14.6.2 Mathematical Functions

Table 14.10 Mathematical Functions

Name	Description
`ABS()`	Return the absolute value
`ACOS()`	Return the arc cosine
`ASIN()`	Return the arc sine
`ATAN()`	Return the arc tangent
`ATAN2()`, `ATAN()`	Return the arc tangent of the two arguments
`CEIL()`	Return the smallest integer value not less than the argument
`CEILING()`	Return the smallest integer value not less than the argument
`CONV()`	Convert numbers between different number bases
`COS()`	Return the cosine
`COT()`	Return the cotangent
`CRC32()`	Compute a cyclic redundancy check value
`DEGREES()`	Convert radians to degrees
`EXP()`	Raise to the power of
`FLOOR()`	Return the largest integer value not greater than the argument
`LN()`	Return the natural logarithm of the argument
`LOG()`	Return the natural logarithm of the first argument
`LOG10()`	Return the base-10 logarithm of the argument
`LOG2()`	Return the base-2 logarithm of the argument
`MOD()`	Return the remainder
`PI()`	Return the value of pi
`POW()`	Return the argument raised to the specified power
`POWER()`	Return the argument raised to the specified power
`RADIANS()`	Return argument converted to radians
`RAND()`	Return a random floating-point value
`ROUND()`	Round the argument
`SIGN()`	Return the sign of the argument
`SIN()`	Return the sine of the argument
`SQRT()`	Return the square root of the argument
`TAN()`	Return the tangent of the argument
`TRUNCATE()`	Truncate to specified number of decimal places

All mathematical functions return NULL in the event of an error.

ABS(X)
Returns the absolute value of X, or NULL if X is NULL.
The result type is derived from the argument type. An implication of this is that ABS(-9223372036854775808) produces an error because the result cannot be stored in a signed BIGINT value.
```
mysql> SELECT ABS(2);
        -> 2
mysql> SELECT ABS(-32);
        -> 32
```
This function is safe to use with BIGINT values.

ACOS(X)

Returns the arc cosine of X, that is, the value whose cosine is X. Returns NULL if X is not in the range -1 to 1, or if X is NULL.

mysql> SELECT ACOS(1);
        -> 0
mysql> SELECT ACOS(1.0001);
        -> NULL
mysql> SELECT ACOS(0);
        -> 1.5707963267949

ASIN(X)

Returns the arc sine of X, that is, the value whose sine is X. Returns NULL if X is not in the range -1 to 1, or if X is NULL.

mysql> SELECT ASIN(0.2);
        -> 0.20135792079033
mysql> SELECT ASIN('foo');

+-------------+
| ASIN('foo') |
+-------------+
|           0 |
+-------------+
1 row in set, 1 warning (0.00 sec)

mysql> SHOW WARNINGS;
+---------+------+-----------------------------------------+
| Level   | Code | Message                                 |
+---------+------+-----------------------------------------+
| Warning | 1292 | Truncated incorrect DOUBLE value: 'foo' |
+---------+------+-----------------------------------------+

ATAN(X)

Returns the arc tangent of X, that is, the value whose tangent is X. Returns NULL if X is NULL

mysql> SELECT ATAN(2);
        -> 1.1071487177941
mysql> SELECT ATAN(-2);
        -> -1.1071487177941

ATAN(Y,X), ATAN2(Y,X)
Returns the arc tangent of the two variables X and Y. It is similar to calculating the arc tangent of Y / X, except that the signs of both arguments are used to determine the quadrant of the result. Returns NULL if X or Y is NULL.
```
mysql> SELECT ATAN(-2,2);
        -> -0.78539816339745
mysql> SELECT ATAN2(PI(),0);
        -> 1.5707963267949
```
CEIL(X)
CEIL() is a synonym for CEILING().
CEILING(X)
Returns the smallest integer value not less than X. Returns NULL if X is NULL.
```
mysql> SELECT CEILING(1.23);
        -> 2
mysql> SELECT CEILING(-1.23);
        -> -1
```
For exact-value numeric arguments, the return value has an exact-value numeric type. For string or floating-point arguments, the return value has a floating-point type.
CONV(N,from_base,to_base)
Converts numbers between different number bases. Returns a string representation of the number N, converted from base from_base to base to_base. Returns NULL if any argument is NULL. The argument N is interpreted as an integer, but may be specified as an integer or a string. The minimum base is 2 and the maximum base is 36. If from_base is a negative number, N is regarded as a signed number. Otherwise, N is treated as unsigned. CONV() works with 64-bit precision.
CONV() returns NULL if any of its arguments are NULL.
```
mysql> SELECT CONV('a',16,2);
        -> '1010'
mysql> SELECT CONV('6E',18,8);
        -> '172'
mysql> SELECT CONV(-17,10,-18);
        -> '-H'
mysql> SELECT CONV(10+'10'+'10'+X'0a',10,10);
        -> '40'
```
COS(X)
Returns the cosine of X, where X is given in radians. Returns NULL if X is NULL.
```
mysql> SELECT COS(PI());
        -> -1
```

