Floating-point numbers sometimes cause confusion because they are approximate. That is, they are not stored as exact values inside computer architecture. What you can see on the screen usually is not the exact value of the number. The FLOAT and DOUBLE data types are such, and DECIMAL operations before MySQL 5.0.3 are approximate as well.

Prior to MySQL 5.0.3, DECIMAL columns store values with exact precision because they are represented as strings, but calculations on DECIMAL values are done using floating-point operations. As of 5.0.3, MySQL performs DECIMAL operations with a precision of 64 decimal digits, which should solve most common inaccuracy problems when it comes to DECIMAL columns. (If your server is from MySQL 5.0.3 or higher, but you have DECIMAL columns in tables that were created before 5.0.3, the old behavior still applies to those columns. To convert the tables to the newer DECIMAL format, dump them with mysqldump and reload them.)

The following example (for versions of MySQL older than 5.0.3) demonstrates the problem. It shows that even for older DECIMAL columns, calculations that are done using floating-point operations are subject to floating-point error. (Were you to replace the DECIMAL columns with FLOAT, similar problems would occur for all versions of MySQL.)

mysql> CREATE TABLE t1 (i INT, d1 DECIMAL(9,2), d2 DECIMAL(9,2));
mysql> 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 should not satisfy the comparison (the values of a and b do not appear to be different), they may do so because the difference between the numbers shows up around the tenth decimal or so, depending on factors such as computer architecture or the compiler version or optimization level. For example, different CPUs may evaluate floating-point numbers differently.

As of MySQL 5.0.3, you will get only the last row in the above result.

The problem cannot be solved by using ROUND() or similar functions, because the result is still a floating-point number:

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 when displayed with more decimal places:

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 your computer architecture, you may or may not see similar results. For example, on some machines you may get the “correct” results by multiplying both arguments by 1, as the following example shows.

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 that the preceding example seems to work is that on the particular machine where the test was done, CPU floating-point arithmetic happens to round the numbers to the same value. However, there is no rule that any CPU should do so, so this method cannot be trusted.

The correct way to do floating-point number comparison is to first decide on an acceptable tolerance for differences between the numbers and then do the comparison against the tolerance value. For example, if we agree that floating-point numbers should be regarded the same if they are same within a precision of one in ten thousand (0.0001), the comparison should be written to find differences larger than the tolerance value:

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)

Conversely, to get rows where the numbers are the same, the test should find differences within the tolerance value:

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 |
+------+-------+-------+