Related
Why does List<T> increase its capacity by a factor of 2?
private void EnsureCapacity(int min)
{
if (this._items.Length < min)
{
int num = (this._items.Length == 0) ? 4 : (this._items.Length * 2);
if (num < min)
{
num = min;
}
this.Capacity = num;
}
}
Why does Dictionary<K,V> use prime numbers as capacity?
private void Resize()
{
int prime = HashHelpers.GetPrime(this.count * 2);
int[] numArray = new int[prime];
for (int i = 0; i < numArray.Length; i++)
{
numArray[i] = -1;
}
Entry<TKey, TValue>[] destinationArray = new Entry<TKey, TValue>[prime];
Array.Copy(this.entries, 0, destinationArray, 0, this.count);
for (int j = 0; j < this.count; j++)
{
int index = destinationArray[j].hashCode % prime;
destinationArray[j].next = numArray[index];
numArray[index] = j;
}
this.buckets = numArray;
this.entries = destinationArray;
}
Why doesn't it also just multiply by 2? Both are dealing with finding continues memory location...correct?
It's common to use prime numbers for hash table sizes because it reduces the probability of collisions.
Hash tables typically use the modulo operation to find the bucket where an entry belongs, as you can see in your code:
int index = destinationArray[j].hashCode % prime;
Suppose your hashCode function results in the following hashCodes among others {x , 2x, 3x, 4x, 5x, 6x...}, then all these are going to be clustered in just m number of buckets, where m = table_length/GreatestCommonFactor(table_length, x). (It is trivial to verify/derive this). Now you can do one of the following to avoid clustering:
Make sure that you don't generate too many hashCodes that are multiples of another hashCode like in {x, 2x, 3x, 4x, 5x, 6x...}.But this may be kind of difficult if your hashTable is supposed to have millions of entries.
Or simply make m equal to the table_length by making GreatestCommonFactor(table_length, x) equal to 1, i.e by making table_length coprime with x. And if x can be just about any number then make sure that table_length is a prime number.
(from http://srinvis.blogspot.com/2006/07/hash-table-lengths-and-prime-numbers.html)
HashHelpers.GetPrime(this.count * 2)
should return a prime number. Look at the definition of HashHelpers.GetPrime().
Dictionary puts all its objects into buckets depending on their GetHashCode value, i.e.
Bucket[object.GetHashCode() % DictionarySize] = object;
It uses a prime number for size to avoid the chance of collisions. Presumably a size with many divisors would be bad for poorly designed hash codes.
From a question in SO;
Dictionary or hash table relies on hashing the key to get a smaller
index to look up into corresponding store (array). So choice of hash
function is very important. Typical choice is to get hash code of a
key (so that we get good random distribution) and then divide the code
by a prime number and use reminder to index into fixed number of
buckets. This allows to convert arbitrarily large hash codes into a
bounded set of small numbers for which we can define an array to look
up into. So its important to have array size in prime number and then
the best choice for the size become the prime number that is larger
than the required capacity. And that's exactly dictionary
implementation does.
List<T> employs arrays to store data; and increasing the capacity of an array requires copying the array to a new memory location; which is time consuming. I guess, in order to lower the occurence of copying arrays, list doubles it's capacity.
I'm not computer scientist, but ...
Most probabbly its related to a HashTable's Load factor (the last link just a math definition), and for not creating more confusion, for not math auditory, it's important to define that:
loadFactor = FreeCells/AllCells
this we can write as
loadFactor = (AllBuckets - UsedBuckets)/AllBuckets
loadFactor defines a probabbilty of collision in hash map.
So by using a Prime Number,a number that
..is a natural number greater than 1 that
has no positive divisors other than 1 and itself.
we decrease (but do not erase) a risk of collision in our hashmap.
If loadFactor tends to 0, we have more secure hashmap, so we always has to keep it as low as possible. By MS blog, they found out that the value of that loadFactor (optimal one) has to be arround 0.72, so if it becomes bigger, we increase the capacity following nearest prime number.
EDIT
To be more clear on this: having a prime number, ensures, as mush as it possible, uniform destribution of the hashes in this concrete implementation of the hash we have in .NET dictionary. It's not about efficency of the retrieval of the values, but efficiency of the memory used and collision risk reduction.
Hope this helps.
Dictionary needs some heuristic so that hash code distribution among buckets is more uniform.
.NET's Dictionary uses prime number of buckets to do that, and then calculates bucket index like this:
int num = this.comparer.GetHashCode(key) & 2147483647; // make hash code positive
// get the remainder from division - that's our bucket index
int num2 = this.buckets[num % ((int)this.buckets.Length)];
When it grows, it doubles the number of buckets and then adds some more to make the number prime again.
