Floating-point numbers sometimes cause confusion because they
are approximate and not stored as exact values. A
floating-point value as written in an SQL statement may not be
the same as the value represented internally. Attempts to
treat floating-point values as exact in comparisons may lead
to problems. They are also subject to platform or
implementation dependencies. The
`FLOAT`

and
`DOUBLE`

data types are subject
to these issues. Before MySQL 5.0.3,
`DECIMAL`

comparison operations
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 5.0.6, MySQL performs
`DECIMAL`

operations with a
precision of 65 decimal digits (64 digits from 5.0.3 to
5.0.5), 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>mysql>`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),`

mysql>`(6, 0.00, 0.00), (6, -51.40, 0.00);`

->`SELECT i, SUM(d1) AS a, SUM(d2) AS 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 | +------+--------+-------+`FROM t1 GROUP BY i HAVING a <> b;`

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`

+------+--------+-------+ | 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 | +------+--------+-------+`FROM t1 GROUP BY i HAVING a <> b;`

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,`

+------+----------------------+-------+ | 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 | +------+----------------------+-------+`ROUND(SUM(d2), 2) AS b FROM t1 GROUP BY i HAVING a <> b;`

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.

Warning

Never use this method in your applications. It is not an example of a trustworthy method!

mysql>->`SELECT i, ROUND(SUM(d1), 2)*1 AS a, ROUND(SUM(d2), 2)*1 AS b`

+------+--------+------+ | i | a | b | +------+--------+------+ | 6 | -51.40 | 0.00 | +------+--------+------+`FROM t1 GROUP BY i HAVING a <> b;`

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`

+------+--------+------+ | i | a | b | +------+--------+------+ | 6 | -51.40 | 0.00 | +------+--------+------+ 1 row in set (0.00 sec)`GROUP BY i HAVING ABS(a - b) > 0.0001;`

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`

+------+-------+-------+ | 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 | +------+-------+-------+`GROUP BY i HAVING ABS(a - b) <= 0.0001;`

Floating-point values are subject to platform or implementation dependencies. Suppose that you execute the following statements:

CREATE TABLE t1(c1 FLOAT(53,0), c2 FLOAT(53,0)); INSERT INTO t1 VALUES('1e+52','-1e+52'); SELECT * FROM t1;

On some platforms, the `SELECT`

statement
returns `inf`

and `-inf`

. On
others, it returns `0`

and
`-0`

.

An implication of the preceding issues is that if you attempt
to create a replication slave by dumping table contents with
**mysqldump** on the master and reloading the
dump file into the slave, tables containing floating-point
columns might differ between the two hosts.