Redis hash function and data partition

As it is known, Redis uses the CRC16 algorithm to map keys to hash slots. Is it safe to assume that crc uses some kind of "distribution" in order to assign keys to nodes? And if yes, what kind of distribution?

Also, with the hash function on every key, can we ensure that we have an evenly load on the nodes concerning the amount of keys? Suppose that a client make 3000 insertions random, in a 3 nodes cluster. After that, the keys will be evenly distributed in the nodes (M1 ≈ 1000, M2 ≈ 1000, M3 ≈ 1000)?

To test these, i created a function in python:

list1= []
list2= []
list3= []

def RedisClusterCRC16(keysslot):

    XMODEMCRC16Lookup = [
        0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50a5, 0x60c6, 0x70e7,
        0x8108, 0x9129, 0xa14a, 0xb16b, 0xc18c, 0xd1ad, 0xe1ce, 0xf1ef,
        0x1231, 0x0210, 0x3273, 0x2252, 0x52b5, 0x4294, 0x72f7, 0x62d6,
        0x9339, 0x8318, 0xb37b, 0xa35a, 0xd3bd, 0xc39c, 0xf3ff, 0xe3de,
        0x2462, 0x3443, 0x0420, 0x1401, 0x64e6, 0x74c7, 0x44a4, 0x5485,
        0xa56a, 0xb54b, 0x8528, 0x9509, 0xe5ee, 0xf5cf, 0xc5ac, 0xd58d,
        0x3653, 0x2672, 0x1611, 0x0630, 0x76d7, 0x66f6, 0x5695, 0x46b4,
        0xb75b, 0xa77a, 0x9719, 0x8738, 0xf7df, 0xe7fe, 0xd79d, 0xc7bc,
        0x48c4, 0x58e5, 0x6886, 0x78a7, 0x0840, 0x1861, 0x2802, 0x3823,
        0xc9cc, 0xd9ed, 0xe98e, 0xf9af, 0x8948, 0x9969, 0xa90a, 0xb92b,
        0x5af5, 0x4ad4, 0x7ab7, 0x6a96, 0x1a71, 0x0a50, 0x3a33, 0x2a12,
        0xdbfd, 0xcbdc, 0xfbbf, 0xeb9e, 0x9b79, 0x8b58, 0xbb3b, 0xab1a,
        0x6ca6, 0x7c87, 0x4ce4, 0x5cc5, 0x2c22, 0x3c03, 0x0c60, 0x1c41,
        0xedae, 0xfd8f, 0xcdec, 0xddcd, 0xad2a, 0xbd0b, 0x8d68, 0x9d49,
        0x7e97, 0x6eb6, 0x5ed5, 0x4ef4, 0x3e13, 0x2e32, 0x1e51, 0x0e70,
        0xff9f, 0xefbe, 0xdfdd, 0xcffc, 0xbf1b, 0xaf3a, 0x9f59, 0x8f78,
        0x9188, 0x81a9, 0xb1ca, 0xa1eb, 0xd10c, 0xc12d, 0xf14e, 0xe16f,
        0x1080, 0x00a1, 0x30c2, 0x20e3, 0x5004, 0x4025, 0x7046, 0x6067,
        0x83b9, 0x9398, 0xa3fb, 0xb3da, 0xc33d, 0xd31c, 0xe37f, 0xf35e,
        0x02b1, 0x1290, 0x22f3, 0x32d2, 0x4235, 0x5214, 0x6277, 0x7256,
        0xb5ea, 0xa5cb, 0x95a8, 0x8589, 0xf56e, 0xe54f, 0xd52c, 0xc50d,
        0x34e2, 0x24c3, 0x14a0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405,
        0xa7db, 0xb7fa, 0x8799, 0x97b8, 0xe75f, 0xf77e, 0xc71d, 0xd73c,
        0x26d3, 0x36f2, 0x0691, 0x16b0, 0x6657, 0x7676, 0x4615, 0x5634,
        0xd94c, 0xc96d, 0xf90e, 0xe92f, 0x99c8, 0x89e9, 0xb98a, 0xa9ab,
        0x5844, 0x4865, 0x7806, 0x6827, 0x18c0, 0x08e1, 0x3882, 0x28a3,
        0xcb7d, 0xdb5c, 0xeb3f, 0xfb1e, 0x8bf9, 0x9bd8, 0xabbb, 0xbb9a,
        0x4a75, 0x5a54, 0x6a37, 0x7a16, 0x0af1, 0x1ad0, 0x2ab3, 0x3a92,
        0xfd2e, 0xed0f, 0xdd6c, 0xcd4d, 0xbdaa, 0xad8b, 0x9de8, 0x8dc9,
        0x7c26, 0x6c07, 0x5c64, 0x4c45, 0x3ca2, 0x2c83, 0x1ce0, 0x0cc1,
        0xef1f, 0xff3e, 0xcf5d, 0xdf7c, 0xaf9b, 0xbfba, 0x8fd9, 0x9ff8,
         0x6e17, 0x7e36, 0x4e55, 0x5e74, 0x2e93, 0x3eb2, 0x0ed1, 0x1ef0
    ]

    crc = 0
    for byte in keysslot.encode( "utf-8" ):
        crc = ((crc << 8) & 0xff00) ^ XMODEMCRC16Lookup[((crc >> 8) &  0xff) ^ ord( byte )]





    metr1=0
    metr2=0
    metr3=0

    if ((crc & 0xffff)% 16384) <= 5460:
        metr1 = metr1+1
        list1.append(metr1)
    elif  (((crc & 0xffff)% 16384) > 5460) and (((crc & 0xffff)% 16384) <= 10922):
        metr2 = metr2+1
        list2.append(metr2)
    else:
        metr3 = metr3+1
        list3.append(metr3)





for i in range(2000000):
    RedisClusterCRC16(str(i))


print "M1 holds: ", sum(list1)
print "M2 holds: ", sum(list2)
print "M3 holds: ", sum(list3)

With input 2000000 the results are:

M1 holds:  666625
M2 holds:  666744
M3 holds:  666631

I observe that the distribution of slots are near-equal on every node (pseudo-node in this example).

Solution

After search i found proofs:

A hash function maps keys to small integers (buckets). An ideal hash function maps the keys to the integers in a random-like manner, so that bucket values are evenly distributed even if there are regularities in the input data.

This process can be divided into two steps:

Map the key to an integer.
Map the integer to a bucket.

Also, here: https://en.wikipedia.org/wiki/Hash_function, explains Uniformity and says that "This method (crc) may produce a sufficiently uniform distribution of hash values, as long as the hash range size n is small compared to the range of the checksum or fingerprint function".

With that things in mind and with the execution code above, it is clear that crc may produce a uniform distribution of hash values.