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# 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 9-13.

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

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
`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 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).