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I am looking for a hash-function which operates on a small integer (say in the range 0...1000) and outputs a 64 bit int.
The result-set should look like a random distribution of 64 bit ints: a uniform distribution with no linear correlation between the results.
I was hoping for a function that only takes a few CPU-cycles to execute. (the code will be in C++).
I considered multiplying the input by a big prime number and taking the modulo 2**64 (something like a linear congruent generator), but there are obvious dependencies between the outputs (in the lower bits).
Googling did not show up anything, but I am probably using wrong search terms.
Does such a function exist?
Some Background-info:
I want to avoid using a big persistent table with pseudo random numbers in an algorithm, and calculate random-looking numbers on the fly.
Security is not an issue.
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The most commonly used method for hashing integers is called modular hashing: we choose the array size M to be prime, and, for any positive integer key k, compute the remainder when dividing k by M. This function is very easy to compute (k % M, in Java), and is effective in dispersing the keys evenly between 0 and M-1.
A technique for randomizing the input to a cryptographic hash function. Source(s): NIST SP 800-106. A process by which the input to a hash function is randomized before being processed by the hash function. Source(s):
The 32-bit long hash value is a hexadecimal number of 8 characters. MD4 is a Message Digest Algorithm developed by Ronald L. Rivest from RSA Data Security, Inc. Currently it's considered insecure, but it's very fast on 32-bit mashines and it's used for calculating EDonkey 2000 hashes in the EDonkey p2p network.
If you use a random function instead of the hash function, you'll always end with all bits set to 1 (like in the case L≫1), and you cannot use it to approximate the number of distinct elements.
I tested the 64-bit finalizer of MurmurHash3 (suggested by @aix and this SO post). This gives zero if the input is zero, so I increased the input parameter by 1 first:
typedef unsigned long long uint64;
inline uint64 fasthash(uint64 i)
{
i += 1ULL;
i ^= i >> 33ULL;
i *= 0xff51afd7ed558ccdULL;
i ^= i >> 33ULL;
i *= 0xc4ceb9fe1a85ec53ULL;
i ^= i >> 33ULL;
return i;
}
Here the input argument i is a small integer, for example an element of {0, 1, ..., 1000}. The output looks random:
i fasthash(i) decimal: fasthash(i) hex:
0 12994781566227106604 0xB456BCFC34C2CB2C
1 4233148493373801447 0x3ABF2A20650683E7
2 815575690806614222 0x0B5181C509F8D8CE
3 5156626420896634997 0x47900468A8F01875
... ... ...
There is no linear correlation between subsequent elements of the series:
The range of both axes is 0..2^64-1
61
Why not use an existing hash function, such as MurmurHash3 with a 64-bit finalizer? According to the author, the function takes tens of CPU cycles per key on current Intel hardware.
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