Perform Hamming Distance Calculation on Signed 64bit integer in sqlite3

Question

i have a database that contains some signed 64bits integers, these were hash that we converted to signed integer for easy db operation, i want to perform the hamming distance calculation and return the top 5 hashes that are closest to the reference hash. but somehow i cant pull it off, using other databases is not an option now, here is the query i am currently struggling with.

WITH RECURSIVE HammingDistance AS (
  SELECT signed_hash,
         ABS(signed_hash - reference_signed_hash) AS xor_result,
         0 AS hamming_distance
  FROM hashdb
  UNION ALL
  SELECT signed_hash,
         xor_result >> 1,
         hamming_distance + (xor_result & 1)
  FROM HammingDistance
  WHERE xor_result > 0
)
SELECT signed_hash, hamming_distance
FROM HammingDistance
ORDER BY hamming_distance
LIMIT 5;

this is just me trying to see what sticks with the query, any help is appreciated.