COT(X)

Returns the cotangent of X. Returns NULL if X is NULL.

mysql> SELECT COT(12);
        -> -1.5726734063977
mysql> SELECT COT(0);
        -> out-of-range error

CRC32(expr)
Computes a cyclic redundancy check value and returns a 32-bit unsigned value. The result is NULL if the argument is NULL. The argument is expected to be a string and (if possible) is treated as one if it is not.
```
mysql> SELECT CRC32('MySQL');
        -> 3259397556
mysql> SELECT CRC32('mysql');
        -> 2501908538
```

DEGREES(X)

Returns the argument X, converted from radians to degrees. Returns NULL if X is NULL.

mysql> SELECT DEGREES(PI());
        -> 180
mysql> SELECT DEGREES(PI() / 2);
        -> 90

EXP(X)
Returns the value of e (the base of natural logarithms) raised to the power of X. The inverse of this function is LOG() (using a single argument only) or LN().
If X is NULL, this function returns NULL.
```
mysql> SELECT EXP(2);
        -> 7.3890560989307
mysql> SELECT EXP(-2);
        -> 0.13533528323661
mysql> SELECT EXP(0);
        -> 1
```
FLOOR(X)
Returns the largest integer value not greater than X. Returns NULL if X is NULL.
```
mysql> SELECT FLOOR(1.23), FLOOR(-1.23);
        -> 1, -2
```
For exact-value numeric arguments, the return value has an exact-value numeric type. For string or floating-point arguments, the return value has a floating-point type.
FORMAT(X,D)
Formats the number X to a format like '#,###,###.##', rounded to D decimal places, and returns the result as a string. For details, see Section 14.8, “String Functions and Operators”.
HEX(N_or_S)
This function can be used to obtain a hexadecimal representation of a decimal number or a string; the manner in which it does so varies according to the argument's type. See this function's description in Section 14.8, “String Functions and Operators”, for details.
LN(X)
Returns the natural logarithm of X; that is, the base-e logarithm of X. If X is less than or equal to 0.0E0, the function returns NULL and a warning “Invalid argument for logarithm” is reported. Returns NULL if X is NULL.
```
mysql> SELECT LN(2);
        -> 0.69314718055995
mysql> SELECT LN(-2);
        -> NULL
```
This function is synonymous with LOG(X). The inverse of this function is the EXP() function.
LOG(X), LOG(B,X)
If called with one parameter, this function returns the natural logarithm of X. If X is less than or equal to 0.0E0, the function returns NULL and a warning “Invalid argument for logarithm” is reported. Returns NULL if X or B is NULL.
The inverse of this function (when called with a single argument) is the EXP() function.
```
mysql> SELECT LOG(2);
        -> 0.69314718055995
mysql> SELECT LOG(-2);
        -> NULL
```
If called with two parameters, this function returns the logarithm of X to the base B. If X is less than or equal to 0, or if B is less than or equal to 1, then NULL is returned.
```
mysql> SELECT LOG(2,65536);
        -> 16
mysql> SELECT LOG(10,100);
        -> 2
mysql> SELECT LOG(1,100);
        -> NULL
```
LOG(B,X) is equivalent to LOG(X) / LOG(B).
LOG2(X)
Returns the base-2 logarithm of X. If X is less than or equal to 0.0E0, the function returns NULL and a warning “Invalid argument for logarithm” is reported. Returns NULL if X is NULL.
```
mysql> SELECT LOG2(65536);
        -> 16
mysql> SELECT LOG2(-100);
        -> NULL
```
LOG2() is useful for finding out how many bits a number requires for storage. This function is equivalent to the expression LOG(X) / LOG(2).
LOG10(X)
Returns the base-10 logarithm of X. If X is less than or equal to 0.0E0, the function returns NULL and a warning “Invalid argument for logarithm” is reported. Returns NULL if X is NULL.
```
mysql> SELECT LOG10(2);
        -> 0.30102999566398
mysql> SELECT LOG10(100);
        -> 2
mysql> SELECT LOG10(-100);
        -> NULL
```
LOG10(X) is equivalent to LOG(10,X).
MOD(N,M), N % M, N MOD M
Modulo operation. Returns the remainder of N divided by M. Returns NULL if M or N is NULL.
```
mysql> SELECT MOD(234, 10);
        -> 4
mysql> SELECT 253 % 7;
        -> 1
mysql> SELECT MOD(29,9);
        -> 2
mysql> SELECT 29 MOD 9;
        -> 2
```
This function is safe to use with BIGINT values.
MOD() also works on values that have a fractional part and returns the exact remainder after division:
```
mysql> SELECT MOD(34.5,3);
        -> 1.5
```
MOD(N,0) returns NULL.
PI()
Returns the value of π (pi). The default number of decimal places displayed is seven, but MySQL uses the full double-precision value internally.
Because the return value of this function is a double-precision value, its exact representation may vary between platforms or implementations. This also applies to any expressions making use of PI(). See Section 13.1.4, “Floating-Point Types (Approximate Value) - FLOAT, DOUBLE”.
```
mysql> SELECT PI();
        -> 3.141593
mysql> SELECT PI()+0.000000000000000000;
        -> 3.141592653589793000
```

