Hi Nicolas,
On 6/3/19, 7:48 am, "Nicolas Paris" wrote:
Hi Huon
Good catch. A 64 bit hash is definitely a useful function.
> the birthday paradox implies >50% chance of at least one for tables larger than 77000 rows
Do you know how many rows to have 50% chances for a 64 bit hash ?
5 billion: it's roughly equal to the square root of the total number of possible hash values. You can see detailed table at https://en.wikipedia.org/wiki/Birthday_problem#Probability_table .
Note, for my application a few collisions is fine. There's a few ways of trying to quantify this, and one is the maximum number of items that all hash to a single particular hash value: if one has 4 billion rows with 32-bit hash, the size of this largest set is likely to be 14 (and, there's going to be many other smaller sets of colliding values). With a 64-bit hash, it is likely to be 2, and the table size can be as large as ~8 trillion before the expected maximum exceeds 3. (https://en.wikipedia.org/wiki/Balls_into_bins_problem#Random_allocation)
Another way is the expected number of collisions, for the three cases above it is 1.6 billion (32-bit hash, 4 billion rows), 0.5 (64-bit, 4 billion), and 2.1 million (64-bit, 8 trillion). (http://matt.might.net/articles/counting-hash-collisions/)
About the seed column, to me there is no need for such an argument: you
just can add an integer as a regular column.
You are correct that this works, but it increases the amount of computation (doubles it, when just trying to hash a single column). For multiple columns, col1, col2, ... colN, the `hash` function works approximately like (in pseudo-scala, and simplified from Spark's actual implementation):
val InitialSeed = 42L
def hash(col1, col2, ..., colN) = {
var value = InitialSeed
value = hashColumn(col1, seed = value)
value = hashColumn(col2, seed = value)
...
value = hashColumn(colN, seed = value)
return value
}
If that starting value can be customized, then a call like `hash(lit(mySeed), column)` (which has to do the work to hash two columns) can be changed to instead just start at `mySeed`, and only hash one column. That said, for the hashes spark uses (xxHash and MurmurHash3), the hashing operation isn't too expensive, especially for ints/longs.
Huon
About the process for pull requests, I cannot help much
On Tue, Mar 05, 2019 at 04:30:31AM +0000, Huon.Wilson@data61.csiro.au wrote:
> Hi,
>
> I’m working on something that requires deterministic randomness, i.e. a row gets the same “random” value no matter the order of the DataFrame. A seeded hash seems to be the perfect way to do this, but the existing hashes have various limitations:
>
> - hash: 32-bit output (only 4 billion possibilities will result in a lot of collisions for many tables: the birthday paradox implies >50% chance of at least one for tables larger than 77000 rows)
> - sha1/sha2/md5: single binary column input, string output
>
> It seems there’s already support for a 64-bit hash function that can work with an arbitrary number of arbitrary-typed columns: XxHash64, and exposing this for DataFrames seems like it’s essentially one line in sql/functions.scala to match `hash` (plus docs, tests, function registry etc.):
>
> def hash64(cols: Column*): Column = withExpr { new XxHash64(cols.map(_.expr)) }
>
> For my use case, this can then be used to get a 64-bit “random” column like
>
> val seed = rng.nextLong()
> hash64(lit(seed), col1, col2)
>
> I’ve created a (hopefully) complete patch by mimicking ‘hash’ at https://github.com/apache/spark/compare/master...huonw:hash64; should I open a JIRA and submit it as a pull request?
>
> Additionally, both hash and the new hash64 already have support for being seeded, but this isn’t exposed directly and instead requires something like the `lit` above. Would it make sense to add overloads like the following?
>
> def hash(seed: Int, cols: Columns*) = …
> def hash64(seed: Long, cols: Columns*) = …
>
> Though, it does seem a bit unfortunate to be forced to pass the seed first.
>
> - Huon
>
>
>
>
> ---------------------------------------------------------------------
> To unsubscribe e-mail: user-unsubscribe@spark.apache.org
--
nicolas
---------------------------------------------------------------------
To unsubscribe e-mail: user-unsubscribe@spark.apache.org