Thanks for working on the feature! Most of it looks good!

I noticed that the time complexity of the function per-row is O(n^2) where n is the size of the array. We should mention that in the documentation. Additionally, the other issue is that if the array contains millions of elements, which is not very uncommon, the function will never finish executing.

There are some advanced O(nlogn) algorithms but they may be bit complicated which we can add later as an improvement. However, since normally users are only interested in the result of first few lags, we can offer them the signature arrayAutocorrelation(array, max_lag); then the time complexity will become O(n * max_lag). We can keep the max_lag optional and if it's not given then we compute result for all lags. In that way, if max_lag is small, our function will be still be useful even if array contains millions of elements.

Looks good. Previous issues are mostly resolved. I found some queries that do not work as expected:

If we mix const column (first argument) and non-const column for second argument, it cannot handle it. You can have a look at src/Functions/array/arrayDotProduct.cpp for an example of how to handle when one of the argument is constant.

SELECT arrayAutocorrelation([1,2,3], number) FROM numbers(3);

Gives:

Code: 44. DB::Exception: Argument must be an array: while executing function arrayAutocorrelation on arguments _CAST([1, 2, 3]_Array(UInt8), 'Array(UInt8)'_String) Array(UInt8) Const(size = 0, Array(size = 1, UInt64(size = 1), UInt8(size = 3))), __table1.number UInt64 UInt64(size = 0). (ILLEGAL_COLUMN)

Since we read max_lag via getInt(i), if we pass a big UInt64, we will wrap around and produce incorrect result silently.

SELECT arrayAutocorrelation([1, 2, 3], toUInt64('9223372036854775808'))

Gives incorrectly []. You can look at src/Functions/repeat.cpp for an example of how we can get the numbers column properly.

For the following query, I was expecting it to return [] because the rule seems to be output array length = min(array_size, max_lag) . But returns [nan].

SELECT arrayAutocorrelation([1], 0);