B.5.5.8 Problems with Floating-Point Values

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. For DECIMAL columns, MySQL performs operations with a precision of 65 decimal digits, which should solve most common inaccuracy problems.

The following example uses DOUBLE to demonstrate how calculations that are done using floating-point operations are subject to floating-point error.

mysql> CREATE TABLE t1 (i INT, d1 DOUBLE, d2 DOUBLE);
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 |  21.4 | 21.4 |
|    2 |  76.8 | 76.8 |
|    3 |   7.4 |  7.4 |
|    4 |  15.4 | 15.4 |
|    5 |   7.2 |  7.2 |
|    6 | -51.4 |    0 |

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.

If columns d1 and d2 had been defined as DECIMAL rather than DOUBLE, the result of the SELECT query would have contained only one row—the last one shown above.

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 | -51.4 |    0 |
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 | 21.4 | 21.4 |
|    2 | 76.8 | 76.8 |
|    3 |  7.4 |  7.4 |
|    4 | 15.4 | 15.4 |
|    5 |  7.2 |  7.2 |
5 rows in set (0.03 sec)

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');

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.

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User Comments
  Posted by Mohamed Infiyaz Zaffer Khalid on June 1, 2010
I've just implemented a PHP-MySQL-based application and it took me a while to figure this out. I hope all of you coders out there will benefit from this tip.

In PHP, I calculated a value that arrives at the amount 20072.64 and I wrote this into a mysql field of type FLOAT.

Strangely (despite the technical specs indicating a large range), the number that got stored was 20072.6 - note truncation!

Solution: I changed the field type to DOUBLE and this was resolved.

Alternatives that did not work: Even type-casting in PHP did not do any good since ultimately the values had to be stored by MySQL.

Happy coding!
  Posted by Felipph Calado on December 29, 2010
I had this problem too. It's happen sometimes randomly. My solution was expecify colunm to float(10,2) with 2 decimals. This looks solve my problem.

Anyway I will try double fields
  Posted by Geoffrey Downs on March 10, 2011
Khalid -
This is not a mystery. The problem is that Float columns only store 4-bytes per entry. This means that the precision available to the decimal portion of your number depends on the size of the non-decimal portion of your number. The more bytes are requires to represent the non-decimal portion of your number, the fewer bytes are available to represent the approximate decimal value of your number. If you store a sufficiently large number, your entire decimal value will be truncated to 0. You have solved the problem by increasing your per-entry storage to 8 bytes instead of 4.
  Posted by Geoffrey Downs on March 10, 2011
Following up... I *think* this is correct for the default float columns in mysql:

var yourNumber = some floating point value
max decimal precision = 10 ^ (-5 + floor(yourNumber log 10))
0 < x < 10 -> max precision is 0.00001
10 <= x < 100 -> max precision is 0.0001
100 <= x < 1000 -> max precision is 0.001
  Posted by Peter Soltesz on March 26, 2012
Geoffrey Downs is right!

Selecting a tolerance level is not good, because the tolerance level differs from value to value depending on the number. As I inspected duplicates in my db for example two float stored values both 13442 compared as NOT EQUAL to each other when using too high (0.01) tolerance level, however they were EQUAL when I used lower (0.1) tolerance level.

Therefore I also recommend to change the documentation because the recommended solution (compare the difference to a selected threshold) is not safe.

I translated the equation of Geoffrey Downs to MySQL as follows for FLOAT values:

IF(ABS(yourFloat1-yourFloat2)<POW(10,FLOOR(LOG10(GREATEST(ABS(yourFloat1),ABS(yourFloat2)))-5)),"E Q U A L","N O T - E Q U A L")

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