# 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

OperatorDescriptionExampleResult
- subtraction2 - 3-1
* multiplication2 * 36
/ division (integer division truncates results)4 / 22
% modulo (remainder)5 % 41
^ exponentiation2.0 ^ 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 are also available for the bit string types bit and bit varying, as shown in Table 9-3. Bit string operands of &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown in the table.

Table 9-3. Bit String Bitwise Operators

ExampleResult
B'10001' & B'01101'00001
B'10001' | B'01101'11101
B'10001' # B'01101'11100
~ B'10001'01110
B'10001' << 301000
B'10001' >> 200100

Table 9-4 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 9-4. Mathematical Functions

FunctionReturn TypeDescriptionExampleResult
`abs`(x)(same as x)absolute valueabs(-17.4)17.4
`cbrt`(dp)dpcube rootcbrt(27.0)3
`ceil`(dp or numeric)(same as input)smallest integer not less than argumentceil(-42.8)-42
`degrees`(dp)dpradians to degreesdegrees(0.5)28.6478897565412
`exp`(dp or numeric)(same as input)exponentialexp(1.0)2.71828182845905
`floor`(dp or numeric)(same as input)largest integer not greater than 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
`pow`(a dp, b dp)dpa raised to the power of bpow(9.0, 3.0)729
`pow`(a numeric, b numeric)numerica raised to the power of bpow(9.0, 3.0)729
`radians`(dp)dpdegrees to radiansradians(45.0)0.785398163397448
`random`()dprandom value between 0.0 and 1.0random()
`round`(dp or numeric)(same as input)round to nearest integerround(42.4)42
`round`(v numeric, s integer)numericround to s decimal placesround(42.4382, 2)42.44
`setseed`(dp)int32set seed for subsequent random() callssetseed(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 rootsqrt(2.0)1.4142135623731
`trunc`(dp or numeric)(same as input)truncate toward zerotrunc(42.8)42
`trunc`(v numeric, s integer)numerictruncate to s decimal placestrunc(42.4382, 2)42.43

Finally, Table 9-5 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision.

Table 9-5. Trigonometric Functions

FunctionDescription
`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