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

+ addition2 + 35
- 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 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

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
ceiling(dp or numeric)(same as input)smallest integer not less than argument (alias for ceil)ceiling(-95.3)-95
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
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
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 int)numericround to s decimal placesround(42.4382, 2)42.44
setseed(dp)intset 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 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(op numeric, b1 numeric, b2 numeric, count int)intreturn the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2width_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

acos(x)inverse cosine
asin(x)inverse sine
atan(x)inverse tangent
atan2(x, y)inverse tangent of x/y