POW(X,Y)

Returns the value of X raised to the power of Y. Returns NULL if X or Y is NULL.

mysql> SELECT POW(2,2);
        -> 4
mysql> SELECT POW(2,-2);
        -> 0.25

POWER(X,Y)
This is a synonym for POW().
RADIANS(X)
Returns the argument X, converted from degrees to radians. (Note that π radians equals 180 degrees.) Returns NULL if X is NULL.
```
mysql> SELECT RADIANS(90);
        -> 1.5707963267949
```
RAND([N])
Returns a random floating-point value v in the range 0 <= v < 1.0. To obtain a random integer R in the range i <= R < j, use the expression FLOOR(i + RAND() * (j − i)). For example, to obtain a random integer in the range the range 7 <= R < 12, use the following statement:
```
SELECT FLOOR(7 + (RAND() * 5));
```
If an integer argument N is specified, it is used as the seed value:
- With a constant initializer argument, the seed is initialized once when the statement is prepared, prior to execution.
- With a nonconstant initializer argument (such as a column name), the seed is initialized with the value for each invocation of RAND().
One implication of this behavior is that for equal argument values, RAND(N) returns the same value each time, and thus produces a repeatable sequence of column values. In the following example, the sequence of values produced by RAND(3) is the same both places it occurs.
```
mysql> CREATE TABLE t (i INT);
Query OK, 0 rows affected (0.42 sec)

mysql> INSERT INTO t VALUES(1),(2),(3);
Query OK, 3 rows affected (0.00 sec)
Records: 3  Duplicates: 0  Warnings: 0

mysql> SELECT i, RAND() FROM t;
+------+------------------+
| i    | RAND()           |
+------+------------------+
|    1 | 0.61914388706828 |
|    2 | 0.93845168309142 |
|    3 | 0.83482678498591 |
+------+------------------+
3 rows in set (0.00 sec)

mysql> SELECT i, RAND(3) FROM t;
+------+------------------+
| i    | RAND(3)          |
+------+------------------+
|    1 | 0.90576975597606 |
|    2 | 0.37307905813035 |
|    3 | 0.14808605345719 |
+------+------------------+
3 rows in set (0.00 sec)

mysql> SELECT i, RAND() FROM t;
+------+------------------+
| i    | RAND()           |
+------+------------------+
|    1 | 0.35877890638893 |
|    2 | 0.28941420772058 |
|    3 | 0.37073435016976 |
+------+------------------+
3 rows in set (0.00 sec)

mysql> SELECT i, RAND(3) FROM t;
+------+------------------+
| i    | RAND(3)          |
+------+------------------+
|    1 | 0.90576975597606 |
|    2 | 0.37307905813035 |
|    3 | 0.14808605345719 |
+------+------------------+
3 rows in set (0.01 sec)
```
RAND() in a WHERE clause is evaluated for every row (when selecting from one table) or combination of rows (when selecting from a multiple-table join). Thus, for optimizer purposes, RAND() is not a constant value and cannot be used for index optimizations. For more information, see Section 10.2.1.20, “Function Call Optimization”.
Use of a column with RAND() values in an ORDER BY or GROUP BY clause may yield unexpected results because for either clause a RAND() expression can be evaluated multiple times for the same row, each time returning a different result. If the goal is to retrieve rows in random order, you can use a statement like this:
```
SELECT * FROM tbl_name ORDER BY RAND();
```
To select a random sample from a set of rows, combine ORDER BY RAND() with LIMIT:
```
SELECT * FROM table1, table2 WHERE a=b AND c<d ORDER BY RAND() LIMIT 1000;
```
RAND() is not meant to be a perfect random generator. It is a fast way to generate random numbers on demand that is portable between platforms for the same MySQL version.
This function is unsafe for statement-based replication. A warning is logged if you use this function when binlog_format is set to STATEMENT.
ROUND(X), ROUND(X,D)
Rounds the argument X to D decimal places. The rounding algorithm depends on the data type of X. D defaults to 0 if not specified. D can be negative to cause D digits left of the decimal point of the value X to become zero. The maximum absolute value for D is 30; any digits in excess of 30 (or -30) are truncated. If X or D is NULL, the function returns NULL.
```
mysql> SELECT ROUND(-1.23);
        -> -1
mysql> SELECT ROUND(-1.58);
        -> -2
mysql> SELECT ROUND(1.58);
        -> 2
mysql> SELECT ROUND(1.298, 1);
        -> 1.3
mysql> SELECT ROUND(1.298, 0);
        -> 1
mysql> SELECT ROUND(23.298, -1);
        -> 20
mysql> SELECT ROUND(.12345678901234567890123456789012345, 35);
        -> 0.123456789012345678901234567890
```
The return value has the same type as the first argument (assuming that it is integer, double, or decimal). This means that for an integer argument, the result is an integer (no decimal places):
```
mysql> SELECT ROUND(150.000,2), ROUND(150,2);
+------------------+--------------+
| ROUND(150.000,2) | ROUND(150,2) |
+------------------+--------------+
|           150.00 |          150 |
+------------------+--------------+
```
ROUND() uses the following rules depending on the type of the first argument:
- For exact-value numbers, ROUND() uses the “round half away from zero” or “round toward nearest” rule: A value with a fractional part of .5 or greater is rounded up to the next integer if positive or down to the next integer if negative. (In other words, it is rounded away from zero.) A value with a fractional part less than .5 is rounded down to the next integer if positive or up to the next integer if negative.
- For approximate-value numbers, the result depends on the C library. On many systems, this means that ROUND() uses the “round to nearest even” rule: A value with a fractional part exactly halfway between two integers is rounded to the nearest even integer.
The following example shows how rounding differs for exact and approximate values:
```
mysql> SELECT ROUND(2.5), ROUND(25E-1);
+------------+--------------+
| ROUND(2.5) | ROUND(25E-1) |
+------------+--------------+
| 3          |            2 |
+------------+--------------+
```
For more information, see Section 14.25, “Precision Math”.
The data type returned by ROUND() (and TRUNCATE()) is determined according to the rules listed here:
- When the first argument is of any integer type, the return type is always BIGINT.
- When the first argument is of any floating-point type or of any non-numeric type, the return type is always DOUBLE.
- When the first argument is a DECIMAL value, the return type is also DECIMAL.
- The type attributes for the return value are also copied from the first argument, except in the case of DECIMAL, when the second argument is a constant value.
  When the desired number of decimal places is less than the scale of the argument, the scale and the precision of the result are adjusted accordingly.
  In addition, for ROUND() (but not for the TRUNCATE() function), the precision is extended by one place to accommodate rounding that increases the number of significant digits. If the second argument is negative, the return type is adjusted such that its scale is 0, with a corresponding precision. For example, ROUND(99.999, 2) returns 100.00—the first argument is DECIMAL(5, 3), and the return type is DECIMAL(5, 2).
  If the second argument is negative, the return type has scale 0 and a corresponding precision; ROUND(99.999, -1) returns 100, which is DECIMAL(3, 0).
SIGN(X)
Returns the sign of the argument as -1, 0, or 1, depending on whether X is negative, zero, or positive. Returns NULL if X is NULL.
```
mysql> SELECT SIGN(-32);
        -> -1
mysql> SELECT SIGN(0);
        -> 0
mysql> SELECT SIGN(234);
        -> 1
```

