hashing a small number to a random looking 64 bit integer

Question

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 dis

Answer 1

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

Answer 2

1,000 * 1,000 = 1,000,000. That fits well within an Int32.

Subtract the low bound of your range, from the number. Square it, and use it as a direct subscript into some sort of bitmap.

Answer 3

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.

Answer 4

Given: input i in the range of 0 to 1,000.

const MaxInt which is the maximum value that cna be contained in a 64 bit int. (you did not say if it is signed or unsigned; 2^64 = 18446744073709551616 )

and a function rand() that returns a value between 0 and 1 (most languages have such a function)

compute hashvalue = i * rand() * ( MaxInt / 1000 )