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

OperatorDescriptionExampleResult
- subtraction2 - 3-1
* multiplication2 * 36
/ division (integer division truncates the result)4 / 22
% modulo (remainder)5 % 41
^ exponentiation (associates left to right)2.0 ^ 3.08
|/ square root|/ 25.05
||/ cube root||/ 27.03
! factorial5 !120
!! factorial (prefix operator)!! 5120
@ absolute value@ -5.05
& bitwise AND91 & 1511
| bitwise OR32 | 335
# bitwise XOR17 # 520
~ bitwise NOT~1-2
<< bitwise shift left1 << 416
>> bitwise shift right8 >> 22

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 9-13.

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

FunctionReturn TypeDescriptionExampleResult
`abs(x)` (same as input)absolute valueabs(-17.4)17.4
`cbrt(dp)` dpcube rootcbrt(27.0)3
`ceil(dp or numeric)` (same as input)nearest integer greater than or equal to argumentceil(-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)` dpradians to degreesdegrees(0.5)28.6478897565412
```div(y numeric, x numeric)``` numericinteger quotient of y/xdiv(9,4)2
`exp(dp or numeric)` (same as input)exponentialexp(1.0)2.71828182845905
`floor(dp or numeric)` (same as input)nearest integer less than or equal to argumentfloor(-42.8)-43
`ln(dp or numeric)` (same as input)natural logarithmln(2.0)0.693147180559945
`log(dp or numeric)` (same as input)base 10 logarithmlog(100.0)2
```log(b numeric, x numeric)```numericlogarithm to base blog(2.0, 64.0)6.0000000000
```mod(y, x)``` (same as argument types)remainder of y/xmod(9,4)1
`pi()` dp"π" constantpi()3.14159265358979
```power(a dp, b dp)``` dpa raised to the power of bpower(9.0, 3.0)729
```power(a numeric, b numeric)```numerica raised to the power of bpower(9.0, 3.0)729
`radians(dp)` dpdegrees to radiansradians(45.0)0.785398163397448
`round(dp or numeric)` (same as input)round to nearest integerround(42.4)42
`round(v numeric, s int)`numericround to s decimal placesround(42.4382, 2)42.44
`scale(numeric)` integerscale 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 rootsqrt(2.0)1.4142135623731
`trunc(dp or numeric)` (same as input)truncate toward zerotrunc(42.8)42
`trunc(v numeric, s int)`numerictruncate to s decimal placestrunc(42.4382, 2)42.43
`width_bucket(operand dp, b1 dp, b2 dp, count int)`intreturn 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 rangewidth_bucket(5.35, 0.024, 10.06, 5)3
`width_bucket(operand numeric, b1 numeric, b2 numeric, count int)`intreturn 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 rangewidth_bucket(5.35, 0.024, 10.06, 5)3
`width_bucket(operand anyelement, thresholds anyarray)`intreturn 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 obtainedwidth_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[])2

Table 9-6 shows functions for generating random numbers.

Table 9-6. Random Functions

FunctionReturn TypeDescription
`random()` dprandom value in the range 0.0 <= x < 1.0
`setseed(dp)` voidset seed for subsequent random() calls (value between -1.0 and 1.0, inclusive)

The characteristics of the values returned by `random()` depend on the system implementation. It is not suitable for cryptographic applications; see pgcrypto module for an alternative.

Finally, Table 9-7 shows the available trigonometric functions. All trigonometric 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

`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 roundoff error for special cases such as sind(30).