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# 4.3. 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 4-2. Mathematical Operators

NameDescriptionExampleResult
- 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
& Binary AND91 & 1511
| Binary OR32 | 335
# Binary XOR17 # 520
~ Binary NOT~1-2
<< Binary shift left1 << 416
>> Binary shift right8 >> 22

The "binary" operators are also available for the bit string types BIT and BIT VARYING.

Table 4-3. Bit String Binary Operators

ExampleResult
B'10001' & B'01101'00001
B'10001' | B'01101'11101
B'10001' # B'01101'11110
~ B'10001'01110
B'10001' << 301000
B'10001' >> 200100
Bit string arguments to &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown here.

Table 4-4. Mathematical Functions

FunctionReturn TypeDescriptionExampleResult
abs(x)(same as x)absolute valueabs(-17.4)17.4
cbrt(dp)dpcube rootcbrt(27.0)3
ceil(numeric)numericsmallest integer not less than argumentceil(-42.8)-42
exp(dp)dpexponentialexp(1.0)2.71828182845905
floor(numeric)numericlargest integer not greater than argumentfloor(-42.8)-43
ln(dp)dpnatural logarithmln(2.0)0.693147180559945
log(dp)dpbase 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"Pi" constantpi()3.14159265358979
pow(e dp, n dp)dpraise a number to exponent epow(9.0, 3.0)729
random()dpvalue between 0.0 to 1.0random()
round(dp)dpround to nearest integerround(42.4)42
round(v numeric, s integer)numericround to s decimal placesround(42.4382, 2)42.44
sign(numeric)numericsign of the argument (-1, 0, +1)sign(-8.4)-1
sqrt(dp)dpsquare rootsqrt(2.0)1.4142135623731
trunc(dp)dptruncate toward zerotrunc(42.8)42
trunc(numeric, s integer)numerictruncate to s decimal placestrunc(42.4382, 2)42.43

In the table above, dp indicates double precision. The functions exp, ln, log, pow, round (1 argument), sqrt, and trunc (1 argument) are also available for the type numeric in place of double precision. Functions returning a numeric result take numeric input arguments, unless otherwise specified. Many of these functions are implemented on top of the host system's C library; accuracy and behavior in boundary cases could therefore vary depending on the host system.

Table 4-5. Trigonometric Functions

FunctionDescription
acos(x)inverse cosine
asin(x)inverse sine
atan(x)inverse tangent
atan2(x, y)inverse tangent of y/x
cos(x)cosine
cot(x)cotangent
sin(x)sine
tan(x)tangent

All trigonometric functions have arguments and return values of type double precision.