Same problem:

<verbatim>
  CREATE TABLE t1(a REAL);
  INSERT INTO t1 VALUES( 836627109860825358 );
  SELECT * FROM t1 WHERE a = CAST(836627109860825358 AS REAL); -- returns 1 row

  CREATE INDEX i1 ON t1(a);
  SELECT * FROM t1 WHERE a = CAST(836627109860825358 AS REAL); -- same query now returns 0 rows
</verbatim>