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Table 14.10 Mathematical Functions

• ABS(X)

  Returns the absolute value ofX, orNULL ifX isNULL.

  The result type is derived from the argument type. An implication of this is thatABS(-9223372036854775808) produces an error because the result cannot be stored in a signedBIGINT value.

  mysql> SELECT ABS(2);        -> 2mysql> SELECT ABS(-32);        -> 32

  This function is safe to use withBIGINT values.

• ACOS(X)

  Returns the arc cosine ofX, that is, the value whose cosine isX. ReturnsNULL ifX is not in the range-1 to1, or ifX isNULL.

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

• ASIN(X)

  Returns the arc sine ofX, that is, the value whose sine isX. ReturnsNULL ifX is not in the range-1 to1, or ifX isNULL.

  mysql> SELECT ASIN(0.2);        -> 0.20135792079033mysql> 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 ofX, that is, the value whose tangent isX. ReturnsNULL ifX isNULL

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

• ATAN(Y,X),ATAN2(Y,X)

  Returns the arc tangent of the two variablesX andY. It is similar to calculating the arc tangent ofY /X, except that the signs of both arguments are used to determine the quadrant of the result. ReturnsNULL ifX orY isNULL.

  mysql> SELECT ATAN(-2,2);        -> -0.78539816339745mysql> SELECT ATAN2(PI(),0);        -> 1.5707963267949

• CEIL(X)

  CEIL() is a synonym forCEILING().

• CEILING(X)

  Returns the smallest integer value not less thanX. ReturnsNULL ifX isNULL.

  mysql> SELECT CEILING(1.23);        -> 2mysql> 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 numberN, converted from basefrom_base to baseto_base. ReturnsNULL if any argument isNULL. The argumentN is interpreted as an integer, but may be specified as an integer or a string. The minimum base is2 and the maximum base is36. Iffrom_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() returnsNULL if any of its arguments areNULL.

  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 ofX, whereX is given in radians. ReturnsNULL ifX isNULL.

  mysql> SELECT COS(PI());        -> -1

• COT(X)

  Returns the cotangent ofX. ReturnsNULL ifX isNULL.

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

• CRC32(expr)

  Computes a cyclic redundancy check value and returns a 32-bit unsigned value. The result isNULL if the argument isNULL. The argument is expected to be a string and (if possible) is treated as one if it is not.

  mysql> SELECT CRC32('MySQL');        -> 3259397556mysql> SELECT CRC32('mysql');        -> 2501908538

• DEGREES(X)

  Returns the argumentX, converted from radians to degrees. ReturnsNULL ifX isNULL.

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

• EXP(X)

  Returns the value ofe (the base of natural logarithms) raised to the power ofX. The inverse of this function isLOG() (using a single argument only) orLN().

  IfX isNULL, this function returnsNULL.

  mysql> SELECT EXP(2);        -> 7.3890560989307mysql> SELECT EXP(-2);        -> 0.13533528323661mysql> SELECT EXP(0);        -> 1

• FLOOR(X)

  Returns the largest integer value not greater thanX. ReturnsNULL ifX isNULL.

  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 numberX to a format like'#,###,###.##', rounded toD decimal places, and returns the result as a string. For details, seeSection 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 inSection 14.8, “String Functions and Operators”, for details.

• LN(X)

  Returns the natural logarithm ofX; that is, the base-e logarithm ofX. IfX is less than or equal to 0.0E0, the function returnsNULL and a warning“Invalid argument for logarithm” is reported. ReturnsNULL ifX isNULL.

  mysql> SELECT LN(2);        -> 0.69314718055995mysql> SELECT LN(-2);        -> NULL

  This function is synonymous withLOG(X). The inverse of this function is theEXP() function.

• LOG(X),LOG(B,X)

  If called with one parameter, this function returns the natural logarithm ofX. IfX is less than or equal to 0.0E0, the function returnsNULL and a warning“Invalid argument for logarithm” is reported. ReturnsNULL ifX orB isNULL.

  The inverse of this function (when called with a single argument) is theEXP() function.

  mysql> SELECT LOG(2);        -> 0.69314718055995mysql> SELECT LOG(-2);        -> NULL

  If called with two parameters, this function returns the logarithm ofX to the baseB. IfX is less than or equal to 0, or ifB is less than or equal to 1, thenNULL is returned.

  mysql> SELECT LOG(2,65536);        -> 16mysql> SELECT LOG(10,100);        -> 2mysql> SELECT LOG(1,100);        -> NULL

  LOG(B,X) is equivalent toLOG(X) / LOG(B).

• LOG2(X)

  Returns the base-2 logarithm ofX. IfX is less than or equal to 0.0E0, the function returnsNULL and a warning“Invalid argument for logarithm” is reported. ReturnsNULL ifX isNULL.

  mysql> SELECT LOG2(65536);        -> 16mysql> SELECT LOG2(-100);        -> NULL

  LOG2() is useful for finding out how many bits a number requires for storage. This function is equivalent to the expressionLOG(X) / LOG(2).

• LOG10(X)

  Returns the base-10 logarithm ofX. IfX is less than or equal to 0.0E0, the function returnsNULL and a warning“Invalid argument for logarithm” is reported. ReturnsNULL ifX isNULL.

  mysql> SELECT LOG10(2);        -> 0.30102999566398mysql> SELECT LOG10(100);        -> 2mysql> SELECT LOG10(-100);        -> NULL

  LOG10(X) is equivalent toLOG(10,X).

