PostgreSQL 7.4 Documentation
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# 9.3. Mathematical Functions and Operators

Mathematical operators are provided for many PostgreSQL types. For types without common mathematical conventions for all possible permutations (e.g., date/time types) we describe the actual behavior in subsequent sections.

Table 9-2 shows the available mathematical operators.

Table 9-2. Mathematical Operators

Operator | Description | Example | Result
--- | --- | --- | ---
+ | addition | 2 + 3 | 5
- | subtraction | 2 - 3 | -1
* | multiplication | 2 * 3 | 6
/ | division (integer division truncates results) | 4 / 2 | 2
% | modulo (remainder) | 5 % 4 | 1
^ | exponentiation | 2.0 ^ 3.0 | 8
|/ | square root | |/ 25.0 | 5
||/ | cube root | ||/ 27.0 | 3
! | factorial | 5 ! | 120
!! | factorial (prefix operator) | !! 5 | 120
@ | absolute value | @ -5.0 | 5
& | bitwise AND | 91 & 15 | 11
| | bitwise OR | 32 | 3 | 35
# | bitwise XOR | 17 # 5 | 20
~ | bitwise NOT | ~1 | -2
<< | bitwise shift left | 1 << 4 | 16
>> | bitwise shift right | 8 >> 2 | 2

The bitwise operators are also available for the bit string types `bit` and `bit varying`, as shown in Table 9-3. Bit string operands of &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown in the table.

Table 9-3. Bit String Bitwise Operators

Example | Result
--- | ---
B'10001' & B'01101' | 00001
B'10001' | B'01101' | 11101
B'10001' # B'01101' | 11110
~ B'10001' | 01110
B'10001' << 3 | 01000
B'10001' >> 2 | 00100

Table 9-4 shows the available mathematical functions. In the table, dp indicates `double precision`. Many of these functions are provided in multiple forms with different argument types. Except where noted, any given form of a function returns the same data type as its argument. The functions working with `double precision` data are mostly implemented on top of the host system's C library; accuracy and behavior in boundary cases may therefore vary depending on the host system.

Table 9-4. Mathematical Functions

Function | Return Type | Description | Example | Result
--- | --- | --- | --- | ---
`abs`(x) | (same as x) | absolute value | abs(-17.4) | 17.4
`cbrt`(`dp`) | `dp` | cube root | cbrt(27.0) | 3
`ceil`(`dp` or `numeric`) | (same as input) | smallest integer not less than argument | ceil(-42.8) | -42
`degrees`(`dp`) | `dp` | radians to degrees | degrees(0.5) | 28.6478897565412
`exp`(`dp` or `numeric`) | (same as input) | exponential | exp(1.0) | 2.71828182845905
`floor`(`dp` or `numeric`) | (same as input) | largest integer not greater than argument | floor(-42.8) | -43
`ln`(`dp` or `numeric`) | (same as input) | natural logarithm | ln(2.0) | 0.693147180559945
`log`(`dp` or `numeric`) | (same as input) | base 10 logarithm | log(100.0) | 2
`log`(b `numeric`, x `numeric`) | `numeric` | logarithm to base b | log(2.0, 64.0) | 6.0000000000
`mod`(y, x) | (same as argument types) | remainder of y/x | mod(9,4) | 1
`pi`() | `dp` | "π" constant | pi() | 3.14159265358979
`pow`(a `dp`, b `dp`) | `dp` | a raised to the power of b | pow(9.0, 3.0) | 729
`pow`(a `numeric`, b `numeric`) | `numeric` | a raised to the power of b | pow(9.0, 3.0) | 729
`radians`(`dp`) | `dp` | degrees to radians | radians(45.0) | 0.785398163397448
`random`() | `dp` | random value between 0.0 and 1.0 | random() |
`round`(`dp` or `numeric`) | (same as input) | round to nearest integer | round(42.4) | 42
`round`(v `numeric`, s `integer`) | `numeric` | round to s decimal places | round(42.4382, 2) | 42.44
`setseed`(`dp`) | `int32` | set seed for subsequent random() calls | setseed(0.54823) | 1177314959
`sign`(`dp` or `numeric`) | (same as input) | sign of the argument (-1, 0, +1) | sign(-8.4) | -1
`sqrt`(`dp` or `numeric`) | (same as input) | square root | sqrt(2.0) | 1.4142135623731
`trunc`(`dp` or `numeric`) | (same as input) | truncate toward zero | trunc(42.8) | 42
`trunc`(v `numeric`, s `integer`) | `numeric` | truncate to s decimal places | trunc(42.4382, 2) | 42.43

Finally, Table 9-5 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type `double precision`.

Table 9-5. Trigonometric Functions

Function | Description
--- | ---
`acos`(x) | inverse cosine
`asin`(x) | inverse sine
`atan`(x) | inverse tangent
`atan2`(x, y) | inverse tangent of x/y
`cos`(x) | cosine
`cot`(x) | cotangent
`sin`(x) | sine
`tan`(x) | tangent

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