MySQL Manual
A Problems and Common Errors
A.5.7 Problems with Floating-Point Comparison
floating-point numbers cause confusion sometimes, because these numbers are not stored as exact values inside computer architecture. What one can see on the screen usually is not the exact value of the number.
Field types FLOAT, DOUBLE and DECIMAL are such.
CREATE TABLE t1 (i INT, d1 DECIMAL(9,2), d2 DECIMAL(9,2));
INSERT INTO t1 VALUES (1, 101.40, 21.40), (1, -80.00, 0.00),
(2, 0.00, 0.00), (2, -13.20, 0.00), (2, 59.60, 46.40),
(2, 30.40, 30.40), (3, 37.00, 7.40), (3, -29.60, 0.00),
(4, 60.00, 15.40), (4, -10.60, 0.00), (4, -34.00, 0.00),
(5, 33.00, 0.00), (5, -25.80, 0.00), (5, 0.00, 7.20),
(6, 0.00, 0.00), (6, -51.40, 0.00);
mysql> SELECT i, SUM(d1) AS a, SUM(d2) AS b
-> FROM t1 GROUP BY i HAVING a <> b;
+------+--------+-------+
| i | a | b |
+------+--------+-------+
| 1 | 21.40 | 21.40 |
| 2 | 76.80 | 76.80 |
| 3 | 7.40 | 7.40 |
| 4 | 15.40 | 15.40 |
| 5 | 7.20 | 7.20 |
| 6 | -51.40 | 0.00 |
+------+--------+-------+
The result is correct. Although the first five records look like they shouldn't pass the comparison test, they may do so because the difference between the numbers show up around tenth decimal, or so depending on computer architecture.
The problem cannot be solved by using ROUND() (or similar function), because the result is still a floating-point number. Example:
mysql> SELECT i, ROUND(SUM(d1), 2) AS a, ROUND(SUM(d2), 2) AS b
-> FROM t1 GROUP BY i HAVING a <> b;
+------+--------+-------+
| i | a | b |
+------+--------+-------+
| 1 | 21.40 | 21.40 |
| 2 | 76.80 | 76.80 |
| 3 | 7.40 | 7.40 |
| 4 | 15.40 | 15.40 |
| 5 | 7.20 | 7.20 |
| 6 | -51.40 | 0.00 |
+------+--------+-------+
This is what the numbers in column 'a' look like:
mysql> SELECT i, ROUND(SUM(d1), 2)*1.0000000000000000 AS a,
-> ROUND(SUM(d2), 2) AS b FROM t1 GROUP BY i HAVING a <> b;
+------+----------------------+-------+
| i | a | b |
+------+----------------------+-------+
| 1 | 21.3999999999999986 | 21.40 |
| 2 | 76.7999999999999972 | 76.80 |
| 3 | 7.4000000000000004 | 7.40 |
| 4 | 15.4000000000000004 | 15.40 |
| 5 | 7.2000000000000002 | 7.20 |
| 6 | -51.3999999999999986 | 0.00 |
+------+----------------------+-------+
Depending on the computer architecture you may or may not see similar results. Each CPU may evaluate floating-point numbers differently. For example in some machines you may get 'right' results by multiplying both arguments with 1, an example follows.
WARNING: NEVER TRUST THIS METHOD IN YOUR APPLICATION, THIS IS AN EXAMPLE OF A WRONG METHOD!!!
mysql> SELECT i, ROUND(SUM(d1), 2)*1 AS a, ROUND(SUM(d2), 2)*1 AS b
-> FROM t1 GROUP BY i HAVING a <> b;
+------+--------+------+
| i | a | b |
+------+--------+------+
| 6 | -51.40 | 0.00 |
+------+--------+------+
The reason why the above example seems to be working is that on the particular machine where the test was done, the CPU floating-point arithmetics happens to round the numbers to same, but there is no rule that any CPU should do so, so it cannot be trusted.
The correct way to do floating-point number comparison is to first decide on what is the wanted tolerance between the numbers and then do the comparison against the tolerance number. For example, if we agree on that floating-point numbers should be regarded the same, if they are same with precision of one of ten thousand (0.0001), the comparison should be done like this:
mysql> SELECT i, SUM(d1) AS a, SUM(d2) AS b FROM t1
-> GROUP BY i HAVING ABS(a - b) > 0.0001;
+------+--------+------+
| i | a | b |
+------+--------+------+
| 6 | -51.40 | 0.00 |
+------+--------+------+
1 row in set (0.00 sec)
And vice versa, if we wanted to get rows where the numbers are the same, the test would be:
mysql> SELECT i, SUM(d1) AS a, SUM(d2) AS b FROM t1
-> GROUP BY i HAVING ABS(a - b) < 0.0001;
+------+-------+-------+
| i | a | b |
+------+-------+-------+
| 1 | 21.40 | 21.40 |
| 2 | 76.80 | 76.80 |
| 3 | 7.40 | 7.40 |
| 4 | 15.40 | 15.40 |
| 5 | 7.20 | 7.20 |
+------+-------+-------+