• MOD(N,M),N %M,N MODM

  Modulo operation. Returns the remainder ofN divided byM. ReturnsNULL ifM orN isNULL.

  mysql> SELECT MOD(234, 10);        -> 4mysql> SELECT 253 % 7;        -> 1mysql> SELECT MOD(29,9);        -> 2mysql> SELECT 29 MOD 9;        -> 2

  This function is safe to use withBIGINT 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) returnsNULL.

• 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 ofPI(). SeeSection 13.1.4, “Floating-Point Types (Approximate Value) - FLOAT, DOUBLE”.

  mysql> SELECT PI();        -> 3.141593mysql> SELECT PI()+0.000000000000000000;        -> 3.141592653589793000

• POW(X,Y)

  Returns the value ofX raised to the power ofY. ReturnsNULL ifX orY isNULL.

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

• POWER(X,Y)

  This is a synonym forPOW().

• RADIANS(X)

  Returns the argumentX, converted from degrees to radians. (Note that π radians equals 180 degrees.) ReturnsNULL ifX isNULL.

  mysql> SELECT RADIANS(90);        -> 1.5707963267949

• RAND([N])

  Returns a random floating-point valuev in the range0 <=v <1.0. To obtain a random integerR in the rangei <=R <j, use the expressionFLOOR(i + RAND() * (j −i)). For example, to obtain a random integer in the range the range7 <=R <12, use the following statement:

  SELECT FLOOR(7 + (RAND() * 5));

  If an integer argumentN 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 ofRAND().

  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 byRAND(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: 0mysql> 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 aWHERE 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, seeSection 10.2.1.20, “Function Call Optimization”.

  Use of a column withRAND() values in anORDER BY orGROUP BY clause may yield unexpected results because for either clause aRAND() 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 * FROMtbl_name ORDER BY RAND();

  To select a random sample from a set of rows, combineORDER BY RAND() withLIMIT:

  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 whenbinlog_format is set toSTATEMENT.

• ROUND(X),ROUND(X,D)

  Rounds the argumentX toD decimal places. The rounding algorithm depends on the data type ofX.D defaults to 0 if not specified.D can be negative to causeD digits left of the decimal point of the valueX to become zero. The maximum absolute value forD is 30; any digits in excess of 30 (or -30) are truncated. IfX orD isNULL, the function returnsNULL.

  mysql> SELECT ROUND(-1.23);        -> -1mysql> SELECT ROUND(-1.58);        -> -2mysql> SELECT ROUND(1.58);        -> 2mysql> SELECT ROUND(1.298, 1);        -> 1.3mysql> SELECT ROUND(1.298, 0);        -> 1mysql> SELECT ROUND(23.298, -1);        -> 20mysql> 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 thatROUND() 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, seeSection 14.25, “Precision Math”.

  The data type returned byROUND() (andTRUNCATE()) is determined according to the rules listed here:

  • When the first argument is of any integer type, the return type is alwaysBIGINT.

  • When the first argument is of any floating-point type or of any non-numeric type, the return type is alwaysDOUBLE.

  • When the first argument is aDECIMAL value, the return type is alsoDECIMAL.

  • The type attributes for the return value are also copied from the first argument, except in the case ofDECIMAL, 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, forROUND() (but not for theTRUNCATE() 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) returns100.00—the first argument isDECIMAL(5, 3), and the return type isDECIMAL(5, 2).

    If the second argument is negative, the return type has scale 0 and a corresponding precision;ROUND(99.999, -1) returns100, which isDECIMAL(3, 0).

• SIGN(X)

  Returns the sign of the argument as-1,0, or1, depending on whetherX is negative, zero, or positive. ReturnsNULL ifX isNULL.

  mysql> SELECT SIGN(-32);        -> -1mysql> SELECT SIGN(0);        -> 0mysql> SELECT SIGN(234);        -> 1

• SIN(X)

  Returns the sine ofX, whereX is given in radians. ReturnsNULL ifX isNULL.

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

• SQRT(X)

  Returns the square root of a nonnegative numberX. IfX isNULL, the function returnsNULL.

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

• TAN(X)

  Returns the tangent ofX, whereX is given in radians. ReturnsNULL ifX isNULL.

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

• TRUNCATE(X,D)

  Returns the numberX, truncated toD decimal places. IfD is0, the result has no decimal point or fractional part.D can be negative to causeD digits left of the decimal point of the valueX to become zero. IfX orD isNULL, the function returnsNULL.

  mysql> SELECT TRUNCATE(1.223,1);        -> 1.2mysql> SELECT TRUNCATE(1.999,1);        -> 1.9mysql> SELECT TRUNCATE(1.999,0);        -> 1mysql> SELECT TRUNCATE(-1.999,1);        -> -1.9mysql> SELECT TRUNCATE(122,-2);       -> 100mysql> SELECT TRUNCATE(10.28*100,0);       -> 1028

  All numbers are rounded toward zero.

  The data type returned byTRUNCATE() follows the same rules that determine the return type of theROUND() function; for details, see the description forROUND().