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 may 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 ) int set seed for subsequent random() calls (value between 0 and 1.0) 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 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

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``` ( x , y ) inverse tangent of x / y
``` cos``` ( x ) cosine
``` cot``` ( x ) cotangent
``` sin``` ( x ) sine
``` tan``` ( x ) tangent