Hamming weight/population count in T-SQL

Question

I\'m looking for a fast way to calculate the hamming weight/population count/\"the number of 1 bits\" of a BINARY(1024) field. MySQL has a BIT_COUNT functio

Answer 1

You could use a helper table with precalculated Hamming weights for small numbers, like bytes, then split the value accordingly, join to the helper table and get the sum of partial Hamming weights as the value's Hamming weight:

-- define Hamming weight helper table
DECLARE @hwtally TABLE (byte tinyint, hw int);
INSERT INTO @hwtally (byte, hw) VALUES (0, 0);
INSERT INTO @hwtally (byte, hw) SELECT   1 - byte, 1 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT   3 - byte, 2 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT   7 - byte, 3 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT  15 - byte, 4 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT  31 - byte, 5 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT  63 - byte, 6 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT 127 - byte, 7 - hw FROM @hwtally;
INSERT INTO @hwtally (byte, hw) SELECT 255 - byte, 8 - hw FROM @hwtally;

-- calculate
WITH split AS (
  SELECT SUBSTRING(@value, number, 1) AS byte
  FROM master.dbo.spt_values
  WHERE type = 'P' AND number BETWEEN 1 AND LEN(@value)
)
SELECT
  Value = @value,
  HammingWeight = SUM(t.hw)
FROM split s
  INNER JOIN @hwtally t ON s.byte = t.byte