PostgreSQL 8.3.1 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 work only on integral data types, whereas the others are available for all numeric data types. The bitwise operators are also available for the bit string types `bit` and `bit varying`, as shown in Table 9-10.

Table 9-3 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 can therefore vary depending on the host system.

Table 9-3. 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`
``ceiling`(`dp` or `numeric`)` | (same as input) | smallest integer not less than argument (alias for `ceil`) | `ceiling(-95.3)` | `-95`
``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`
``power`(`a` `dp`, `b` `dp`)` | `dp` | `a` raised to the power of `b` | `power(9.0, 3.0)` | `729`
``power`(`a` `numeric`, `b` `numeric`)` | `numeric` | `a` raised to the power of `b` | `power(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` `int`)` | `numeric` | round to `s` decimal places | `round(42.4382, 2)` | `42.44`
``setseed`(`dp`)` | `void` | set seed for subsequent `random()` calls (value between 0 and 1.0) | `setseed(0.54823)` |
``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` `int`)` | `numeric` | truncate to `s` decimal places | `trunc(42.4382, 2)` | `42.43`
``width_bucket`(`op` `numeric`, `b1` `numeric`, `b2` `numeric`, `count` `int`)` | `int` | return the bucket to which `operand` would be assigned in an equidepth histogram with `count` buckets, in the range `b1` to `b2` | `width_bucket(5.35, 0.024, 10.06, 5)` | `3`
``width_bucket`(`op` `dp`, `b1` `dp`, `b2` `dp`, `count` `int`)` | `int` | return the bucket to which `operand` would be assigned in an equidepth histogram with `count` buckets, in the range `b1` to `b2` | `width_bucket(5.35, 0.024, 10.06, 5)` | `3`

Finally, Table 9-4 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type `double precision`.

Table 9-4. Trigonometric Functions

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

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