## 9.3. Mathematical Functions and Operators

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

Table 9.4 shows the available mathematical operators.

Table 9.4. Mathematical Operators

Operator | Description | Example | Result
--- | --- | --- | ---
`+` | addition | `2 + 3` | `5`
`-` | subtraction | `2 - 3` | `-1`
`*` | multiplication | `2 * 3` | `6`
`/` | division (integer division truncates the result) | `4 / 2` | `2`
`%` | modulo (remainder) | `5 % 4` | `1`
`^` | exponentiation (associates left to right) | `2.0 ^ 3.0` | `8`
`|/` | square root | `|/ 25.0` | `5`
`||/` | cube root | `||/ 27.0` | `3`
`!` | factorial (deprecated, use `factorial()` instead) | `5 !` | `120`
`!!` | factorial as a prefix operator (deprecated, use `factorial()` instead) | `!! 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 and are also available for the bit string types `bit` and `bit varying`, as shown in Table 9.14.

Table 9.5 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 9.5. Mathematical Functions

Function | Return Type | Description | Example | Result
--- | --- | --- | --- | ---
``abs(`x`)`` | (same as input) | absolute value | `abs(-17.4)` | `17.4`
``cbrt(`dp`)`` | `dp` | cube root | `cbrt(27.0)` | `3`
``ceil(`dp` or `numeric`)`` | (same as input) | nearest integer greater than or equal to argument | `ceil(-42.8)` | `-42`
``ceiling(`dp` or `numeric`)`` | (same as input) | nearest integer greater than or equal to argument (same as `ceil`) | `ceiling(-95.3)` | `-95`
``degrees(`dp`)`` | `dp` | radians to degrees | `degrees(0.5)` | `28.6478897565412`
``div(`y` `numeric`, `x` `numeric`)`` | `numeric` | integer quotient of `y`/`x` | `div(9,4)` | `2`
``exp(`dp` or `numeric`)`` | (same as input) | exponential | `exp(1.0)` | `2.71828182845905`
``factorial(`bigint`)`` | `numeric` | factorial | `factorial(5)` | `120`
``floor(`dp` or `numeric`)`` | (same as input) | nearest integer less than or equal to 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`
``log10(`dp` or `numeric`)`` | (same as input) | base 10 logarithm | `log10(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`
``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`
``scale(`numeric`)`` | `integer` | scale of the argument (the number of decimal digits in the fractional part) | `scale(8.41)` | `2`
``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(`operand` `dp`, `b1` `dp`, `b2` `dp`, `count` `int`)`` | `int` | return the bucket number to which `operand` would be assigned in a histogram having `count` equal-width buckets spanning the range `b1` to `b2`; returns `0` or ``count`+1` for an input outside the range | `width_bucket(5.35, 0.024, 10.06, 5)` | `3`
``width_bucket(`operand` `numeric`, `b1` `numeric`, `b2` `numeric`, `count` `int`)`` | `int` | return the bucket number to which `operand` would be assigned in a histogram having `count` equal-width buckets spanning the range `b1` to `b2`; returns `0` or ``count`+1` for an input outside the range | `width_bucket(5.35, 0.024, 10.06, 5)` | `3`
``width_bucket(`operand` `anyelement`, `thresholds` `anyarray`)`` | `int` | return the bucket number to which `operand` would be assigned given an array listing the lower bounds of the buckets; returns `0` for an input less than the first lower bound; the `thresholds` array must be sorted, smallest first, or unexpected results will be obtained | `width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[])` | `2`

Table 9.6 shows functions for generating random numbers.

Table 9.6. Random Functions

Function | Return Type | Description
--- | --- | ---
``random()`` | `dp` | random value in the range 0.0 <= x < 1.0
``setseed(`dp`)`` | `void` | set seed for subsequent `random()` calls (value between -1.0 and 1.0, inclusive)

The `random()` function uses a simple linear congruential algorithm. It is fast but not suitable for cryptographic applications; see the pgcrypto module for a more secure alternative. If `setseed()` is called, the results of subsequent `random()` calls in the current session are repeatable by re-issuing `setseed()` with the same argument.

Table 9.7 shows the available trigonometric functions. All these functions take arguments and return values of type `double precision`. Each of the trigonometric functions comes in two variants, one that measures angles in radians and one that measures angles in degrees.

Table 9.7. Trigonometric Functions

Function (radians) | Function (degrees) | Description
--- | --- | ---
``acos(`x`)`` | ``acosd(`x`)`` | inverse cosine
``asin(`x`)`` | ``asind(`x`)`` | inverse sine
``atan(`x`)`` | ``atand(`x`)`` | inverse tangent
``atan2(`y`, `x`)`` | ``atan2d(`y`, `x`)`` | inverse tangent of ``y`/`x``
``cos(`x`)`` | ``cosd(`x`)`` | cosine
``cot(`x`)`` | ``cotd(`x`)`` | cotangent
``sin(`x`)`` | ``sind(`x`)`` | sine
``tan(`x`)`` | ``tand(`x`)`` | tangent

### Note

Another way to work with angles measured in degrees is to use the unit transformation functions ``radians()`` and ``degrees()`` shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids round-off error for special cases such as `sind(30)`.

Table 9.8 shows the available hyperbolic functions. All these functions take arguments and return values of type `double precision`.

Table 9.8. Hyperbolic Functions

Function | Description | Example | Result
--- | --- | --- | ---
``sinh(`x`)`` | hyperbolic sine | `sinh(0)` | `0`
``cosh(`x`)`` | hyperbolic cosine | `cosh(0)` | `1`
``tanh(`x`)`` | hyperbolic tangent | `tanh(0)` | `0`
``asinh(`x`)`` | inverse hyperbolic sine | `asinh(0)` | `0`
``acosh(`x`)`` | inverse hyperbolic cosine | `acosh(1)` | `0`
``atanh(`x`)`` | inverse hyperbolic tangent | `atanh(0)` | `0`