It's not the only heuristic possible. Java's HashMap, for example, takes another approach. The number of buckets there is always a power of 2 and on grow it just doubles the number of buckets:
resize(2 * table.length);
But when calculating bucket index it modifies hash:
static int hash(int h) {
// This function ensures that hashCodes that differ only by
// constant multiples at each bit position have a bounded
// number of collisions (approximately 8 at default load factor).
h ^= (h >>> 20) ^ (h >>> 12);
return h ^ (h >>> 7) ^ (h >>> 4);
}
static int indexFor(int h, int length) {
return h & (length-1);
}
// from put() method
int hash = hash(key.hashCode()); // get modified hash
int i = indexFor(hash, table.length); // trim the hash to the bucket count
List on the other hand doesn't need any heuristic, so they didn't bother.
Addition: Grow behavior doesn't influence Add's complexity at all. Dictionary, HashMap and List each have amortized Add complexity of O(1).
Grow operation takes O(N) but occurs only N-th time, so to cause grow operation we need to call Add N times. For N=8 the time it takes to do N Adds has the value
O(1)+O(1)+O(1)+O(1)+O(1)+O(1)+O(1)+O(N) = O(N)+O(N) = O(2N) = O(N)
So, N Adds take O(N), then one Add takes O(1).
Increasing the capacity by a constant factor (instead of for example increasing the capacity by a additive constant) when resizing is required to guarantee some amortized running times. For example adding to or removing from the end of an array based list requires O(1) time except when you have to increase or decrease the capacity requiring to copy the list content and therefore requiring O(n) time. Changing the capacity by a constant factor guarantees that the amortized runtime is still O(1). The optimal value of the factor depends on the expected usage. Some more information on Wikipedia.
Choosing the capacity of a hash table to be prime is used to improve the distribution of the items. bucket[hash % capacity] will yield a more uniform distribution if hash is not uniformly distributed if capacity is prime. (I can not give the math behind that but I am looking for a good reference.) The combination of this with the first point is exactly what the implementation does - increasing the capacity by a factor (of at least) 2 and also ensure that the capacity is prime.
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.
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.
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.
I'm need a pseudo-random generator which takes a number as input and returns another number witch is reproducible and seems to be random.
Each input number should match to exactly one output number and vice versa
same input numbers always result in same output numbers
sequential input numbers that are close together (eg. 1 and 2) should produce completely different output numbers (eg. 1 => 9783526, 2 => 283)
It must not be perfect, it's just to create random but reproducible test data.
I use C#.
I wrote this funny piece of code some time ago which produced something random.
public static long Scramble(long number, long max)
{
// some random values
long[] scramblers = { 3, 5, 7, 31, 343, 2348, 89897 };
number += (max / 7) + 6;
number %= max;
// shuffle according to divisibility
foreach (long scrambler in scramblers)
{
if (scrambler >= max / 3) break;
number = ((number * scrambler) % max)
+ ((number * scrambler) / max);
}
return number % max;
}
I would like to have something better, more reliable, working with any size of number (no max argument).
Could this probably be solved using a CRC algorithm? Or some bit shuffling stuff.
I remove the microsoft code from this answer, the GNU code file is a lot longer but basically it contains this from http://cs.uccs.edu/~cs591/bufferOverflow/glibc-2.2.4/stdlib/random_r.c :
int32_t val = state[0];
val = ((state[0] * 1103515245) + 12345) & 0x7fffffff;
state[0] = val;
*result = val;
for your purpose, the seed is state[0] so it would look more like
int getRand(int val)
{
return ((val * 1103515245) + 12345) & 0x7fffffff;
}
You (maybe) can do this easily in C# using the Random class:
public int GetPseudoRandomNumber(int input)
{
Random random = new Random(input);
return random.Next();
}
Since you're explicitly seeding Random with the input, you will get the same output every time given the same input value.
A tausworthe generator is simple to implement and pretty fast. The following pseudocode implementation has full cycle (2**31 - 1, because zero is a fixed point):
def tausworthe(seed)
seed ^= seed >> 13
seed ^= seed << 18
return seed & 0x7fffffff
I don't know C#, but I'm assuming it has XOR (^) and bit shift (<<, >>) operators as in C.
Set an initial seed value, and invoke with seed = tausworthe(seed).
The first two rules suggest a fixed or input-seeded permutation of the input, but the third rule requires a further transform.
Is there any further restriction on what the outputs should be, to guide that transform? - e.g. is there an input set of output values to choose from?
If the only guide is "no max", I'd use the following...
Apply a hash algorithm to the whole input to get the first output item. A CRC might work, but for more "random" results, use a crypto hash algorithm such as MD5.
Use a next permutation algorithm (plenty of links on Google) on the input.
Repeat the hash-then-next-permutation until all required outputs are found.
The next permutation may be overkill though, you could probably just increment the first input (and maybe, on overflow, increment the second and so on) before redoing the hash.
For crypto-style hashing, you'll need a key - just derive something from the input before you start.