Pseudoisotopy theorem

30 year-old Entertainer or Range Artist Wesley from Drumheller, really loves vehicle, property developers properties for sale in singapore singapore and horse racing. Finds inspiration by traveling to Works of Antoni Gaudí. MurmurHash is a non-cryptographic hash function suitable for general hash-based lookup. It was created by Austin Appleby in 2008, and exists in a number of variants, all of which have been released into the public domain. When compared to other popular hash functions, MurmurHash performed well in a random distribution of regular keys.

Variants

The current version is MurmurHash3, which yields a 32-bit or 128-bit hash value.

The older MurmurHash2 yields a 32-bit or 64-bit value. Slower versions of MurmurHash2 are available for big-endian and aligned-only machines. The MurmurHash2A variant adds the Merkle–Damgård construction so that it can be called incrementally. There are two variants which generate 64-bit values; MurmurHash64A, which is optimized for 64-bit processors, and MurmurHash64B, for 32-bit ones. MurmurHash2-160 generates the 160-bit hash, and MurmurHash1 is obsolete.

Implementations

The canonical implementation is in C++, but there are efficient ports for a variety of popular languages, including Python, C, C#, Perl, Ruby, PHP, Haskell, Scala, Java, Erlang, and JavaScript.

It has been adopted into a number of open-source projects, most notably libstdc++ (ver 4.6), Perl, nginx (ver 1.0.1), Rubinius, libmemcached (the C driver for Memcached), maatkit, Hadoop, Kyoto Cabinet, RaptorDB, OlegDB, and Cassandra.

Algorithm

Murmur3_32(key, len, seed)
    // Note: In this version, all integer arithmetic is performed with unsigned 32 bit integers.
    //       In the case of overflow, the result is constrained by the application of modulo $2^{32}$ arithmetic.
    
    c1 $\gets$ 0xcc9e2d51
    c2 $\gets$ 0x1b873593
    r1 $\gets$ 15
    r2 $\gets$ 13
    m $\gets$ 5
    n $\gets$ 0xe6546b64
 
    hash $\gets$ seed

    for each fourByteChunk of key
        k $\gets$ fourByteChunk

        k $\gets$ k * c1
        k $\gets$ (k << r1) OR (k >> (32-r1))
        k $\gets$ k * c2

        hash $\gets$ hash XOR k
        hash $\gets$ (hash << r2) OR (hash >> (32-r2))
        hash $\gets$ hash * m + n

    with any remainingBytesInKey
        remainingBytes $\gets$ SwapEndianOrderOf(remainingBytesInKey)
        // Note: Endian swapping is only necessary on big-endian machines.
        //       The purpose is to place the meaningful digits towards the low end of the value,
        //       so that these digits have the greatest potential to affect the low range digits
        //       in the subsequent multiplication.  Consider that locating the meaningful digits
        //       in the high range would produce a greater effect upon the high digits of the
        //       multiplication, and notably, that such high digits are likely to be discarded
        //       by the modulo arithmetic under overflow.  We don't want that.
        
        remainingBytes $\gets$ remainingBytes * c1
        remainingBytes $\gets$ (remainingBytes << r1) OR (remainingBytes >> (32 - r1))
        remainingBytes $\gets$ remainingBytes * c2

        hash $\gets$ hash XOR remainingBytes
 
    hash $\gets$ hash XOR len

    hash $\gets$ hash XOR (hash >> 16)
    hash $\gets$ hash * 0x85ebca6b
    hash $\gets$ hash XOR (hash >> 13)
    hash $\gets$ hash * 0xc2b2ae35
    hash $\gets$ hash XOR (hash >> 16)

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

See also

• Fowler–Noll–Vo hash function
• Jenkins hash function
• CityHash