But we can do much better.
public static int CustomHash(int seed, int factor, params int[] vals)
{
int hash = seed;
foreach (int i in vals)
{
hash = (hash * factor) + i;
}
return hash;
}
I wrote a Monte Carlo sampling search loop that tested the method above with various values for seed and factor over various random n-tuples of random integers i. Allowed ranges were 2 <= n <= 25 (where n was random but biased toward the lower end of the range) and -1000 <= i <= 1000. At least 12 million unique collision tests were performed for each seed and factor pair.
After about 7 hours running, the best pair found (where the seed and factor were both limited to 4 digits or less) was: seed = 1009, factor = 9176, with a collision rate of 0.1131%. In the 5- and 6-digit areas, even better options exist. But I selected the top 4-digit performer for brevity, and it peforms quite well in all common int and char hashing scenarios. It also seems to work fine with integers of much greater magnitudes.
It is worth noting that "being prime" did not seem to be a general prerequisite for good performance as a seed and/or factor although it likely helps. 1009 noted above is in fact prime, but 9176 is not. I explicitly tested variations on this where I changed factor to various primes near 9176 (while leaving seed = 1009) and they all performed worse than the above solution.
Lastly, I also compared against the generic ReSharper recommendation function family of hash = (hash * factor) ^ i; and the original CustomHash() as noted above seriously outperforms it. The ReSharper XOR style seems to have collision rates in the 20-30% range for common use case assumptions and should not be used in my opinion.

Use the combination logic in tuple. The example is using c#7 tuples.
(field1, field2).GetHashCode();

I presume that .NET Framework team did a decent job in testing their System.String.GetHashCode() implementation, so I would use it:
// System.String.GetHashCode(): http://referencesource.microsoft.com/#mscorlib/system/string.cs,0a17bbac4851d0d4
// System.Web.Util.StringUtil.GetStringHashCode(System.String): http://referencesource.microsoft.com/#System.Web/Util/StringUtil.cs,c97063570b4e791a
public static int CombineHashCodes(IEnumerable<int> hashCodes)
{
int hash1 = (5381 << 16) + 5381;
int hash2 = hash1;
int i = 0;
foreach (var hashCode in hashCodes)
{
if (i % 2 == 0)
hash1 = ((hash1 << 5) + hash1 + (hash1 >> 27)) ^ hashCode;
else
hash2 = ((hash2 << 5) + hash2 + (hash2 >> 27)) ^ hashCode;
++i;
}
return hash1 + (hash2 * 1566083941);
}
Another implementation is from System.Web.Util.HashCodeCombiner.CombineHashCodes(System.Int32, System.Int32) and System.Array.CombineHashCodes(System.Int32, System.Int32) methods. This one is simpler, but probably doesn't have such a good distribution as the method above:
// System.Web.Util.HashCodeCombiner.CombineHashCodes(System.Int32, System.Int32): http://referencesource.microsoft.com/#System.Web/Util/HashCodeCombiner.cs,21fb74ad8bb43f6b
// System.Array.CombineHashCodes(System.Int32, System.Int32): http://referencesource.microsoft.com/#mscorlib/system/array.cs,87d117c8cc772cca
public static int CombineHashCodes(IEnumerable<int> hashCodes)
{
int hash = 5381;
foreach (var hashCode in hashCodes)
hash = ((hash << 5) + hash) ^ hashCode;
return hash;
}

This is a repackaging of Special Sauce's brilliantly researched solution.
It makes use of Value Tuples (ITuple).
This allows defaults for the parameters seed and factor.
public static int CombineHashes(this ITuple tupled, int seed=1009, int factor=9176)
{
var hash = seed;
for (var i = 0; i < tupled.Length; i++)
{
unchecked
{
hash = hash * factor + tupled[i].GetHashCode();
}
}
return hash;
}
Usage:
var hash1 = ("Foo", "Bar", 42).CombineHashes();
var hash2 = ("Jon", "Skeet", "Constants").CombineHashes(seed=17, factor=31);

If your input hashes are the same size, evenly distributed and not related to each other then an XOR should be OK. Plus it's fast.
The situation I'm suggesting this for is where you want to do
H = hash(A) ^ hash(B); // A and B are different types, so there's no way A == B.
of course, if A and B can be expected to hash to the same value with a reasonable (non-negligible) probability, then you should not use XOR in this way.

If you're looking for speed and don't have too many collisions, then XOR is fastest. To prevent a clustering around zero, you could do something like this:
finalHash = hash1 ^ hash2;
return finalHash != 0 ? finalHash : hash1;
Of course, some prototyping ought to give you an idea of performance and clustering.

Assuming you have a relevant toString() function (where your different fields shall appear), I would just return its hashcode:
this.toString().hashCode();
This is not very fast, but it should avoid collisions quite well.

I would recommend using the built-in hash functions in System.Security.Cryptography rather than rolling your own.