SIN(X)

Returns the sine of X, where X is given in radians. Returns NULL if X is NULL.

mysql> SELECT SIN(PI());
        -> 1.2246063538224e-16
mysql> SELECT ROUND(SIN(PI()));
        -> 0

SQRT(X)

Returns the square root of a nonnegative number X. If X is NULL, the function returns NULL.

mysql> SELECT SQRT(4);
        -> 2
mysql> SELECT SQRT(20);
        -> 4.4721359549996
mysql> SELECT SQRT(-16);
        -> NULL

TAN(X)

Returns the tangent of X, where X is given in radians. Returns NULL if X is NULL.

mysql> SELECT TAN(PI());
        -> -1.2246063538224e-16
mysql> SELECT TAN(PI()+1);
        -> 1.5574077246549

TRUNCATE(X,D)
Returns the number X, truncated to D decimal places. If D is 0, the result has no decimal point or fractional part. D can be negative to cause D digits left of the decimal point of the value X to become zero. If X or D is NULL, the function returns NULL.
```
mysql> SELECT TRUNCATE(1.223,1);
        -> 1.2
mysql> SELECT TRUNCATE(1.999,1);
        -> 1.9
mysql> SELECT TRUNCATE(1.999,0);
        -> 1
mysql> SELECT TRUNCATE(-1.999,1);
        -> -1.9
mysql> SELECT TRUNCATE(122,-2);
       -> 100
mysql> SELECT TRUNCATE(10.28*100,0);
       -> 1028
```
All numbers are rounded toward zero.
The data type returned by TRUNCATE() follows the same rules that determine the return type of the ROUND() function; for details, see the description for ROUND().