Comparison operators give wrong results with keyset pagination

Question

I implemented keyset pagination on these tables

CREATE TABLE profiles (
    id serial primary key,
    username varchar(255),
    followers bigint,
    tsv tsvector
);

CREATE TABLE profile_categories (
    username varchar(255),
    category varchar(255),
    primary key (username, category)
);

with the following query:

SELECT profiles.*, categories,
       ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers) AS rank
  FROM profiles
  JOIN plainto_tsquery($1) AS q ON tsv @@ q
  LEFT OUTER JOIN profile_categories ON profiles.username = profiles_categories.username
  WHERE followers IS NOT NULL AND
    followers > 0 AND
    (ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers), -id) < ($2, $3)
  ORDER BY (
    ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers),
    -id
  ) DESC
  LIMIT 50;

The idea is to use ts_rank_cd to rank documents with full-text search queries, and to scale the rank by the logarithm of the followers.

The problem is that when I query for the second page by supplying the last rank and id ($2 and $3) of the previous page, I still get the last result from the previous page as the first result (so I effectively get only 49 new results)! I have no idea how this is possible since I'm using strict inequality operators.

EDIT Even if I cast the ranks to decimal the same problem persists -- I get duplicates results at the end of one page and at the start of the next:

SELECT profiles.*, categories,
       (ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal AS rank
  FROM profiles
  JOIN plainto_tsquery($1) AS q ON tsv @@ q
  WHERE followers IS NOT NULL AND
    followers > 0 AND
    ((ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal, -id) < ($2, $3)
  ORDER BY (
    (ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal,
    -id
  ) DESC
  LIMIT 50

Answer 1

Floating point numbers are subject to representation/rounding errors. When translated to the client and back again, it is unlikely to be exactly equal to the original.

Answer 2

I solved the issue by explicitly excluding the id corresponding to the last seen id (the addition is highlighted in bold):

SELECT profiles.*, categories,
       (ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal AS rank
  FROM profiles
  JOIN plainto_tsquery($1) AS q ON tsv @@ q
  WHERE followers IS NOT NULL AND
    followers > 0 AND
    id <> $3
    ((ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal, -id) < ($2, $3)
  ORDER BY (
    (ts_rank_cd(tsv, plainto_tsquery($1)) * log(followers))::decimal,
    -id
  ) DESC
  LIMIT 50;